- Email: [email protected]
Lateral load distribution in I-girder bridges
Pergamon
computers & Srructures Vol. 54. No. 2. pp. 351-354. I995 Copyright 0 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0045-794919s $9.50 + 0.00
0045-7949(94)E023GU
TECHNICAL NOTE LATERAL
LOAD DISTRIBUTION K. M. TarhiS@
and
Valparaiso
IN I-GIRDER
G. R. Frederickt
TDepartment
of Civil Engineering,
fDepartment
of Civil and Environmental Engineering, University of Nevada, 4505 Maryland Parkway, Las Vegas, NV 89154-4015, U.S.A. (Received
BRIDGES
University,
22 August
Valparaiso,
IN 46383,
U.S.A.
Las Vegas,
1993)
Abstract-The results of a new lateral load distribution formula to be applied in the analysis or design of steel girders are compared with recently published field test data as well as the current AASHTO load distribution factor method. The developed formula was the result of a study of lateral load distribution in a bridge superstructure employing the finite element analysis techniques. The finite element models were developed to represent the actual geometry of the bridge deck and analyzed to obtain a better understanding of the elastic behavior of the concrete slab-on-steel girder highway bridges. The developed load distribution formula compares well with field data in predicting the behavior of bridge superstructures under highway loadings. Therefore, this paper will assist bridge engineers and researchers in predicting the actual load distribution and bending moments in I-girder highway bridges.
action is commonly neglected. The spacing of longitudinal beams in a bridge deck varies and a common practice is to select a beam spacing ranging between 6 and 12 ft, which yields an economical design. The spacing of the beams is ordinarily the same throughout the span length of the bridge (unless the width of the bridge deck varies). This research considered short and medium span bridges (span lengths between 30 and 120 ft). A typical cross-section of a two-lane bridge superstructure is shown in Fig. 1. The longitudinal beams are usually connected by cross-bracing at their ends and at intervals of up to 25 ft between supports. The thickness of the concrete slab commonly varies between 6 and 12 in (depending upon the girder spacing and the desired cover for slab reinforcing steel). The concrete is usually reinforced in both directions near both faces of the slab with primary reinforcing perpendicular to traffic.
INTRODUCTION Many types of bridges, ranging from suspension structures to short-span girder bridges, are in use today. The most common component of all bridges is the roadway deck. While the bridge deck may be constructed in different ways, the most common one is a reinforced concrete slab placed over steel beams. Since the bridge deck is in direct contact with wheel loads, the applied loading greatly affects the behavior of the deck as well as the bridge substructure. Therefore, an understanding of the lateral load distribution from the slab to the beam is required to develop realistic analyses and design methodologies. The bridge specifications of the AASHTO [I] are generally simple to use and have led to the design of safe bridges. However, it has frequently been criticized as being conservative, particularly with respect to the methods used for lateral distribution of wheel loads to girders. The specifications are based primarily on the general type of supporting beams and the beam spacing. The method of analysis presented in this paper will assist bridge engineers in predicting the actual behavior of the bridge deck and lead to the calculation of realistic live load distribution factors. Realistic live load distribution factors are essential for the structural engineer to economically design new bridges and to evaluate existing bridges for their load capacities. The bridge geometry considered in this research is typical of interstate overpass or grade separation structure where the shoulders are not carried across the bridge. In practice, the longitudinal beams may be simply supported at their ends or continuous over several supports. In addition, they can be bonded to the concrete slab using shear lugs producing a composite section in which the concrete acts as part of the beam in the positive moment region. For noncomposite bridges, even where no shear lugs are present, some limited bonding action usually takes place between the beam and slab. However, during analysis, this bonding
Extensive research using analytical, numerical and experimental methods has been conducted to improve the techniques used in the analysis and design of slab-on-beam highway bridges. Available theoretical methods are varied in their approaches as well as in their accuracy and assumptions. Stress distributions at critical cross-sections can be found after introducing simplifying assumptions to create the idealized analytical model and reduce the problem to one that can be solved with a reasonable amount of calculations. Bridge superstructures can be idealized for theoretical analysis in many different ways. The various assumptions and simplifications used in formulating and idealizing the bridge superstructure can have a significant effect on how closely the calculated results match the actual behavior. The major analytical and numerical approaches reported in the literature are:
$Author addressed.
