Modeling & Load Rating of Two Bridges Designed with …docs.trb.org/prp/13-2212.pdf · 3 Modeling & Load Rating of Two Bridges Designed with 4 AASHTO and Florida I-Beam Girders 5

Catbas, Darwash, Fadul 1/13

Title Page: 1

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Modeling & Load Rating of Two Bridges Designed with 3 AASHTO and Florida I-Beam Girders 4

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F.N. Catbas, H. Darwash and M. Fadul 6 7 8

Dr. F. Necati Catbas, P.E. 9 Associate Professor & Associate Chair 10 Civil and Environmental Engineering Department 11 University of Central Florida, Orlando, FL 32816 12 Phone: 407-823-3743; Fax: 407-823-3315 ; e-mail: [email protected] 13 (corresponding author) 14 15 Mr. Haider Darwash 16 Ph.D. Student and Research Assistant 17 Civil and Environmental Engineering Department 18 University of Central Florida, Orlando, FL 32816 19 Phone: 407-823-4122; Fax: 407-823-4553 20

21 Ms. Manar Fadul 22 Ph.D. Student and Research Assistant 23 Civil and Environmental Engineering Department 24 University of Central Florida, Orlando, FL 32816 25 Phone: 407-823-4122; Fax: 407-823-4553 26

27 28 29 30 31 32 33 Word Count: 34 Abstract, Manuscript & References = 3,743 35 Figures and Tables (8+3) = 2,750 36 TOTAL = 6,493 37

TRB 2013 Annual Meeting Paper revised from original submittal.


ABSTRACT 1 Florida I-Beam (FIB) girders provide a number of advantages such as higher load 2

carrying capacity, more efficient fabrication, safer construction, increased lateral stiffness, larger 3 vertical clearance and reduction in the overall cost of bridges. A comparative study incorporating 4 two bridges, one with AASHTO Type III and the other with new Florida I-Beam (FIB) girders is 5 presented. The first bridge is a 3 span bridge designed with 6 AASHTO Type III girders. The 6 second bridge has the same length, width and girder depth; however, it has 4 FIB girders. Both 7 bridges are analyzed using the conventional AASHTO LRFD girder line analysis method and 8 also with a more sophisticated finite element method using a commercial software. The details of 9 the FE model are also presented with the critical considerations of link elements, boundary 10 conditions, pre-stressing tendons. Based on the FE model results, it is shown that it is possible to 11 expect 20% higher live load capacity for interior girders and 40% higher live load capacity for 12 exterior girders using FIB-45 girders compared to AASHTO Type III girders, while also 13 reducing the cost by about 24%. 14

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INTRODUCTION 1 Concrete bridges are commonly used in the US. Initially, short and single span bridge 2

superstructures were designed and constructed using concrete girders until the middle of the 20th 3 century when the pre-stressed bridge girders gained more acceptance and longer spans with pre-4 stressed concrete bridges increased dramatically. Today, almost 50% of all the new bridges built 5 in the US are pre-stressed concrete bridges [1]. Prestressed concrete bridges are considered due 6 to their high strength and durability. Pre-stressed concrete girders perform well for longer spans 7 by the application of a tensile force to reinforcing tendons. This application increases the internal 8 compression in the concrete beam where the tension is anticipated under the given loading 9 conditions. The pre-stressing force can be applied before the concrete is poured (beam is 10 pretensioned) or after the concrete is cured (beam is post-tensioned). There are a number of 11 different pre-stressed concrete girders with a variety of cross-sectional geometries and strands for 12 a required span length and loading. AASHTO I-beams and bulb T-beams have been employed 13 by a many Departments of Transportation as concrete bridge girders. 14

