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Weigh-in-Motion-Based Fatigue Damage Assessment


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Weigh-in-motion (WIM) data provide an excellent opportunity to study the effects of actual traffic loads on bridges. Here procedures are presented for using WIM data to quantify the fatigue damage accumulated in steel bridges. These procedures allow comparisons of the impacts of truck traffic on various routes beyond simple comparisons of the numbers and gross vehicles weights of trucks in the traffic streams. The fatigue damage accumulation procedures are demonstrated using WIM traffic data collected in the state of Alabama. The results of the analysis show that approximately 20% of trucks are overloaded, that is, permit loads and illegal loads, and those trucks create more than 50% of the total damage based on the combined data from all the WIM locations in the state. The contribution of overloaded trucks to the total fatigue damage varies so that their contribution is less significant along some routes. A typical steel bridge with bottom flange coverplates was evaluated using the WIM data from 1 year for a heavily traveled route. This analysis shows that the fatigue life of the bridge was consumed at an annual rate consistent with a mean life of 100 years. These procedures have applications in planning weight limit enforcement, budgeting, and maintenance, and they have the potential for future use in planning inspection intervals.
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Research Article
Transportation Research Record
ÓNational Academy of Sciences:
Transportation Research Board 2020
Article reuse guidelines:
DOI: 10.1177/0361198120919758
Weigh-in-Motion-Based Fatigue Damage
Olga Iatsko
, Anjan Ramesh Babu
, J. Michael Stallings
and Andrzej S. Nowak
Weigh-in-motion (WIM) data provide an excellent opportunity to study the effects of actual traffic loads on bridges. Here
procedures are presented for using WIM data to quantify the fatigue damage accumulated in steel bridges. These procedures
allow comparisons of the impacts of truck traffic on various routes beyond simple comparisons of the numbers and gross
vehicles weights of trucks in the traffic streams. The fatigue damage accumulation procedures are demonstrated using WIM
traffic data collected in the state of Alabama. The results of the analysis show that approximately 20% of trucks are over-
loaded, that is, permit loads and illegal loads, and those trucks create more than 50% of the total damage based on the com-
bined data from all the WIM locations in the state. The contribution of overloaded trucks to the total fatigue damage varies
so that their contribution is less significant along some routes. A typical steel bridge with bottom flange coverplates was eval-
uated using the WIM data from 1 year for a heavily traveled route. This analysis shows that the fatigue life of the bridge was
consumed at an annual rate consistent with a mean life of 100 years. These procedures have applications in planning weight
limit enforcement, budgeting, and maintenance, and they have the potential for future use in planning inspection intervals.
The service life of a bridge is affected by many factors
such as, but not limited to, traffic loads, natural hazards,
and defects in material production. Traffic-induced loads
may cause damage to a bridge by fatigue, overload, or
both. Steel bridges are generally more prone to fatigue
cracking compared with other types of bridges, so steel
bridges are the main focus of this paper. Every passage of
a truck across a bridge creates one or more stress cycles
in the structural components, which results in the accu-
mulation of fatigue damage over time. During the service
life of a steel bridge located on a busy highway, the bridge
experiences millions of cycles of fatigue loading from
heavily loaded trucks. If these stress cycles are of suffi-
cient magnitude and number, they will likely result in fati-
gue cracking. The entire fatigue process in a member
includes the formation of a fatigue crack, crack growth,
and final failure (1). The number of stress cycles required
for the formation of a fatigue crack is typically much
larger than the number of cycles required to subsequently
grow the crack to a size that will cause failure. After for-
mation, if a fatigue crack is not detected and properly
repaired, it may lead to failure of the member. So, in
broad terms, the passage of each heavy truck uses a por-
tion of the fatigue life of a bridge. The goal here is to
quantify the damage produced by an individual truck and
the accumulated damage resulting from many trucks.
The AASHTO LRFD Bridge Design Specifications (2)
have a design approach for fatigue. The stress range cal-
culated for a code-specified fatigue design truck is limited
to avoid fatigue cracking caused by the accumulation of
damage from repetitive truck loading. The AASHTO
fatigue design truck is intended to represent truck traffic.
