AASHTO-LRFD Live Load Distribution for Beam-and-Slab

Bridges: Limitations and Applicability

Zaher Yousif1 and Riyadh Hindi, M.ASCE2
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Abstract: This paper presents a comparison between the live load distribution factors of simple span slab-on-girders concrete bridges
based on the current AASHTO-LRFD and finite-element analysis. In this comparison, the range of applicability limits specified by the
current AASHTO-LRFD is fully covered and investigated in terms of span length, slab thickness, girder spacing and longitudinal stiffness.
All the AASHTO-PCI concrete girders 共Types I–VI兲 are considered to cover the complete range of longitudinal stiffness specified in the
AASHTO-LRFD. Several finite-elements linear elastic models were investigated to obtain the most accurate method to represent the
bridge superstructure. The bridge deck was modeled as four-node quadrilateral shell elements, whereas the girders were modeled using
two-node space frame elements. The live load used in the analysis is the vehicular load plus the standard lane load as specified by
AASHTO-LRFD. The live load is positioned at the longitudinal location that produced the extreme effect, and then it is moved trans-
versely across the bridge width in order to investigate all possibilities of one-lane, two-lane and three-lane design loads. A total of 886
bridge superstructure models were built and analyzed using the computer program SAP2000 to perform this comparison. The results of
this study are presented in terms of figures to be practically useful to bridge engineers. This study showed that the AASHTO-LRFD may
significantly overestimate the live load distribution factors compared to the finite-element analysis.
DOI: 10.1061/共ASCE兲1084-0702共2007兲12:6共765兲
CE Database subject headings: Load and resistance factor design; Load distribution; Live loads; Finite element method; Girders;
Slabs.

Introduction ered as a vital issue concerning the safety and economy of high-
way bridges. Therefore, it is of critical importance in designing
The AASHTO-LRFD 共2004兲 was initially calibrated by trial de- new bridges and in evaluating existing bridges.
sign to provide a high level of safety in new bridges. The safety Since the 1930s, the AASHTO simple S / D formula has been
level is expressed by a reliability index 共␤兲. AASHTO-LRFD used for live load distribution factors in most common cases to
provides a uniform reliability index 共␤兲 of 3.5 for different types calculate the bending moment and shear in bridge design, where
and configurations of bridges. This reliability index 共␤ = 3.5兲 en- S⫽girder spacing and D⫽a constant that depends on the type of
sures that only 2 out of 10,000 design elements or components the bridge superstructure and the number of the design lanes
will have the sum of the factored loads greater than the factored loaded. This formula allows the designer to simply calculate the
resistance during the design lifetime of the bridge. part of live load to be transferred to the girders without any con-
The current AASHTO standards 共2002兲 共LFD兲 do not provide sideration for the bridge deck, girder stiffness, and span. Further,
a safety level and the reliability index ␤ can be as low as 2.0 or as some bridge designers apply the above-mentioned formula even
high as 4.5. If it is equal to 2.0, 4 out of 100 design elements and to more complicated bridges such as skewed, curved, continuous,
components would probably be overloaded and would experience and large spans with wide and different girder spacing, even
a problem during the design lifetime of the bridge. Based on that, though, the formula is developed for simple bridges with typical
the requirement for the AASHTO-LRFD specifications was nec- geometry. Therefore, these bridges will be constructed either in a
essary in order to provide better safety. conservative way which involves the unnecessary additional cost
The major change in the AASHTO-LRFD is the distribution of or unconservative way which is related to bridge service life and
vehicular live load on highway bridges, which is considered to be safety.
a key quantity in determining the bridge component size and de- In 1993, the National Cooperative Highway Research Program
tail, consequently, strength and serviceability, which are consid- developed new live load distribution factors “Project 12-26–
Distribution of live load on highway bridges” based on the study
1
Bridge Engineer, Earth Tech 共Canada兲 Inc., 300-340 Midpark Way by Zokaie et al. 共1991兲. Additional parameters were included in
S.E., Calgary, AB, Canada T2X 1P1. E-mail: zaher.yousif@earthtech.ca the new formulas to obtain more accurate distribution factors,
2
Associate Professor, Dept. of Civil Engineering and Construction, such as bridge span 共L兲, slab thickness 共ts兲, girder spacing 共S兲,
Bradley Univ., Peoria, IL 61625. E-mail: hindi@bradley.edu and the longitudinal stiffness parameter 共Kg兲. The first edition of
Note. Discussion open until April 1, 2008. Separate discussions must AASHTO-LRFD Specification 共1994兲 was based on this study.
be submitted for individual papers. To extend the closing date by one
Many studies 共Chen 1999; Tabsh and Sahajwani 1997; Chen
month, a written request must be filed with the ASCE Managing Editor.
The manuscript for this paper was submitted for review and possible and Aswad 1996; Huo et al. 2004; Eom and Nowak 2001; Mab-
publication on December 28, 2005; approved on October 4, 2006. This sout et al. 1997; Cai 2005; Barr et al. 2001; Amer et al. 1999兲
paper is part of the Journal of Bridge Engineering, Vol. 12, No. 6, have been conducted to compare the AASHTO-LRFD distribu-
November 1, 2007. ©ASCE, ISSN 1084-0702/2007/6-765–773/$25.00. tion factors with the standard AASHTO, refined methods of