While the AASHTO I-beam and Bulb T-beam girders are commonly used in the state of 15 Florida, Florida Department of Transportation (FDOT), in collaboration with Prof. M. Tadros, 16 developed a new prestressed beam called the Florida I-beam (FIB) to replace these beams in 17 order to enhance the efficiency, to provide a larger vertical clearance and to reduce the overall 18 cost of bridges. FIBs are designed to have higher load carrying capacity, more efficient 19 fabrication, safer construction, increased lateral stiffness because of thicker top and bottom 20 flanges. In addition, FIBs are more economical in comparison to the prestressed beams that are 21 currently being used [2,3]. FIBs are designed to have high concrete strength, ranging from 8 to 22 10 ksi, and a large bottom flange compared to the traditional AASHTO and Bulb T-beams, to 23 allow a larger space for more prestressing strands that are usually needed in longer span girders 24 or wider girder spacing. The enhanced design of FIBs is expected to allow bridge designers to 25 reduce the number of beams needed and to reduce the bridge cost. FIBs have improved stability 26 during handling, storage and erection than the other prestressed beams due to a significantly 27 wider bottom flange and low center of gravity. One of the advantages is that FIBs with shallower 28 depth may be used in place of their deeper AASHTO equivalents. This in turn provides a larger 29 vertical clearance that has been a concern for many bridges. In addition, FIBs have identical top 30 and bottom flange shapes for their full range of standard sizes, and since the only varied 31 dimension between FIB standard sizes is the height of the web. The option of using adjustable 32 height forms during fabrication process of all FIB standard sizes is applicable for ease of 33 manufacturing. FIBs can accommodate the largest number of prestressing strands in the USA (up 34 to 72 – 0.6 in diameter strands). Based on the development and progressive studies of FDOT on 35 FIBs, the FDOT developed design bulletins for designers and manufacturers. As a result, FDOT 36 recommended FIBs to be used in all new bridges and bridge widening designs where applicable, 37 while AASHTO beams and Bulb T-beams will no longer be used for any new design [2]. 38

Objectives and Scope of the Paper 39 FDOT prepared a comparative design of AASHTO Type III beam, which can span 40

approximately 90 feet (6 beams with a depth of 45” and spacing of 7’-6”) with a FIB 45” (4 41 beams with a depth of 45” and a spacing of 11’-9”) which can accomplish the same span by 42 reducing the number of girders. The bridge sections under investigation were used in a 43 comparative cost analysis in the FDOT design bulletin. It was found that estimated savings by 44



using four FIB girders for this specific structure is about 24% of the original cost when 1 AASHTO type III girders are used instead [2,3]. This saving increases when the number of 2 required girders of the bridge increases. Such cost reduction has a significant effect on the 3 overall cost of bridges given that the large number of bridges that are built in Florida state each 4 year. 5

In the study presented in this paper, the structural responses and the load rating factors of 6 these two bridges are presented along with the cost saving information given in the FDOT design 7 bulletin. The first bridge has six AASHTO type III girders (Figure 1) and the second bridge with 8 the same general geometry and load-carrying characteristics has four FIBs (Figure 2). Both of 9 these bridges are analyzed using the standard AASHTO LRFD girder line analysis as well as 10 using finite element (FE) analysis with a commercial software. The critical details for the 11 appropriate FE modeling of the prestressed sections are presented with the necessary 12 assumptions made for this study. The flexural responses and load rating factors from these 13 analyses are presented in a comparative fashion. 14

15 Figure 1: AASHTO Type III Bridge 16

17

18 Figure 2: Florida I-Beam (FIB) 45 Bridge 19



DESCRIPTION OF THE TWO BRIDGES 1 The bridges, which are studied in this paper, consist of three simply supported spans 2

made up of pre-stressed girders. Each span is 90-ft long and supported by a 41.5- ft long beam 3 cap and this beam cap is supported by three circular columns. The 43’-1” wide cross section is 4 the same for both bridges as shown in Figure 1 and Figure 2. Only two 12’-0” lanes are 5 considered to be loaded with an additional 10’-0” emergency lane and another 6’-0” pedestrian 6 lane. Both types of girders are 45 in. deep, the first being AASHTO Type III girders, and the 7 second being Florida I-beams. The FIB bridge utilizes four 45-in. I-beams spaced at 11’-9”. 8 Each FIB contains 42- 0.6 in low-relaxation strands (Figure 3). The AASHTO cross section 9 contains six girders spaced at 7’-6” in each with 26-0.6 in low-relaxation prestressing strands 10 (Figure 4). The deck is 8” thick and topped with a 3” bituminous wearing surface, and has end 11 barriers that are 1 ft-6 ½ in. wide. The pretensioned girders have a 2” thick haunched beam in 12 order to control the camber. The prestressing strands are assumed to be straight with eccentricity 13 equal to 11.65 in for AASHTO bridge and 15.08 in for FIB bridge. These eccentricities are 14 computed by the AASHTO LRFD calculation method and all stresses are checked with the 15 allowable stresses. In addition, the moment capacity is also checked to be within the allowable 16 capacity range. The concrete strength is 8.5 ksi concrete (6 ksi at release) and the ultimate tendon 17 strength is taken as 270 Ksi. 18 19