1. Orthotropic plate theory; where the actual bridge superstructure is replaced with an equivalent plate having different elastic properties in two orthogonal directions.
to
whom
all
correspondence
should
BRIEF HISTORICAL
be
351
REVIEW
Technical
352
Note
Concrete. slab
Steel girder 1
Cross-bracing
A
+s+s+--t---s--cl Girder spacing Fig. 1. Typical
cross-section
Grid analysis; where the actual bridge superstructure is replaced with an equivalent grid system. The resulting structure is a framework of intersecting bars whose stiffnesses are adjusted to approximate those of the slab and girders. Combination of plate and grid analysis; this is represented by two theories-harmonic analysis and numerical moment distribution. Special methods: (a) approximate grid work solution, (b) beam on elastic foundation analogy, (c) finite strip method, (d) finite element method. (e) others. The finite element method can be used to predict the actual behavior of complex structures [3]. Bridge superstructures can be modeled using finite element analysis (FEA) in many different ways. It is in the idealization phase of the analysis, the selection of the finite element models, that the greatest differences in approaches are encountered. The idealizations, which have been used by various researchers, include mixing three-dimensional plate elements and plane or space frame members with the centerline of the girders coinciding with the center of the concrete slab [4]. Others have imposed rigid links between the concrete slab and beams to accommodate the eccentricity of the beams and slab [5]. Still others have attempted to model the concrete slab using plate elements, the girder flanges
Fig. 2. Typical
section
through
of I-girder
bridge.
as space frame members, and the girder web as plate elements [2]. Even though the concrete slab exhibits a ‘plate bending’ phenomenon, the actual behavior of the bridge superstructure can be obtained by modeling the concrete slab using three-dimensional eight-node brick solid elements with three degrees of freedom at each node, and the girder components (flanges and web) are modeled using rectangular plate elements (or shallow shell elements) with five degrees of freedom at each node [7]. The nodes at the interface between the concrete slab and steel girder upper flange were either modeled as rigid connection to simulate composite bridge action or three linear springs were imposed at each interface node to simulate non-composite bridge action. The latter permitted the concrete slab to slide with respect to the upper flanges of the girders in the longitudinal direction. The spring elements were assigned different stiffnesses in three orthogonal directions at each interface node to allow load transfer and relative movements at interface nodes. Crossbracing frames were modeled using space truss members. The reported finite element idealization provided a very good approximation of the bridge superstructure; its use predicted the actual stress distribution and permitted the calculation of the actual bending moment at critical crosssections. Typical elements of a concrete slab on I-girder bridge deck with rigid connections at the interface nodes, which were used to model composite bridge action, are shown in Fig. 2. The results of this finite element analysis technique are represented in this paper and compared with
part of the finite element
model
Technical field test data. A rigorous analysis revealed that the entire bridge superstructure acts as a unit rather than a collection of individual structural elements, as is commonly assumed in the current AASHTO design procedures. This paper correlates the distribution factor results obtained from published field testing data with the developed formula as well as the AASHTO method.
Note
353
the current AASHTO formula (S/5.5). Simply supported bridges could be single or multi-span with composite or non-composite decks. This formula provides a simple and more realistic prediction of the behavior of concrete slab-onsteel girder highway bridges than the current available methods.