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 Table 1. Bridge Parameters Summary
Number of AASHTO-PCI Girder
Span Bridge width design lanes girder spacing Slab thickness Number of
共m兲 共m兲 loaded type 共m兲 共m兲 bridge models
6,13,19,25,31,37,43,49,55,61,67,73 11.80 1, 2, and 3 I–VI 1.10 0.11 216
6,13,19,25,31,37,43,49,55,61,67,73 11.72 1, 2, and 3 I–VI 2.20 0.19 227
6,13,19,25,31,37,43,49,55,61,67,73 18.88 1, 2, and 3 I–VI 2.94 0.24 227
6,13,19,25,31,37,43,49,55,61,67,73 18.88 1, 2, and 3 I–VI 4.90 0.30 216

analysis 共i.e., finite elements兲 and/or field test data. Although most its specified by the AASHTO-LRFD 共2004兲 for such bridges, sev-
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of these studies concluded that AASHTO-LRFD may be less con- eral hundreds of bridge models are required to be analyzed. Table
servative than the standard AASHTO, they also showed that the 1 summarizes the bridge parameters and their combinations as
AASHTO-LRFD may be conservative for specific bridge param- considered in this study. Eight hundred eighty-six bridge models
eters and geometries compared to several refined methods of were needed to perform such a study. This study considers the
analysis. These studies were performed on specific types of same database of bridges as considered by Zokaie et al. 共1991兲 for
bridges and limited to specific bridge geometry. Therefore, the the development of vehicular live load distribution factors formu-
objective of this study is to carry out a comprehensive compari- las for the “National Cooperative Highway Research Program-
son between the AASHTO-LRFD 共2004兲 distribution factors and Project 12-26” in order to make a fair comparison. The girder
a refined method of analysis using the finite-element analysis. concrete strength used in this study was f ⬘c = 48 MPa, which gave
In bridge industry, the beam-and-slab concrete bridges are the a modular of elasticity of E = 35,027 MPa, whereas the deck
most common type of bridges due to the durability of concrete, 共slab兲 concrete strength was f ⬘c = 27.5 MPa, which gave
flexibility in construction, and speed of construction. Therefore, a E = 26,550 MPa.
very high percentage of bridges in the United States are cast-in- The bridge span as specified by the AASHTO-LRFD 共2004兲
place concrete deck with precast prestressed concrete girders. The should range between 6 and 73 m. In order to cover the entire
girders are mainly AASHTO-PCI concrete girders 共Types I–VI兲. range, 12 bridge spans were selected; 6, 13, 19, 25, 31, 37, 43, 49,
The current AASHTO-LRFD 共2004兲 imposes limitations in 55, 61, 67, and 73 m as shown in Table 1. Each of these spans
terms of range of applicability on its live load distribution factors was considered in combination with other bridge parameters. Fig.
of highway bridges. These limitations are specified in terms of 1 shows a typical cross section of the selected bridges.
bridge span, slab thickness, girder spacing, and longitudinal stiff- The girder spacing is another key parameter specified in the
ness. In order to ensure the safety of highway bridges, these limits AASHTO-LRFD 共2004兲. For beam-and-slab bridges, the girder
must be studied and verified. The effect of these parameters on spacing is limited to a minimum of 1,100 mm and a maximum of
the live load distribution factor should be carefully studied and 4,900 mm. In this study, the outer limits 共1,100 and 4,900 mm兲
examined to make sure that not only safety is guaranteed but also plus two intermediate spacing 共2,200 and 2,940 mm兲 were se-
economy is achieved. lected and studied as shown in Table 1. The two intermediate
The objective of this paper is to investigate the range of appli- spacing are very common spacing used with beam-and-slab
cability limits specified in the AASHTO-LRFD 共2004兲 in terms of bridges in the United States.
span length, slab thickness, girder spacing, and longitudinal stiff- The limits for concrete slab 共deck兲 thickness specified in the
ness. This is performed through a comparison between the distri- AASHTO-LRFD 共2004兲 are a minimum of 110 mm and a maxi-
bution factors of simple span concrete bridges 共beam-and-slab兲 mum of 300 mm. Four values of bridge slab thickness were
due to live load calculated in accordance with the AASHTO- selected in this study; 110, 190, 240, and 300 mm as shown in
LRFD 共2004兲 formulas and the finite-element analysis. One pa- Table 1. Two intermediate slab thicknesses 共190 and 240 mm兲
rameter at a time is considered, whereas the other parameters were selected and studied since they are very common in the
remain fixed. All the AASHTO-PCI concrete girders 共Types I–VI兲 United States. As the slab thickness 共ts兲 is directly related to the
are considered to cover the wide range of longitudinal stiffness girder spacing 共S兲, logically higher girder spacing was used and
共Kg兲 specified in the AASHTO-LRFD 共2004兲. This comparison is combined with thicker slab. Therefore, smaller slab thickness was
presented in terms of figures to help bridge engineers understand combined with smaller girder spacing. Each of these slab thick-
the difference between the live load analysis for bridges with ness was considered in combination with other bridge parameters
AASHTO-PCI girders using the AASHTO-LRFD 共2004兲 and as shown in Table 1.
finite-element analysis to decide if a refined method of analysis is The longitudinal stiffness 共Kg兲, as shown in the following
necessary.