20 21

Figure 3: Florida I-Beam (FIB) Typical Cross-Section 22 23



1 Figure 4: AASHTO Type III Girder 2

3 A generalized cost calculation for these two bridges (one with AASHTO Type III Girder, 4

and other with FIB-45) are provided in the FDOT Design Bulletin C09-01 [2] as follows: 5 6

3 Span Bridge with 6 AASHTO Type III Beams: 7 Total Linear Foot = (90 ft long beams) x (3 spans) x (6 beams per span) = 1620 LF 8 Approximate Cost = (1620 LF) x ($185 /LF) = $299,700 9 10 3 Span Bridge with 4 Florida I-Beams (FIB-45): 11 Total Linear Foot = (90 ft long beams) x (3 spans) x (4 beams per span) = 1080 LF 12 Approximate Cost = (1080 LF) x ($210 /LF) = $226,800 13 14 Estimated Savings = 24% = ($299,700-$226,800)/$299,700 15

16 It is noted that costs per linear foot were determined using price estimates from 17

manufacturers and contractors. The values above include only bridge items affected by differing 18 beam types. These items include beam fabrication, beam placement, placed bearing pads, placed 19 diaphragms, placed stay-in-place forms and deck rebar seats [2]. While the total cost can vary 20 based on many other factors, this calculation provides a reasonably accurate comparison. 21

MODELING AND ANALYSIS OF THE BRIDGES 22

AASHTO Girderline Analysis and Calculations 23 As part of the comparative analysis for the structural responses, the AASHTO methods 24

are utilized as engineers commonly, and in fact, this approach can be used as the first approach 25 in many cases even before detailed modeling methods such as FEMs. In this paper, the authors 26



also conduct calculations and provide results according to the AASHTO LRFD Bridge Design 1 Specifications [4]. The same loading considerations and assumptions are employed for the 2 analysis of the bridges, which are designed to carry interstate traffic in Florida. The AASHTO 3 and FIB girder sections are evaluated for HL-93 Design Truck and Design Lane Loads. A 4 dynamic load allowance of 33% is considered, distribution and load rating factors for moment 5 are calculated according to the AASHTO Guide. Strength I and Service I limit states are 6 considered. The load effects, load rating, and the distribution factors results are all shown later in 7 Tables 2, 3 and 4, respectively. 8

Overview of the Full Finite Element Model 9 FE Modeling of pre-stressed girder structures has been shown on a number of studies. In 10

one such study, the author and his colleagues presented pre-stressed and post-tensioned monorail 11 guideway structures by accurately modeling using a FE package for load rating and reliability 12 analyses [7,8]. In this current paper, AASHTO Type III and FIB girder bridges are modeled 13 using a commercial FE package (CSiBridge) specifically developed for bridge analysis and 14 design [10,11]. The two lane loaded case is assumed according to the previous study by the 15 FDOT bulletin. Slab thickness is taken as 8 in with 2 in haunch and 3 in bitumen wearing. 16 Compressive strength of 4 ksi is used for the regular concrete, which is used for the deck, the 17 columns, and the beam cap. For the precast girders, 8.5 ksi (6 ksi at release) compressive 18 strength is used. Cross diaphragms with 19 in depth and 12 in width also used every one third 19 points of each span with no cross diaphragms at the abutments. Further list of the assumptions 20 considered for the finite elements models can be seen in Table 1. 21

22 Table 1: List of Parameters and Assumptions 23

Value

Barrier load 0.32 kips/ft length

Wearing load 0.035 kip/ft2

Column dimension 3 circular column 4.5ft dia. (20 - #8 grade 60 steel)

Beam Cab dimension Depth (56 in), width (60 in)

Prestress steel 0.6 in low relaxation strands

fpu 270 ksi

Diaphragm Dimensions Depth (19 in), Width (12 in)

Jacking force 0.7 𝑓!"