However, over the service life of a bridge, there is uncer-
tainty in the traffic loads that the bridge experiences. The
procedure proposed here addresses the fatigue damage
accumulated by bridges as a result of actual heavy truck
traffic recorded at weigh-in-motion (WIM) stations.
Background information is provided along with a review
of the state-of-the-art from literature and the practices in
the other states. Further, the methodology used in this
paper and the implementation of that methodology are
The study of the impacts of vehicular traffic on infra-
structure has been conducted in many states. Some states
have sponsored research based on an experimental
approach and other states have sponsored research based
on analytical studies. In this section, some of the on-site
Department of Civil Engineering, Auburn University, Auburn, AL
Corresponding Author:
Olga Iatsko,
field measurement studies are discussed first, and later
the analytical studies.
Instrumentation and field measurements of fatigue
stresses in steel girder bridges date back many years.
Some of those early studies are documented by Fisher
(3). In the early 1990s Laman and Nowak carried out a
study for Michigan Department of Transportation
(DOT) (4). Nowak et al. performed both experimental
and analytical studies of the Woodrow Wilson Memorial
Bridge (5). Field measurements were also done in
Michigan for five steel bridges by Laman et al. (6) and a
state-specific fatigue truck was proposed. In the early
2000s (7,8) an analytical and experimental study was
conducted on 58 simple-span rolled-girder bridges, 18
continuous-span rolled-girder bridges, and six plate-
girder simple-span bridges located in Birmingham,
Alabama. Based on that study (8), the base metal at the
end of the bottom flange cover plates was identified as
the most fatigue-prone detail of those existing steel girder
bridges. A recent study that includes procedures for
assessing fatigue damage using measured strain data is
reported by Fasl et al. (9).
Past analytical studies looked at various ways to assess
the damage caused to bridges by traffic. Many studies
have used simple beam line theory to assess the damage
by running a single truck on an influence line. Most of
these methods result in very conservative estimates of
fatigue life. In 2012, Bowman et al. (10) performed a
study aimed at improving the methodology for fatigue
evaluation of bridges contained in Section 7 of the
AASHTO Manual for Bridge Evaluation (MBE) (11).
Interpretation of the S-N curves, average life-time single-
lane average daily truck traffic (ADTT), and simplifica-
tion of the structural performance and the variation of
the site-specific truck loads were considered to be sources
of conservatism of fatigue life prediction methods. The
cumulative effect of these conservatisms is a significant
underestimation of fatigue life. As an alternative, a
closed-form solution for future traffic growth, previously
developed by Fu et al. (12), was proposed for inclusion in
Section 7 of the MBE. The multiple presence effect was
studied using WIM data from seven states (California,
Florida, Idaho, New York, Michigan, Texas, and
Vermont). The effect of multiple presence on the fatigue
evaluation results caused by the actual present ADTT,
span length, and number of lanes was determined. These
WIM data were also used to validate the gross vehicle
weight (GVW) of the 54-kip fatigue truck developed in
1978 (13). The proposed remaining fatigue life evaluation
procedure included the traffic volume growth rate, pres-
ent ADTT, current age of the structure, and importance
factor of the structure.
Most of the damage to bridges is caused by over-
weight (OW) trucks. The availability of an enormous
WIM database collected by states has made it possible to
analytically evaluate the damaging effect of the OW
trucks on infrastructure, and many state DOTs have
sponsored studies of these damaging effects. The impact
of the heavy trucks on the bridges, and the potential
impacts of increasing truck weight limits was studied by
Fu et al. in 2003 (14). South Carolina DOT sponsored a
study in 2013 to analyze the impact of heavy vehicle traf-
fic on infrastructure and develop policy recommenda-
tions. Stakeholder interviews were done as part of the
study (15). Ghosn et al. in 2015 (16) investigated the
effect of OW trucks on the infrastructure of New York
State. In modeling the effects of OW trucks on bridges,
the WIM traffic data for OW trucks was categorized to
probable divisible permits, special hauling permits, and
illegals. The structural response to overweight trucks was
considered using the overstress of main bridge members
and cyclic fatigue damage accumulation. A study initi-
ated by the Federal Highway Administration (FHWA)
within the Moving Ahead for Progress in the 21st
Century Act (MAP-21) (17) was partially focused on the
analysis of the effect of the OW and oversize (OS) vehicle
operation on bridges. Fatigue analysis was performed
for the various fatigue-prone details of simply supported
and continuous steel bridges. It was concluded that cost-
wise the fatigue induced repairs were a non-significant
portion of the total bridge cost. The Texas Department
of Transportation (TxDOT) and the FHWA sponsored
a study of infrastructure damage caused by OS and OW
trucks to provide recommendations for permit fee adjust-
ments if required (18). A methodology to quantify the
pavement and bridge consumption rate per mile was
developed as part of the study.