Properties of Selected Bridges

The beam-and-slab bridges are the most common type of bridges

in the United States. The beams 共girders兲 are either steel beams or
precast prestressed concrete beams, mainly AASHTO-PCI 共Type
I–VI兲 girders. The focus of this paper is to study the live load
distribution factors for simple span beam-and-slab concrete
bridges with AASHTO-PCI girders.
In order to carefully investigate the range of applicability lim- Fig. 1. Typical bridge cross section

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J. Bridge Eng. 2007.12:765-773.

 Table 2. Section Properties for AASHTO-PCI Girders Types 1–VI 共Based on Eby et al. 1973兲
Girder type
Properties I II III IV V VI
t1 共m兲 0.140 0.191 0.235 0.279 0.216 0.216
t2 共m兲 0.191 0.229 0.273 0.318 0.330 0.330
D1 共m兲 0.181 0.221 0.269 0.316 0.264 0.264
D2 共m兲 0.221 0.254 0.302 0.350 0.361 0.361
␣1 0.112 0.088 0.083 0.080 0.101 0.101
␣2 0.088 0.073 0.071 0.069 0.066 0.066
Torsional constant, J共m4兲 0.0015 0.0026 0.0057 0.0108 0.0133 0.0140
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Moment of inertia 共m4兲 0.0095 0.0212 0.0522 0.1085 0.2169 0.3052

Section area 共m2兲 0.178 0.238 0.361 0.509 0.654 0.700
Y bot 共m兲 0.320 0.402 0.515 0.628 0.812 0.924
Y top 共m兲 0.391 0.512 0.628 0.743 0.788 0.905
Note: Parameters are defined in Eq. 共3兲.

equation, is another major factor affecting the AASHTO-LRFD In order to obtain more accurate results and comparison, a
共2004兲 live load distribution factors more complex torsional constant 共J兲, as shown in the following
equation, is used in this study as suggested by Eby et al. 共1973兲:
Kg = n共Ig + Ae2g兲 共1兲 1
J = 3 共b1t31 + b2t32 + d3b33兲 + ␣1D41 + ␣2D42 − 0.21共t41 + t42兲 共3兲
where n⫽elasticity modular ratio between girder material and
deck material. where
The longitudinal stiffness is mainly represented by the girder
b23
type, which mainly depends on the moment of inertia 共Ig兲 of the D1 = t1 +
girder, cross-sectional area of the girder 共Ag兲 and the eccentricity 4t1
between the girders and slab centers of gravity 共eg兲. The Kg for
beam-and-slab types of bridges is limited between 4 ⫻ 109 and b23
3 ⫻ 1012 mm4 as per AASHTO-LRFD 共2004兲. In order to cover D2 = t2 +
4t2
this range, AASHTO-PCI girders 共Types I–VI兲 were selected