COMPARISON LOAD DISTRIBUTION
Wheel loads are distributed laterally (as well as longitudinally) to the girders in highway bridges. The current AASHTO bridge specifications for determining the maximum live loads supported by beams use greatly simplified procedures, where longitudinal distribution is neglected and lateral distribution is accomplished by using wheel load distribution factors. For interior girders, the magnitude of these live loads are specified as (S/5.5) times the standard truck wheel load when two or more lanes are supported (where S is the beam spacing in feet). Using refined finite element models to describe the actual geometry, the behavior of the bridge superstructure was predicted [7,8]. A study of the various parameters affecting the load distribution on two-lane highway bridges was performed using finite element analysis. Critical parameters were identified and employed in developing a new load distribution factor formula which is simple to use in the analysis and/or design process of I-girder bridges [8]. The effect of connection at the interface (composite or non-composite), single or multi-span, and the effect of cross-bracing on the wheel load distribution factor was found to be negligible. It was also demonstrated that a relatively large change in the moment of inertia of the bridge deck produced a relatively small change in the load distribution factor. The various practical girder spacings (S-12 ft) and span lengths (35-120 ft) were shown to have significant effects on lateral load distribution. The finite element results indicated that calculated load distribution factors can be considerably less than the conservative AASHTO factors. The span length effect is completely ignored in the AASHTO empirical load distribution formula. Therefore, a flexural formula for wheel load distribution factor (DF) for bending moment related to span length (L in feet) and girder spacing (S in feet) was developed using the results of the finite element analysis [8]
DF = 0.00013L2
- 0.02lL
WITH FIELD TESTS
FACTORS
+ 1.2@
- y
(1)
This formula can be used in the design process of new bridges as well as the evaluation of existing ones instead of
In order to test the validity of the adopted discretization techniques and the developed load distribution factor formula, the final report presented by Moses ef al. [6] on field tests of five bridges was used to compare results. The bridges selected for the field tests were fairly typical representations of bridges in Ohio in terms of design and truck traffic composition. The five sites were all parallel steel stringer (I-girder) bridges, with only one bridge being of composite construction, that were instrumented and studied. The bridges were tested using weigh-in-motion (WIM) techniques to produce field measurements which are capable of providing all pertinent data on the loading and response of highway bridges. The data collected include measured stresses and girder distribution factors in addition to truck weights and volumes. The goal of the study [6] was to provide examples of the use of WIM measurements to assist in bridge evaluation and rating. The WIM system utilizes existing bridges to serve as equivalent static scales to obtain unbiased truck gross and axle weights, classifications, dimensions and speed. The WIM utilizes traffic sensors to obtain axle and speed data, and strain sensors attached to bridge girders to provide weight information. The system operates in a undetectable manner and has been researched and tested at more than 200 sites worldwide [6]. All five sites were typically two-lane and three-span continuous bridges with various girder spacings and span lengths. Typically, one span of a bridge site was instrumented and tested at the maximum positive bending moment. A typical layout of a bridge is shown in Fig. 3. Field strains were measured continuously in each girder and used to determine the girder distribution factors. The maximum distribution factors for side-by-side occurrences were found by summing the average distributions (plus one standard deviation) from each girder for both lanes. The standard deviation was added to the average distribution of each lane to account for possible situations in which the girder under consideration supports a higher than average percentage of the total load. It was found that interior girders were the most heavily loaded. The results of the five sites are summarized along with a comparison with the current AASHTO and the developed distribution factor formulas in Table 1 as follows.
Gage location /
I
I
I 36W150
I
36Wl82
I
/
36Wl50
I
I
Fig. 3. Site 1 layout
I
I
I-90 near Ashtabula
(six girders
at 7.92 ft spacing
[6]).
Technical
354 Table
1. Comparison
Note of distribution
factors
Distribution
Site
I 2 3 4 5
Site
Span (ft) 48.6 40 56 51.5 68
Girder
spacing (ft)
factors
S
1.92 5.15 1.33 7.92 8.54
1
The bridge on I-90 in Ashtabula, Ohio, is a three-span continuous (48.6,81,48.6 ft) two-lane bridge with six girders (spaced at 7.92ft) and 18” skew. The maximum interior girder load distribution for side-by-side occurrence was found using field data to be 1.32. This value can be compared with the developed formula presented by eqn (1) to give a DF of 1.312 and with the conservative AASHTO DF of 1.44 (=7.92/5.5). Site 2 The bridge on Richmond Road over Tinkers Creek is a three-span continuous (40, 50, 40 ft) two-lane bridge with five girders (spaced at 5.75 ft) and 20” skew. The maximum interior girder (center) load distribution for side-by-side occurrences was found to be 1.28. This value is higher than both the AASHTO DF of 1.09 (= 5.75/5.5) and eqn (1) which gave a DF of 1.04. The discrepancy in DF could be attributed to the negligible truck traffic at the site which could be the result of posting. This county-owned bridge had the shortest girder spacing (5.75 ft) considered in this testing program. Site 3 The bridge on Rt 88 over Grand River in Geauga County is a three-span continuous (56, 70, 56 ft) two-lane bridge with five girders (spaced at 7.33 ft) and 0” skew. This bridge is located in a rural area. The maximum interior girder (center) load distribution for side-by-side occurrence was found to be I. 12. This value is compared with eqn (1) which gave a DF of 1.183 and the conservative AASHTO girder distribution of 1.334 (= 7.33/5.5).