Technical Approach
Procedures were developed to use WIM measurements to
calculate the level of accumulated fatigue damage for a
specific bridge and to compare the damage accumulated
in generic bridges characterized by their span length and
the location of a cross-section of interest along the span.
Damage accumulation was quantified for the period of
time over which the WIM measurements were made.
Traffic data for 1 year were used for this paper.
General Methodology
The nominal-stress life approach from the AASHTO
LRFD Bridge Design Specifications (2) was used. The
fatigue resistance of the detail was defined by an S-N
relationship similar to that shown in Figure 1. The resis-
tance relates the magnitude of the applied constant
amplitude stress range (S) to the corresponding number
(N) of cycles to failure of the detail. A family of similar
2Transportation Research Record 00(0)
S-N curves for different detail categories were established
by extensive laboratory testing and is included in the
AASHTO LRFD Bridge Design Specifications (2) for
various categories of fatigue details that are commonly
used in bridge construction.
The design life for a category of details is defined by
the constant A, and the slope constant m which is taken
as 3 for steel members according to the following
NSrm=A ð1Þ
The constant A defines a line on the log(N) versus log(S)
plot that is at a constant value of fatigue damage. Values
of A for the AASHTO fatigue detail categories are giving
in Table of the AASHTO LRFD Bridge
Design Specifications (2). The mean life relationship can
be obtained by multiplying the constant A by a resis-
tance factor R
as given in Table of the MBE
(19). The mean life is the statistically most likely fatigue
life (19).
The S-N curves were developed using constant ampli-
tude stress range test data. However, bridges are sub-
jected to variable amplitude stress cycles. The Palmgren–
Miner (20) rule provides a rational means to account for
the cumulative damage from a spectrum of applied stress
ranges of variable amplitude. Using Miner’s rule, a well-
known equivalent constant amplitude stress range, com-
monly referred to as an effective stress range S
, can be
calculated as:
Seff =Xni
= number of cycles at the ith stress range, S
N = total number of cycles.
At a specific point along a bridge girder, the applied
range of bending moment can be determined by multi-
plying the applied stress range by the section modulus.
Multiplying each side of Equation 2 by the section mod-
ulus results in the effective moment range, M
Meff =Xni
= number of cycles at the ith moment range, M
N = total number of cycles.
Equation 3 was used to process the WIM data. Each
WIM record provides the axle spacing and weights for a
vehicle. These vehicles were analytically passed across a
simple span to calculate the bending moment range.
Each heavy vehicle (truck) in the WIM database was
used for a specified span length to obtain the bending
moment versus time at a specific location along the span.
Some trucks in the WIM database create more than one
cycle of loading as they cross a bridge. Rainflow cycle
counting (21) was used to determine the number and
magnitudes of the individual moment cycles resulting
from the truck crossing. M
was then determined for
the entire set of WIM records.
Two approaches are used in this paper to quantify the
fatigue damage accumulated in steel bridges. One
approach is a WIM site-specific damage measure, which
is useful to quantify the damage in a generic girder
bridge of a specified span length. The other approach is
a measure of the fatigue damage at a specific fatigue-
prone detail in a particular bridge. These two approaches
are described in the next sections.
WIM Site-Specific Damage Ratio. This approach is useful in
comparisons of the fatigue damage from truck traffic at
different WIM sites. Comparisons of routes represented
by those WIM sites are then possible. Also, the damage
caused by different types or classifications of trucks in
the traffic can be easily assessed by sorting the WIM
records based on the truck configuration.