冉冊 冉冊
since they are very common in the United States. 2
b3 b3
In order to cover the four girders spacing discussed earlier, the ␣1 = − 0.042 + 0.2204 − 0.0725
selected bridge widths are shown in Table 1. The widths were t1 t1

冉冊 冉冊
selected so the bridge could be investigated for all loading cases;
2
one, two, and three design lanes. The bridge widths were 11.80, b3 b3
11.72, and 18.88 m as shown in Table 1. For bridge width of ␣2 = − 0.042 + 0.2204 − 0.0725
t2 t2
11.80 m, ten girders were spaced at 1.10 m leaving 0.95 m as a
deck overhang at each side with 0.51 m for a barrier on each side. b1⫽top flange width; t1⫽thickness of the top flange +1 / 2 of the
The distance between the center of the exterior girder and the top tapered part; b2⫽bottom flange width; t2⫽thickness of the
inside edge of the barrier 共de兲 equals to 0.44 m as shown in Fig. 1. bottom flange +1 / 2 of the bottom tapered part; b3⫽web width;
For bridge width of 11.72 m, five girders were spaced at 2.20 m and d3⫽clear depth of the web.
leaving 1.46 m as a deck overhang at each side with 共de兲 equals to The torsional constant of Eby et al. 共1973兲 correlates with the
0.95 m. The third bridge width was 18.88 m. Six girders were exact solution with a minor error of ±3% 共Chen et al., 1997兲. The
spaced at 2.94 m with 共de兲 equals to 1.58 m on each side. This torsional constant 共J兲 for the AASHTO-PCI girders 共Types I–VI兲
bridge width of 18.88 m was also used with four girders spaced at have been calculated based on the formula of Eby et al. 共1973兲
4.9 m, which represents the maximum girder spacing specified by 关Eq. 共3兲兴 as summarized in Table 2.
the AASHTO-LRFD 共2004兲. Table 1 summarizes the bridge pa-
rameters and their combinations as considered and analyzed in
this study. Finite-Element Analysis
The torsional inertia 共J兲 plays a big rule in the live load dis-
tribution factors. The AASHTO-LRFD 共2004兲 specifies the fol- Several finite-elements modeling techniques were investigated in
lowing approximation for computing the torsional inertia for order to select the most accurate and practical one for this study.
stocky open sections 共e.g., I-beams, T-beams, and solid sections兲 The first modeling technique 共Model A兲 is based on a study con-
even though it underestimates the torsional constant 共J兲 for ducted by Hays et al. 共1986兲. The bridge superstructure is ideal-
I-girders ized as a two-dimensional system as shown in Fig. 2共a兲. The main
girders and the ends diaphragm beams are modeled as two-node
A4 space frame elements with 6 degrees-of-freedom 共DOF兲 共3 trans-
J= 共2兲 lations and 3 rotations兲 at each node. The bridge deck is modeled
40I P
as four-node quadrilateral shell elements with 6 DOF at each
where A⫽girder cross-sectional area 共mm2兲 and I p⫽section polar node. The center of gravity of the slab coincides with the center
moment of inertia 共mm4兲. of gravity of the girders; therefore, the girders properties are

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J. Bridge Eng. 2007.12:765-773.

 Table 3. Model Validation Comparison for Moment at Center
Truck load moment 共kN m兲
Girder Hays et al. Chen and Aswad Current Differences
number 共1995兲 共1996兲 research 共%兲
1 380.40 368.90 373.10 −2
共Exterior兲
2 1,133.60 1,159.40 1,127.40 −0.5
3 1,464.30 1,522.60 1,449.70 −1
4 1,110.80 1,118.70 1,103.20 −0.7
5 Not reported Not reported 381.20 —
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6 Not reported Not reported 50.20 —