Field test 1.32 I .28 1.12 I .08 1.12
Equation
(1)
1.312 1.04 1.18 1.29 1.21
AASHTO, s/5.5 1.44 1.09 1.33 1.44 1.55
outside girder it was not instrumented. The maximum interior girder load distribution for side-by-side occurrence was found to be 1.12. This value is compared with eqn (I) which gave a DF of 1.27 and with the conservative AASHTO girder distribution of 1.55 (=8.54/5.5). CONCLUSIONS
A formula is suggested relating the load distribution factor to the span length and girder spacing. The developed formula was derived from the study of finite element results. It can be applied in the design process using the same procedures as AASHTO formula to simply supported onespan or continuous span bridges with composite or noncomposite deck. The formula can be used to give values of the maximum bending moment in interior girders. It was found that the results of the developed formula are consistent with field test data of typical highway bridges with no special provision and less than the conservative AASHTO distribution factor. However, more experimental studies on prototypes and/or scale model bridges are needed to support the application of the developed formula and improve the design process as well as evaluating the live load capacity of slab-on-girder bridges.
REFERENCES 1. AASHTO,
2.
Site 4
3.
The bridge on I-475 in Lucas County (Toledo, Ohio) is a three-span continuous (51.5, 73, 51.5 ft) two-lane bridge with six girders (spaced at 7.92 ft) and 2” skew. This bridge was chosen because of the large number of heavy special vehicles that cross it. The bridge was over-designed according to AASHTO specifications and was allowed high levels of permit trucks. The maximum interior girder load distribution for side-by-side occurrence was found to be 1.08. This value is compared with eqn (1) which gave a DF of 1.289 and with the conservative AASHTO girder distribution of 1.44 (= 7.2/5.5).
4.
Site 5
7.
The bridge on Rt 2 in Lake County is a three-span continuous (68, 85, 68 ft) three-lane bridge with seven girders (spaced at 8.54 ft) and 0” skew. The third lane was treated as ‘part’ of the right lane since it had negligible traffic, and since the seventh girder was the third lane’s
8.
5.
6.
Standard Specifications for Highway Bridges, American Association of State Highway and Transportation Officials, 15th Edn (1992). R. L. Brockenbrough, Distribution factors for curved I-girder bridges. ASCE /. Struct. Engng 112, 22OC-2215 (1986). R. D. Cook, Concepfs and Applications ofFinite Element Analysis, 2nd Edn. John Wiley, New York (1981). C. 0. Hays and A. J. Berry, Further analytical studies on lateral distribution of wheel loads on highway bridges, University of Florida, Structures and Materials Research Report No. 85-2 (1985). R. A. Imbsen and R. V. Nutt. Load distribution study on highway bridges using STRUDL finite element analysis capabilities. Conference on Computing in Civil Engineering. ASCE, Atlanta, GA (1978). F. Moses, M. Ghosn and J. Gobieski, Weigh-in-motion applied to bridge evaluation. Final report, FHWA/OH85/012, Case Western Reserve University, Ohio Department of Transportation (1985). K. M. Tarhini and G. R. Fredrick, Load distribution on highway bridges using ICES-STRUDL FEA. Comput. Struct. 32, 1419-1428 (1989). K. M. Tarhini and G. R. Frederick, Wheel load distribution in I-girder highway bridges. ASCE J. Strucr. Engng 118, 1285-1294 (1992).