To provide comparisons in this paper using the largest
amount of traffic data possible, all lanes of traffic in
both directions of travel are combined. Comparisons are
made between WIM sites where the number of traffic
lanes is the same. Each WIM record from the traffic
database is analyzed for 30, 60, 90, 120, and 200ft span
lengths. All results presented here are for a location 20%
of the span length from the upstream support. This is a
typical location for the end of a bottom flange cover
plate. The upstream cover plate end location rather than
the downstream end location was used because the dam-
age at the upstream cover plate end is higher. Results for
midspan and downstream cover plate end locations are
reported by Babu et al. (22).
Figure 1. Fatigue life relationship.
Iatsko et al 3
The amount of damage D
is calculated from the
effective bending moment determined from the WIM
data using Equation 3 by:
eff ð4Þ
It is important to note that the product of D
and the
section modulus raised to the power m is a constant that
defines a line of constant damage from the applied load-
ing as shown in Figure 1.
Damage at a Specific Fatigue-Prone Detail. Different details
in a steel bridge experience stress ranges of various num-
bers and magnitudes, and therefore, some details accu-
mulate fatigue damage faster than others. Based on the
study performed by Franklin (8), the base metal at the
end of a bottom flange cover plate is considered here as
the most fatigue-prone detail in Alabama’s steel girder
bridges. The bottom flange of the girder at the upstream
cover plate end is typically a Category E’ detail as defined
in the AASHTO LRFD Bridge Design Specifications (2).
For a specific fatigue-prone detail, an index of the
accumulated fatigue damage D
for a bridge along a
route where the WIM data are recorded can be calcu-
lated using
RR*A ð5Þ
is a Miner’s fraction determined by dividing the accu-
mulated fatigue damage caused by the trucks in the WIM
data (NS
) by the value of fatigue damage defining the
mean fatigue life (R
A). This fraction is also equal to the
fatigue life expended (N, total number of cycles) divided
by the mean fatigue life (R
). For example, a D
value of 0.5 indicates that 50% of the mean fatigue life is
expended by the traffic recorded in the WIM dataset.
The D
value is 1 when the mean life is expended.
The effective stress range, S
, for use in Equation 5 is
Seff =Meff*GDF* 1+IMðÞ*P*Rp
= effective moment range from WIM data by
Equation 3
GDF = girder distribution factor for a single loaded
IM = dynamic load allowance
P = ratio of measured to calculated stress range
S = section modulus for the specific fatigue detail
= multiple presence factor.
The effective moment range is calculated for the set of
WIM records for the traffic in one lane and in one direc-
tion. This is consistent with fatigue design by the
AASHTO LRFD Bridge Design Specifications (2). If
WIM data are available for more than one lane in one
direction, then all the records can be combined and the
fraction of trucks assumed to be in a single lane can be
based on Table of the AASHTO LRFD
Bridge Design Specifications. The girder distribution fac-
tor (GDF) and dynamic load allowance (IM) are calcu-
lated according to AASHTO LRFD Bridge Design
Specifications, Articles and 3.6.2, respectively. P
is used to account for the commonly observed difference
between the calculated and field-measured stress ranges.
P is the ratio of the actual stress range to the calculated
stress range. The ratio P is taken as 0.6 here and is based
on results reported by Pearson (7) in which field tests
were conducted on steel girder bridges representative of
those studied here. This ratio may be improved in the
future by more on-site field measurement studies. The
multiple presence factor, R
is calculated according to
MBE (19), Equation (
Values of D
described and reported in this paper are
for a period of 1 year. Values of D
(and D
) are addi-
tive. For example, if values of D
are calculated from
WIM data each month for convenience of data process-
ing, the D
value for the year is the sum of the values
calculated for each month. Similarly, the values of D
for multiple years can be added together.
Finite Life Check. An important question that must be
addressed in the discussion of fatigue damage accumula-
tion is: do all trucks, or traffic-induced stress cycles, con-
tribute to the accumulation of damage and potential
formation of a fatigue crack? Current U.S. practice is
that all stress cycles are considered to contribute to fati-
gue damage if there is a sufficient percentage of the
traffic-induced stress ranges above the constant ampli-
tude fatigue threshold (CAFT). When this is the case,
the finite life relationship between stress range and fati-
gue life is defined by Equation 1 as is assumed in the pro-
cedures described in this paper. Otherwise, the fatigue
detail has an infinite life, and the accumulation of fatigue
damage is inconsequential. In this paper, AASHTO
Category E’ details are the primary focus for which
Fisher et al. (23) show that only 1 in 2,000 stress cycles
must be above the CAFT to result in fatigue cracking.