moving load analysis with such modeling; therefore, this model

can be only investigated under static load.
The fourth model 共Model D兲, based on a study conducted by
Tarhini and Frederick 共1992兲, models the deck slab as 3D solid
elements and the girders as shell elements. However, the bridge
deck, the girders and the end diaphragms are modeled as 3D solid
elements with 3 DOF at each node. Similar to Model C, the
moving load cannot be used with this type of modeling using
SAP2000 共Computers and Structures 2004兲. In addition, it re-
quires more computation time and larger computer memory even
Fig. 2. Finite-element models 共SAP2000兲 with very simple bridge model. Therefore, it is not practical to
select this type of modeling for this study with the number of
analyses required for this study in order to cover the complete
range of applicability limits as per AASHTO-LRFD 共2004兲. Mab-
transformed to the deck center of gravity. The bridge supports sout et al. 共1997兲 suggested that this method can be used to model
consist of hinges at one end of the girders and rollers at the other the boundary conditions of the bridge, whereas the bridge super-
end. Full depth diaphragm is provided at each support to provide structure can be modeled using Model A with sufficient accuracy.
the torsional restrain recommended by AASHTO-LRFD 共2004兲. As suggested by Hays et al. 共1986兲 and Mabsout et al. 共1997兲,
Each girder is divided into equal parts with 500 mm element the shell elements and space frame bridge model 共Model A兲 gives
length 共interval兲. The deck is divided into six equal shell elements better and more satisfactory results compared to the other three
between every two girders. For example, if the girders spacing models. However, in this study additional check has been carried
was 2,940 mm, then the shell length/width aspect ratio is equal to out to validate the selected model 共Model A兲 prior to the imple-
500/ 490= 1.02. Such ratio will give good results as per mentation to the selected bridges. The benchmark used for this
AASHTO-LRFD, which recommends that aspect ratio of finite verification is the bridge reported by Hays et al. 共1995兲, which
elements should not exceed 5. was also verified by Chen and Aswad 共1996兲. The results, as
Model B, as suggested by Imbsen and Nutt 共1978兲, idealizes shown in Table 3, showed good agreement between the three
the bridge superstructure as three-dimensional-systems. As shown studies including this study which gave high level of confidence
in Fig. 2共b兲, the bridge deck is modeled as quadrilateral shell for selecting Model A. The bridge model sample for this check
elements with 6 DOF at each node, the main girders and the ends was built using the SAP2000 共Computers and Structures 2004兲
diaphragm beams are modeled as space frames with 6 DOF at structural analysis computer program. The bridge, as per Hays
each node. The girders are eccentrically connected to the deck et al. 共1995兲 and Chen and Aswad 共1996兲, is a simply supported
with “rigid link” to account for the differences in their centers of with 14.70 m span and six AASHTO-PCI Type III concrete gird-
gravity. The bridge supports are hinges at one side of the bridge ers spaced at 2.26 m with a deck overhang of 0.80 m at each side.
and roller at the other side and are positioned at the center of The deck 共slab兲 thickness is 178 mm and the concrete strength
gravity of each of the girders ends. Full depth diaphragm is added 共f ⬘c 兲 is 23.44 and 34.47 MPa for slab and girders, respectively.
at each end of the bridge to provide the torsional restrain recom- The results of this analysis and the comparison with the above
mended by AASHTO-LRFD 共2004兲. Same dimensions and aspect mentioned studies are summarized in Table 3. More details on
ratio was selected for the finite elements discussed in Model A. this verification can be found in Yousif 共2005兲.
In Model C 共Brockenbrough 1986兲, the girder flanges are The vehicular live load used in this study is based on the load
modeled as two-dimensional shell elements with thickness instead specified by AASHTO-LRFD 共2004兲. The HL-93 design truck
of space frame elements. The bridge superstructure is idealized as plus design lane load or the design tandem plus lane load 共which-
3D system. The bridge deck, the main girders and the diaphragms ever governs兲 is used in this study to calculate the live load dis-
are modeled as four-node quadrilateral shell elements with 6 DOF tribution factors. The HL-93 design truck consists of a 35 kN
at each node. These components are connected together using front axle and two of 145 kN 共middle and back兲 axles 4.3 m away
rigid link to allow for full composite action. This type of model- from the front axle and the spacing between them varies from 4.3
ing is very time consuming in order to calculate the total forces at to 9.0 m. The design tandem consists of two axles weighing
each girder as the output will be in terms of stresses and not 110 kN spaced at 1.2 m. In this study, the tandem load governed
forces 共shear and moment兲. In addition, it is not possible with the for bridges with spans less than 9 m. The design lane load, which
SAP2000 共Computer and Structures 2004兲 program to use the consists of 9.3 kN/ m and occupies a transverse width of 3 m, is

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J. Bridge Eng. 2007.12:765-773.