computers & Srructures Vol. 54. No. 2. pp. 351-354. I995 Copyright 0 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0045-794919s $9.50 + 0.00
0045-7949(94)E023GU
TECHNICAL NOTE LATERAL
LOAD DISTRIBUTION K. M. TarhiS@
and
Valparaiso
IN I-GIRDER
G. R. Frederickt
TDepartment
of Civil Engineering,
fDepartment
of Civil and Environmental Engineering, University of Nevada, 4505 Maryland Parkway, Las Vegas, NV 89154-4015, U.S.A. (Received
BRIDGES
University,
22 August
Valparaiso,
IN 46383,
U.S.A.
Las Vegas,
1993)
Abstract-The results of a new lateral load distribution formula to be applied in the analysis or design of steel girders are compared with recently published field test data as well as the current AASHTO load distribution factor method. The developed formula was the result of a study of lateral load distribution in a bridge superstructure employing the finite element analysis techniques. The finite element models were developed to represent the actual geometry of the bridge deck and analyzed to obtain a better understanding of the elastic behavior of the concrete slab-on-steel girder highway bridges. The developed load distribution formula compares well with field data in predicting the behavior of bridge superstructures under highway loadings. Therefore, this paper will assist bridge engineers and researchers in predicting the actual load distribution and bending moments in I-girder highway bridges.
action is commonly neglected. The spacing of longitudinal beams in a bridge deck varies and a common practice is to select a beam spacing ranging between 6 and 12 ft, which yields an economical design. The spacing of the beams is ordinarily the same throughout the span length of the bridge (unless the width of the bridge deck varies). This research considered short and medium span bridges (span lengths between 30 and 120 ft). A typical cross-section of a two-lane bridge superstructure is shown in Fig. 1. The longitudinal beams are usually connected by cross-bracing at their ends and at intervals of up to 25 ft between supports. The thickness of the concrete slab commonly varies between 6 and 12 in (depending upon the girder spacing and the desired cover for slab reinforcing steel). The concrete is usually reinforced in both directions near both faces of the slab with primary reinforcing perpendicular to traffic.
INTRODUCTION Many types of bridges, ranging from suspension structures to short-span girder bridges, are in use today. The most common component of all bridges is the roadway deck. While the bridge deck may be constructed in different ways, the most common one is a reinforced concrete slab placed over steel beams. Since the bridge deck is in direct contact with wheel loads, the applied loading greatly affects the behavior of the deck as well as the bridge substructure. Therefore, an understanding of the lateral load distribution from the slab to the beam is required to develop realistic analyses and design methodologies. The bridge specifications of the AASHTO [I] are generally simple to use and have led to the design of safe bridges. However, it has frequently been criticized as being conservative, particularly with respect to the methods used for lateral distribution of wheel loads to girders. The specifications are based primarily on the general type of supporting beams and the beam spacing. The method of analysis presented in this paper will assist bridge engineers in predicting the actual behavior of the bridge deck and lead to the calculation of realistic live load distribution factors. Realistic live load distribution factors are essential for the structural engineer to economically design new bridges and to evaluate existing bridges for their load capacities. The bridge geometry considered in this research is typical of interstate overpass or grade separation structure where the shoulders are not carried across the bridge. In practice, the longitudinal beams may be simply supported at their ends or continuous over several supports. In addition, they can be bonded to the concrete slab using shear lugs producing a composite section in which the concrete acts as part of the beam in the positive moment region. For noncomposite bridges, even where no shear lugs are present, some limited bonding action usually takes place between the beam and slab. However, during analysis, this bonding
Extensive research using analytical, numerical and experimental methods has been conducted to improve the techniques used in the analysis and design of slab-on-beam highway bridges. Available theoretical methods are varied in their approaches as well as in their accuracy and assumptions. Stress distributions at critical cross-sections can be found after introducing simplifying assumptions to create the idealized analytical model and reduce the problem to one that can be solved with a reasonable amount of calculations. Bridge superstructures can be idealized for theoretical analysis in many different ways. The various assumptions and simplifications used in formulating and idealizing the bridge superstructure can have a significant effect on how closely the calculated results match the actual behavior. The major analytical and numerical approaches reported in the literature are:
$Author addressed.