Field measurements (7) have confirmed a significant
number of stress cycles above the CAFT in Alabama
bridges at E’ details. Thus, the procedures described in
this paper are judged as valid for the calculation of fati-
gue damage, and all vehicles in the WIM data can be
considered. However, it is also common practice in the
analysis of WIM data to omit light vehicles because of
the extremely large number of vehicle records typically
recorded, and the amount of time that is required to
include the light vehicles in the analysis. Filtering the
4Transportation Research Record 00(0)
lightest vehicles out of the WIM data is often justified by
the small contribution of light vehicles to the total dam-
age is small. In the work reported here, vehicles with
GVW less than 20kips were omitted from the analyses.
Research is ongoing to develop improved finite life check
procedures to be applied to the spectrum of bending
moment ranges obtained from the analysis of WIM data.
Traffic Database
To demonstrate the fatigue damage accumulation proce-
dures described in the previous sections, traffic data col-
lected in the state of Alabama are used. Traffic data consist
of a database of the WIM records and a database of single-
trip permits issued for OW vehicles. Using these databases
allows comparisons of fatigue damage caused by legal
loads, permit loads, and illegal loads. Additional discussion
of these traffic databases is provided in the next sections.
WIM Database
WIM data collected from eight locations around the state
of Alabama are used in this study. All WIM sites except
one were equipped with a permanent bending plate sys-
tem consisting of two scales and inductive loops (24).
The WIM data for the year 2014 are considered in this
paper. A summary of all available records for each WIM
site is provided in Table 1. The following information
was recorded for each vehicle in the WIM database: time
of record, the direction of travel, GVW, vehicle type,
axle spacing, axle loads, and vehicle speed. Two types of
errors can occur in long-term WIM data collection: ran-
dom errors (occurring once in a while), and systematic
errors (occurring frequently and affecting more records)
(25,26). The errors are usually associated with a mal-
functioning of the WIM system, misrecording, non-
typical vehicle configuration or lateral position with
regard to the sensor, and other causes (27,28). A site-
specific quality control (QC) algorithm was used to
improve the quality of the data set by eliminating errors.
A detailed description of the QC checks is provided by
Babu et al. (22). The number of records before QC and
after QC is shown in Table 1.
Permit Database
The Maintenance Bureau of the Alabama DOT
(ALDOT) issues about 500–600 permits per day. About
200 of them are permits for OW vehicles. The permit
data for the year 2014 are considered in this paper. The
annual reports are in the form of tables, and they include
the permit ID, the validity of the permit, original and
final destination, authorized roads, description and
FHWA class of vehicle, GVW, axle load, and axle spac-
ing. Annual permits are issued, but each trip accom-
plished within the annual permit is also listed as a
separate row in the database. The total number of issued
permits was 123,603 for the year 2014.
To identify permitted trucks in the WIM database, the
first step was the separation of legal traffic based on the
truck weight regulations for the state of Alabama (29).
The remaining database included only permit vehicles
and illegal traffic, that is, overloaded trucks. Next, the
database of permits issued by ALDOT for OW vehicles
was processed together with the WIM database of over-
loaded trucks using the developed routines and Google
Maps API. WIM vehicles without permits were sorted
out, and the remaining vehicles were considered to be ille-
gal traffic. A comparison of the permits identified in the
traffic stream with the vehicles that required permits indi-
cates that less than 0.5% of OW vehicles operate with an
OW permit. More detailed discussion of this procedure is
provided by Babu et al. (19)
Table 1. Number of Records in the Weigh-in-Motion Database for the Year 2014
WIM site code County
Number of WIM
records before QC
Number of WIM
records after QC
911 (US280) US280 Sosa Co. 1,092,751 357,854
931 (I65) I65 Limestone Co. 3,655,980 1,584,347
933 (AL157) AL157 US72 Colbert Co. 977,580 427,505
934 (US78) US78 Walker Co. 688,388 169,407
942 (US231) US231 Montgomery Co. 1,262,375 787,426
960 (US84) US84 Clark Co. 521,484 305,566
961 (I65) I65 Mobile Co. 2,136,008 851,213
964 (US231) US231 Dothan Co. 1,217,687 642,337
Total 11,552,253 5,125,655
Note: WIM = weigh-in-motion; QC = quality control.