 0.6 m from the face of the barrier and a standard distance of
1.2 m is maintained between the wheels of different trucks in the
transverse direction as shown in Fig. 3. Discontinuous barrier was
assumed in this study; therefore, its stiffness was not included in
the analysis. The girder distribution factor from the finite-element
analysis 共FEA兲 was obtained for each case by dividing the total
moment carried by the girder composite section obtained from the
FEA by the maximum moment obtained from single beam analy-
sis.
The multiple presence factors recommended by AASHTO-
LRFD 共2004兲 for different number of lanes loaded are already
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taken care of in the AASHTO-LRFD live load distribution factors

except when the Lever Rule method is used. Therefore, the mul-
Fig. 3. Transverse trucks position tiple presence factors were applied to the live load distribution
factors obtained using the Lever Rule method and the finite-
element analysis.
used in combination with the design truck load or tandem load.
In the longitudinal direction, the bridges with different span
length are investigated to locate the truck load on positions which Results and Comparison
will produce the maximum moment or shear. In the transverse
direction, all the possibilities of 1, 2, and 3 design lanes loaded The results are presented in terms of the ratio of the AASHTO-
are investigated to find the maximum moment and shear for the LRFD and finite-element analysis 共LRFD/FEA兲 distribution fac-
interior and exterior girders. First vehicle 共truck兲 is positioned at tors 共DF兲 based on moment in the girders and plotted with the
span length as shown in Figs. 4–11. The variation of the girders

Fig. 4. LRFD/FEA distribution factor ratio, interior girder Fig. 5. LRFD/FEA distribution factor ratio, exterior girder
共S = 1,100 mm, ts = 110 mm兲 共S = 1,100 mm, ts = 110 mm兲

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Fig. 7. LRFD/FEA distribution factor ratio, exterior girder

共S = 2,200 mm, ts = 190 mm兲

Fig. 6. LRFD/FEA distribution factor ratio, interior girder

共S = 2,200 mm, ts = 190 mm兲
For exterior girders as shown in Fig. 5, the three-lane load
gave higher LRFD/FEA with a maximum of almost 1.45. This
ratio decreased by increasing the span length as well to reach a
shear with span length is very small for the considered bridges; maximum of 1.15 and a minimum of 0.97 at 73 m span length as
therefore, only the distribution factors based on girder moment shown in Fig. 5共c兲. The LRFD/FEA ratio became smaller for the
are presented herein. Details about the LRFD/FEA distribution two-lane load as shown in Fig. 5共b兲. The decrease of the longitu-
factor ratio based on girder shear can be found in Yousif 共2005兲. dinal stiffness 共Kg兲 decreased the ratio of the LRFD/FEA distri-
In this paper, it is decided to present all the results for the girders bution factors by about 0.1–0.2. The LRFD/FEA ratio for the
moments DF for one, two, and three design lanes in order to one-lane load increased as the bridge span got longer as shown in
present to the reader how the number of the loaded lanes affects Fig. 5共a兲 to reach a value of almost 1.5. In average, the LRFD and
the results. the FEA for two-lane load gave very similar results for bridge
Figs. 4 and 5 summarize the results for bridges with girder span longer than 36 m. However, the LRFD gave higher results
spacing S = 1,100 mm and slab thickness ts = 110 mm. These re- for shorter spans as shown in Fig. 5共b兲.
sults are in terms of the longitudinal moments in the girders. For Similar trends with slightly different ratios were observed for
interior girders as shown in Fig. 4, the three-lane load gave higher bridges with other girder spacing and slab thickness as shown in
LRFD/FEA with a maximum of almost 1.5. This ratio decreased Figs. 6–11. The LRFD/FEA ratio became less than 1.0 for long
by increasing the span length to reach a maximum of 1.2 at 73 m spans and reached a minimum of about 0.8. It is important to state
span length as shown in Fig. 4共c兲. The LRFD/FEA ratio became that the LRFD gave closer results to the finite elements for me-
smaller by decreasing the number of lanes loaded as shown in dium spans. The LRFD/FEA ratio became closer to 1.0 for
Figs. 4共a and b兲. The decrease of the longitudinal stiffness 共Kg兲, bridges with bigger girders and longer spans; e.g., the LRFD/FEA
which mainly depends on the girder type, decreased the ratio of ratio for 73 m span was about 0.8 for Girder Type I, wheareas the
the LRFD/FEA distribution factors by about 0.1–0.15. The LRFD ratio was almost 1.0 for Girder Type VI as shown in Fig. 6共c兲.
gave higher distribution factor than the FEA except for the one- Also, the LRFD/FEA ratio became closer to 1.0 for bridges with
lane load case for bridge spans longer than 24 m. smaller girders and shorter spans; for example, the LRFD/FEA