1. Orthotropic plate theory; where the actual bridge superstructure is replaced with an equivalent plate having different elastic properties in two orthogonal directions.
to
whom
all
correspondence
should
BRIEF HISTORICAL
be
351
REVIEW
Technical
352
Note
Concrete. slab
Steel girder 1
Cross-bracing
A
+s+s+--t---s--cl Girder spacing Fig. 1. Typical
cross-section
Grid analysis; where the actual bridge superstructure is replaced with an equivalent grid system. The resulting structure is a framework of intersecting bars whose stiffnesses are adjusted to approximate those of the slab and girders. Combination of plate and grid analysis; this is represented by two theories-harmonic analysis and numerical moment distribution. Special methods: (a) approximate grid work solution, (b) beam on elastic foundation analogy, (c) finite strip method, (d) finite element method. (e) others. The finite element method can be used to predict the actual behavior of complex structures [3]. Bridge superstructures can be modeled using finite element analysis (FEA) in many different ways. It is in the idealization phase of the analysis, the selection of the finite element models, that the greatest differences in approaches are encountered. The idealizations, which have been used by various researchers, include mixing three-dimensional plate elements and plane or space frame members with the centerline of the girders coinciding with the center of the concrete slab [4]. Others have imposed rigid links between the concrete slab and beams to accommodate the eccentricity of the beams and slab [5]. Still others have attempted to model the concrete slab using plate elements, the girder flanges
Fig. 2. Typical
section
through
of I-girder
bridge.
as space frame members, and the girder web as plate elements [2]. Even though the concrete slab exhibits a ‘plate bending’ phenomenon, the actual behavior of the bridge superstructure can be obtained by modeling the concrete slab using three-dimensional eight-node brick solid elements with three degrees of freedom at each node, and the girder components (flanges and web) are modeled using rectangular plate elements (or shallow shell elements) with five degrees of freedom at each node [7]. The nodes at the interface between the concrete slab and steel girder upper flange were either modeled as rigid connection to simulate composite bridge action or three linear springs were imposed at each interface node to simulate non-composite bridge action. The latter permitted the concrete slab to slide with respect to the upper flanges of the girders in the longitudinal direction. The spring elements were assigned different stiffnesses in three orthogonal directions at each interface node to allow load transfer and relative movements at interface nodes. Crossbracing frames were modeled using space truss members. The reported finite element idealization provided a very good approximation of the bridge superstructure; its use predicted the actual stress distribution and permitted the calculation of the actual bending moment at critical crosssections. Typical elements of a concrete slab on I-girder bridge deck with rigid connections at the interface nodes, which were used to model composite bridge action, are shown in Fig. 2. The results of this finite element analysis technique are represented in this paper and compared with
part of the finite element
model
Technical field test data. A rigorous analysis revealed that the entire bridge superstructure acts as a unit rather than a collection of individual structural elements, as is commonly assumed in the current AASHTO design procedures. This paper correlates the distribution factor results obtained from published field testing data with the developed formula as well as the AASHTO method.
Note
353
the current AASHTO formula (S/5.5). Simply supported bridges could be single or multi-span with composite or non-composite decks. This formula provides a simple and more realistic prediction of the behavior of concrete slab-onsteel girder highway bridges than the current available methods.