Modeling of Deck and Girders 24 Shell elements with three degrees of freedom are chosen to model the deck section. 25

Frame elements are used to model the precast pretension girders, the columns, and the beam cap. 26 For the AASHTO type III Bridge, 18 precast pre-tensioned AASHTO type III girders are defined 27 with one hundred and fifty six tendons for the entire length of the bridge. For the FIB Bridge, 12 28 45” deep precast FIB girders are defined with one hundred and sixty eight tendons. Each bridge 29 has three piers with 41.5 ft long beam cap. The pier and the abutment foundations are assumed to 30



be fixed for both bridges. Figure 5 and Figure 6 show the finite elements model of AASHTO 1 type III bridge and FIB bridge, respectively with model characteristics and model statistics. 2

3

4 Figure 5: The FE Model of the Bridge with AASHTO Type III Girders 5

6 Figure 6: The FE Model of the Bridge with Florida I-Beams 7

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Modeling of the Link Elements 1 The concrete deck and girder connection is a critical detail to be modeled properly for the 2

effective utilization of the composite connection. As a result, rigid links are used to represent the 3 connection between the girders and the deck. The same type of link is used to model the columns 4 and the beam cap connection. Abutment bearings links (link elements) are used to model the 5 abutments by fixing the vertical and transverse translation of the abutment bearings. All other 6 abutment bearing components are modeled as free since the abutment restraint is assumed to be 7 free in the longitudinal direction. Bent bearings links (link elements) are used to model the 8 bearing plates and the connection between the girders and the beam cap by fixing all the 9 translations of the bent bearings. All the other bent bearing components are defined as free, 10 including the rotation along the layout line. To help visualize the abutment geometry, the 11 drawing shown in Figure 7 illustrates the location of the abutment bearings and the substructure. 12 It also shows the location of the action point, which is the location where the bearing will 13 translate or rotate depending on the bearing definitions. 14

15

16 Figure 7: FE Modeling of the Links 17

Modeling of the Tendons 18 Eighteen precast girders are defined in the FE model of the AASHTO type III bridge. 19

Each girder has 26 0.6 in low relaxation pre-tensioned strands. On the other hand, twelve precast 20 girders are defined in the FE model of the FIB bridge. Each girder has 42 0.6 in low relaxation 21 pre-tensioned strands. Pre-tensioned tendons are modeled as separate elements with 44 kips force 22 embedded in the precast girders to satisfy the design criteria, strength limit state check and for 23 checking the tendon stresses. Because the CSiBridge FEM software provides only bonded post-24 tension tendons, the bonded pre-tensioning tendons are modeled by jacking the post-tensioned 25



tendons from both sides and specifying zero value for the curvature loss coefficient, wobble loss 1 coefficient, and anchorage slip loss coefficient. Figure 8 shows the distribution of the tendons in 2 AASHTO type III beams and Florida I-Beams. 3

4

5 Figure 8: Distribution of the Tendons in AASHTO Type III Beams and Florida I-Beams 6 7

DISTRIBUTION FACTORS AND LOAD RATING 8

Movable Bridge Load Rating 9 After the completion of the FE model and the simple girder line model, the load rating 10

factors of the bridges are computed. Load rating of the bridges is calculated following the 11 AASHTO Guide [5]. The load factors rating procedure is commonly used in identifying the live 12 load carrying capacity of bridges. Bending moment capacity of the bridges under investigation 13 is calculated at the critical position of HL-93 (with design truck and lane load) following the 14 AASHTO Guide. Since each span is considered as a simply supported, the locations of 15 maximum live and dead load moments are located at the midspan section. 16