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Fig. 9. LRFD/FEA distribution factor ratio, exterior girder

共S = 2,940 mm, ts = 240 mm兲
Fig. 8. LRFD/FEA distribution factor ratio, interior girder
共S = 2,940 mm, ts = 240 mm兲
short spans and had less impact on long spans. For interior girder
of bridges subjected to two lanes loaded, The LRFD and FEA
ratio for 6 m span bridge was about 1.4 for girder Type VI, produced similar results for slab thickness and girder spacing
whereas the ratio was about 1.25 for Girder Type VI as shown in ranging between 190–240 and 2,200–2,940 mm, respectively. For
Fig. 6共c兲. It is logical that the long span bridges will be con- spans less than 31 m, the difference between LRFD and FEA is
structed using the bigger girders, which will make the AASHTO- 5–18%. For spans ranging 31–73 m, the difference between
LRFD results closer to the finite-elements analysis. More detailed LRFD and FEA reached 15–30%. The increase in longitudinal
results can be found in Yousif 共2005兲. stiffness 共Kg兲 increased the difference for bridges with slab thick-
In general, for exterior girder of bridges subjected to one lane ness and girder spacing less than 190 and 2,200 mm respectively,
loaded, the maximum LRFD/FEA ratio is 1.55 and the major whereas, it reduced it for larger dimensions.
difference was for spans longer than 31 m. The increase in longi- The FEA results demonstrated that not necessarily the distri-
tudinal stiffness 共Kg兲 reduced the LRFD/FEA ratio to an average bution factors obtained from two lanes loaded will govern the
of about 1.18 in long spans and 1.10 for short spans. For exterior design compared to three lanes loaded as proven for span larger
girder of bridges subjected to multiple lane loaded, the AASHTO- than 31 m with slab thickness and girder spacing ranging 190–
LRFD results were within a range of less than 10% compared to 240 and 2,200–2,940 mm, respectively; therefore, FEA is recom-
the FEA results for most of bridges spanning between 31 and mended for bridges subjected to three lanes loaded.
73 m. Although for bridge spans ranged between 6 and 31 m, the
LRFD results were conservative with a range of 10–30%.
For interior girder of bridges subjected to one lane loaded, the Conclusions
LRFD and FEA produced close results for slab thickness and
girder spacing ranging between 110–190 and 1,100–2,200 mm, Based on the results of this study, the following were concluded:
respectively. The LRFD overestimated the distribution factors by 1. The AASHTO-LRFD overestimated the live load distribution
10–30% for slab thickness and girder spacing ranging between when compared to finite-elements analysis for a significant
240–300 and 2,940–4,900 mm, respectively. The increase in lon- number of cases. The most cases occurred when the LEVR
gitudinal stiffness 共Kg兲 reduced the difference significantly for RULE method is recommended by AASHTO-LRFD. The

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Fig. 11. LRFD/FEA distribution factor ratio, exterior girder

共S = 4,900 mm, ts = 300 mm兲

Fig. 10. LRFD/FEA distribution factor ratio, interior girder FEA is recommended for bridges subjected to three lanes
共S = 4,900 mm, ts = 300 mm兲 loaded.
5. The AASHTO-LRFD limitations on the live load distribution
factors, specially the bridge span length, need to be revisited
AASHTO-LRFD gave a maximum of about 55% more live to reduce the deviation from the finite-elements analysis be-
load distribution than the finite-element analysis. cause it could significantly increase the cost in some cases or
2. In some cases, the AASHTO-LRFD distribution factors gave jeopardize the safety in others.
a lower girder live load distribution when compared to finite-
elements analysis. The AASHTO-LRFD gave a maximum of
about 20% less live load distribution than the finite-element Acknowledgments
analysis.
3. The range of the limitations specified by the AASHTO- This research was supported by Bradley University and the Inter-
LRFD in terms of span length, girder spacing, deck thick- national Road Federation. This financial support is highly appre-
ness, and longitudinal stiffness have significant effect on the ciated.
ratio of the LRFD/FEA live load distribution. The AASHTO-
LRFD seems to give very comparable results to the finite
elements for bridges with parameters within the intermediate References
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