COMPARISON LOAD DISTRIBUTION
Wheel loads are distributed laterally (as well as longitudinally) to the girders in highway bridges. The current AASHTO bridge specifications for determining the maximum live loads supported by beams use greatly simplified procedures, where longitudinal distribution is neglected and lateral distribution is accomplished by using wheel load distribution factors. For interior girders, the magnitude of these live loads are specified as (S/5.5) times the standard truck wheel load when two or more lanes are supported (where S is the beam spacing in feet). Using refined finite element models to describe the actual geometry, the behavior of the bridge superstructure was predicted [7,8]. A study of the various parameters affecting the load distribution on two-lane highway bridges was performed using finite element analysis. Critical parameters were identified and employed in developing a new load distribution factor formula which is simple to use in the analysis and/or design process of I-girder bridges [8]. The effect of connection at the interface (composite or non-composite), single or multi-span, and the effect of cross-bracing on the wheel load distribution factor was found to be negligible. It was also demonstrated that a relatively large change in the moment of inertia of the bridge deck produced a relatively small change in the load distribution factor. The various practical girder spacings (S-12 ft) and span lengths (35-120 ft) were shown to have significant effects on lateral load distribution. The finite element results indicated that calculated load distribution factors can be considerably less than the conservative AASHTO factors. The span length effect is completely ignored in the AASHTO empirical load distribution formula. Therefore, a flexural formula for wheel load distribution factor (DF) for bending moment related to span length (L in feet) and girder spacing (S in feet) was developed using the results of the finite element analysis [8]
DF = 0.00013L2
- 0.02lL
WITH FIELD TESTS
FACTORS
+ 1.2@
- y
(1)
This formula can be used in the design process of new bridges as well as the evaluation of existing ones instead of
In order to test the validity of the adopted discretization techniques and the developed load distribution factor formula, the final report presented by Moses ef al. [6] on field tests of five bridges was used to compare results. The bridges selected for the field tests were fairly typical representations of bridges in Ohio in terms of design and truck traffic composition. The five sites were all parallel steel stringer (I-girder) bridges, with only one bridge being of composite construction, that were instrumented and studied. The bridges were tested using weigh-in-motion (WIM) techniques to produce field measurements which are capable of providing all pertinent data on the loading and response of highway bridges. The data collected include measured stresses and girder distribution factors in addition to truck weights and volumes. The goal of the study [6] was to provide examples of the use of WIM measurements to assist in bridge evaluation and rating. The WIM system utilizes existing bridges to serve as equivalent static scales to obtain unbiased truck gross and axle weights, classifications, dimensions and speed. The WIM utilizes traffic sensors to obtain axle and speed data, and strain sensors attached to bridge girders to provide weight information. The system operates in a undetectable manner and has been researched and tested at more than 200 sites worldwide [6]. All five sites were typically two-lane and three-span continuous bridges with various girder spacings and span lengths. Typically, one span of a bridge site was instrumented and tested at the maximum positive bending moment. A typical layout of a bridge is shown in Fig. 3. Field strains were measured continuously in each girder and used to determine the girder distribution factors. The maximum distribution factors for side-by-side occurrences were found by summing the average distributions (plus one standard deviation) from each girder for both lanes. The standard deviation was added to the average distribution of each lane to account for possible situations in which the girder under consideration supports a higher than average percentage of the total load. It was found that interior girders were the most heavily loaded. The results of the five sites are summarized along with a comparison with the current AASHTO and the developed distribution factor formulas in Table 1 as follows.
Gage location /
I
I
I 36W150
I
36Wl82
I
/
36Wl50
I
I
Fig. 3. Site 1 layout
I
I
I-90 near Ashtabula
(six girders
at 7.92 ft spacing
[6]).
Technical
354 Table
1. Comparison
Note of distribution
factors
Distribution
Site
I 2 3 4 5
Site
Span (ft) 48.6 40 56 51.5 68
Girder
spacing (ft)
factors
S
1.92 5.15 1.33 7.92 8.54
1
The bridge on I-90 in Ashtabula, Ohio, is a three-span continuous (48.6,81,48.6 ft) two-lane bridge with six girders (spaced at 7.92ft) and 18” skew. The maximum interior girder load distribution for side-by-side occurrence was found using field data to be 1.32. This value can be compared with the developed formula presented by eqn (1) to give a DF of 1.312 and with the conservative AASHTO DF of 1.44 (=7.92/5.5). Site 2 The bridge on Richmond Road over Tinkers Creek is a three-span continuous (40, 50, 40 ft) two-lane bridge with five girders (spaced at 5.75 ft) and 20” skew. The maximum interior girder (center) load distribution for side-by-side occurrences was found to be 1.28. This value is higher than both the AASHTO DF of 1.09 (= 5.75/5.5) and eqn (1) which gave a DF of 1.04. The discrepancy in DF could be attributed to the negligible truck traffic at the site which could be the result of posting. This county-owned bridge had the shortest girder spacing (5.75 ft) considered in this testing program. Site 3 The bridge on Rt 88 over Grand River in Geauga County is a three-span continuous (56, 70, 56 ft) two-lane bridge with five girders (spaced at 7.33 ft) and 0” skew. This bridge is located in a rural area. The maximum interior girder (center) load distribution for side-by-side occurrence was found to be I. 12. This value is compared with eqn (1) which gave a DF of 1.183 and the conservative AASHTO girder distribution of 1.334 (= 7.33/5.5).