The load rating can be expressed as the factor of the critical live load effect to the 17 available capacity for a certain limit state. The general formula for the rating factor is [5]; 18

)1( IMLLPDWDCC

RFL

pDWDC

+

±−−=

γ

γγγ (1) 19

where C is the factored load carrying capacity, DC is the dead load of structural 20 components, DW is the dead load of the wearing surface, P is a dead load concentrated at a 21 single point, LL is the live load effect, IM is the impact factor, and γ’s are the load factors. The 22 calculated load ratings for the critical locations are presented in the following sections. 23

The load factors values depend on the type of load rating, i.e. inventory or operating load 24 rating. The load rating for the girder is calculated at the critical section, located at the midspan. 25



The section moment capacity is calculated for both AASHTO and FIB sections and for the 1 exterior and the interior girders as well. The calculated moment capacity, the moments at the 2 critical section due to live and dead load, and also the load rating factors are all presented in 3 Table 2 and Table 3. 4

5 Table 2: Moment Values Obtained from the FEM and AASHTO LRFD Analyses 6

Moment Values

AASHTO Type III Girder FIB Girder

Ext. Girder

(K.ft)

Int. Girder

(K.ft)

Ext. Girder

(K.ft)

Int. Girder

(K.ft)

AASHTO

LRFD results

(Girderline

Analysis)

Section Capacity 5587 5624 8707 8770

Max. D.L 1812 1851 2552 2704

Max. L.L 1750 1537 2285 2217

FEM results

Section Capacity 4659 4715 8229 8320

Max. D.L 1672 1716 2484 2762

Max. L.L 902 970 1281 1538

7 Table 2 indicates that the values of the calculated section capacity and the dead load 8

using LRFD method are close to their corresponding values calculated using FEM. The 9 difference in the dead load values is about 4% on the average. However, the live load values 10 show a significant difference and it is about 40% when the AASHTO LRDF and FEM results are 11 compared. This difference (reduction in LL moments in FEM) can be attributed to better load 12 distribution by means of FE software that represents all the elements of the bridge. When the 13 results of the AASHTO and FIB girder bridges are compared, the FIB has much higher load 14 carrying capacity even though the dead and live load responses are higher for the FIB. Table 3 15 presents the load rating factors obtained using the capacity and demand calculations presented 16 previously. The results given in Table 3 imply that AASHTO LRFD girderline analysis 17 underestimate the load rating and provides lower load rating factors than those obtained using FE 18 model. The ratios of load rating factors (FEM/girderline) for all types of girders variy between 19 1.22 to 1.65, meaning a 22% to 65% more live load carrying possibility. It should also be noted 20 that the girderline method underestimates the load rating factors of the FIB girder bridge more 21 than AASHTO Type III girder bridge. 22

A more significant observation is that the bridge with FIB girders has higher load rating 23 factors than the bridge with AASHTO type III girder regardless of the AASHTO LRFD 24 Girderline analysis or FE analysis. When the two bridges are considered, the exterior and 25 interior girders have 17% and 13%, respectively, more live load capacity using AASHTO 26



girderline analysis. When the two bridges are compared using the FE model results, the exterior 1 and interior girders have 41% and 20% more live load capacity, respectively. 2

3 Table 3: Load Rating of the Bridges Using FEM and AASHTO LRFD 4

Load Rating AASHTO Type III Girder

FIB Girder

Ext. Girder Int. Girder Ext. Girder Int. Girder

AASHTO

LRFD results

(Girderline

Analysis)

Inventory 1.07 1.20 1.36

1.36

Operating

1.50 1.56 1.76 1.76

FEM results

Inventory 1.59 1.47 2.25

1.77

Operating 2.06 1.91 2.91

2.30

5

SUMMARY AND CONCLUSIONS 6 Florida I-Beam (FIB) bridges were developed to be the choice for girder type for new 7

designs in Florida. These girders provide a larger vertical clearance and to reduce the overall cost 8 of bridges. FIBs are designed to have higher load carrying capacity, more efficient fabrication, 9 safer construction, increased lateral stiffness because of thicker top and bottom flanges. 10