Field test 1.32 I .28 1.12 I .08 1.12
Equation
(1)
1.312 1.04 1.18 1.29 1.21
AASHTO, s/5.5 1.44 1.09 1.33 1.44 1.55
outside girder it was not instrumented. The maximum interior girder load distribution for side-by-side occurrence was found to be 1.12. This value is compared with eqn (I) which gave a DF of 1.27 and with the conservative AASHTO girder distribution of 1.55 (=8.54/5.5). CONCLUSIONS
A formula is suggested relating the load distribution factor to the span length and girder spacing. The developed formula was derived from the study of finite element results. It can be applied in the design process using the same procedures as AASHTO formula to simply supported onespan or continuous span bridges with composite or noncomposite deck. The formula can be used to give values of the maximum bending moment in interior girders. It was found that the results of the developed formula are consistent with field test data of typical highway bridges with no special provision and less than the conservative AASHTO distribution factor. However, more experimental studies on prototypes and/or scale model bridges are needed to support the application of the developed formula and improve the design process as well as evaluating the live load capacity of slab-on-girder bridges.
REFERENCES 1. AASHTO,
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Site 4
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The bridge on I-475 in Lucas County (Toledo, Ohio) is a three-span continuous (51.5, 73, 51.5 ft) two-lane bridge with six girders (spaced at 7.92 ft) and 2” skew. This bridge was chosen because of the large number of heavy special vehicles that cross it. The bridge was over-designed according to AASHTO specifications and was allowed high levels of permit trucks. The maximum interior girder load distribution for side-by-side occurrence was found to be 1.08. This value is compared with eqn (1) which gave a DF of 1.289 and with the conservative AASHTO girder distribution of 1.44 (= 7.2/5.5).
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Site 5
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The bridge on Rt 2 in Lake County is a three-span continuous (68, 85, 68 ft) three-lane bridge with seven girders (spaced at 8.54 ft) and 0” skew. The third lane was treated as ‘part’ of the right lane since it had negligible traffic, and since the seventh girder was the third lane’s
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Standard Specifications for Highway Bridges, American Association of State Highway and Transportation Officials, 15th Edn (1992). R. L. Brockenbrough, Distribution factors for curved I-girder bridges. ASCE /. Struct. Engng 112, 22OC-2215 (1986). R. D. Cook, Concepfs and Applications ofFinite Element Analysis, 2nd Edn. John Wiley, New York (1981). C. 0. Hays and A. J. Berry, Further analytical studies on lateral distribution of wheel loads on highway bridges, University of Florida, Structures and Materials Research Report No. 85-2 (1985). R. A. Imbsen and R. V. Nutt. Load distribution study on highway bridges using STRUDL finite element analysis capabilities. Conference on Computing in Civil Engineering. ASCE, Atlanta, GA (1978). F. Moses, M. Ghosn and J. Gobieski, Weigh-in-motion applied to bridge evaluation. Final report, FHWA/OH85/012, Case Western Reserve University, Ohio Department of Transportation (1985). K. M. Tarhini and G. R. Fredrick, Load distribution on highway bridges using ICES-STRUDL FEA. Comput. Struct. 32, 1419-1428 (1989). K. M. Tarhini and G. R. Frederick, Wheel load distribution in I-girder highway bridges. ASCE J. Strucr. Engng 118, 1285-1294 (1992).