In this study, a comparative analysis of two bridges is presented. The first bridge is a 3 11 span bridge designed with 6 AASHTO Type III girders. The second bridge has the same length, 12 width and girder depth; however, it has 4 FIB girders. Both bridges are analyzed using the 13 conventional AASHTO LRFD girderline analysis method and also more sophisticated finite 14 element method using a commercial software. The details of the FE model are also presented 15 with the critical considerations of link elements, boundary conditions, pre-stressing tendons. 16

The cost comparison of these two bridges was presented by FDOT and it is stated that the 17 FIB provides an estimated saving of about 24%. The results provided in this paper also indicate 18 that the bridge with FIB girders has higher load rating factors than the bridge with AASHTO 19 type III girder regardless of the method (AASHTO LRFD Girderline analysis or FE analysis) to 20 calculate the rating factors. The AASHTO girderline analysis underestimates the load rating 21 factors for both AASHTO Type III girder bridge and the FIB bridge. Based on the FE results, it 22 can be stated that it is possible to expect 20% higher live load capacity for interior girders and 23 40% higher live load capacity for exterior girders using FIB-45 girders compared to AASHTO 24 Type III girders, while also reducing the cost by about 24%. 25

ACKNOWLEDGMENTS 26 The authors would like to thank Mr. Sam Fallaha, P.E. from FDOT Structures Research 27

Center and Mr. Neil Kenis, P.E. from FDOT D5 Design Office for their feedback and input for 28 the study presented in this paper. The authors would also like to acknowledge the contributions 29 of Ms. Cara Brown for the FE model development at the initial stages of this study. 30



The opinions, findings, and conclusions expressed in this publication are those of the 1 authors and do not necessarily reflect the views of the sponsoring or anyother organizations. 2

REFERENCES 3 4 1. PCA (2004), “Market Research-The Bridge Market,” Portland Cement Association, October 5

2004. 6 2. Florida department of Transportation (FDOT). Temporary Design Bulletin C09-01. January. 7

2009. 8 3. Florida department of Transportation (FDOT). Temporary Design Bulletin C09-03. June. 9

2009. 10 4. American Association of State Highway and Transportation Officials (AASHTO). (2007). 11

Standard specifications for highway bridges, AASHTO 4th Ed., Washington, D.C. 12

5. AASHTO Guide (2007). "Guide Manual for Condition Evaluation and Load and Resistance 13

Factor Rating (LRFR) of Highway Bridges" 14

6. Barr, P. J., Eberhard, M. O. and Stanton, J. F. “Live-Load Distribution Factors in 15

Prestressed Concrete Girder Bridges.” Journal of Bridge Engineering, ASCE . 16

September/October. 2001. 17

7. Shmerling, R.Z. and Catbas, F.N. (2009), “Load Rating and Reliability Analysis of An 18

Aerial Guideways,” Journal of Bridge Engineering, Volume 14, Issue 4, pp. 247-256 19

(July/August 2009) ASCE, 2009. 20

8. Shmerling, R.Z. and Catbas, F.N. (2010), “Visualization, Finite Element Modeling and 21

Analysis of Aerial Guideways,” Structure and Infrastructure Engineering Journal, SIE, 22

Structure and Infrastructure Engineering: Maintenance, Management, Life-Cycle Design 23

and Performance, Volume 6, Issue 4, First published 2010, Pages 447 – 465 24

9. Barker, R. M. and Puckett, J. A. (2007). Design of Highway Bridges An LRFD Approach, 25

Wiley, N. Y. 26

10. CSiBridge Introduction to CSiBridge. (1995). Computers & Structures, Inc. Berkeley, 27

California 94704 USA. 28

11. CSiBridge Bridge Seismic Design. (1995). Computers & Structures, Inc. Berkeley, 29

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Modeling & Load Rating of Two Bridges Designed with …docs.trb.org/prp/13-2212.pdf · 3 Modeling & Load Rating of Two Bridges Designed with 4 AASHTO and Florida I-Beam Girders 5