Iatsko et al 5
Comparison of WIM Site-Specific Damage
The amount of damage (D
) was calculated
for each WIM site (911–964) for both traffic directions
combined and for the year 2014 for the upstream cover
plate end. All the WIM sites had two lanes of traffic in
each direction (Lane 1 & 2 and Lane 3 & 4). The accu-
mulated damage for each WIM location is calculated for
30, 60, 90, 120, and 200 ft span lengths for the upstream
cover plate end at 0.2 L, where L is the span length. To
cover steel girder bridges without cover plate end, similar
study was performed considering steel girder bottom
flange at midspan (C type detail) as the most fatigue crit-
ical (19).
The results for the upstream cover plate end are shown
in Figure 2. The accumulated damage at WIM site 931
was greater than the accumulated damage at all the other
WIM sites. WIM site 931 was followed by WIM site 961
and 942. The accumulated damage increases rapidly as
the span length increases for all the WIM sites. Because
of this rapid increase with span length, the results for the
200 ft span are not shown in Figure 2 so that the results
for the shorter spans are more visible in the plot. Results
for the 200 ft span are presented separately in Figure 3.
Further, the truck traffic data were sorted into legal
loads, permit loads, and illegal load categories. One of
the objectives for sorting the traffic data was to assess
how the damage compared for these types of vehicles.
The corresponding accumulated damage (NM
) was
computed for each vehicle category.
Legal loads include vehicles that comply with
Alabama’s legal regulations (29), ‘‘grandfather excep-
tions,’’ and annual permits that have a GVW less than
100 kips. The OW vehicle category covers vehicles that
require an individual trip permit to travel legally because
of their weight or axle load combination and annual per-
mits that have a GVW greater 100 kips. Further, the
OW vehicle category was sorted into permit loads and
illegal loads. The identification of legal loads, permitted,
and illegally overloaded vehicles adopted in this paper is
discussed in detail by Babu et al. (22).
Results shown by Babu et al. (22) illustrate that the
relative contributions of different categories of vehicles
are similar for all these span lengths. The accumulated
damage at the upstream cover plate end in the 200 ft
span for the corresponding vehicle categories is shown in
Figure 3a. The corresponding number of vehicles is
shown in Figure 3bfor the year 2014. The accumulated
damage from illegal loads at WIM sites 931, 961, and
960 was about 50% of the total damage for those WIM
Comparing the pie charts shown in Figure 4, the pro-
portion of the vehicles in each category is significantly
different from the proportion of the damage caused by
those vehicles. For example, legal vehicles make up 79%
of the total truck traffic, but they create only 50% of the
total damage. At the same time, OW trucks (legally and
illegally) are responsible for another half of the damage
from the total truck traffic stream.
In Figure 4, the traffic from all WIM sites is combined
for the year 2014, and it can be concluded that the 17%
of trucks that are illegally overloaded (Figure 4a) create
more than 40% of the total damage (Figure 4b).
These results are state specific and can vary from state to
Figure 2. Accumulated damage, D
at the upstream cover plate end.
6Transportation Research Record 00(0)
Damage at a Specific Fatigue-Prone Detail
Studies conducted by Pearson (7) and Franklin (8)
included evaluation and instrumentation of representa-
tive spans from among 58 simple-span rolled-beam
bridges, 18 continuous-span rolled-beam bridges and six
plate-girder simple-span bridges in downtown
Birmingham. Stress ranges were calculated at the follow-
ing fatigue-prone details on the bridges: transverse dia-
phragm connections, longitudinal cover plate fillet weld
connections, shear connectors, and cover plate ends at
the upstream and downstream locations. The study con-
cluded that the base metal at the ends of the cover plates
was the most critical fatigue detail of those bridges. The
bottom flange of the girder at the cover plate end is a
Category E’ detail as defined in the AASHTO LRFD
Bridge Design Specifications (2).
To demonstrate the procedures developed in this
paper, the damage accumulated at this specific fatigue-
prone detail, E’, for the Span 86-W as described by
Franklin (8) was selected. This bridge was selected
because it is a real bridge, typical of steel girder bridges
on highways in Alabama. Also, as an example, WIM
data from site 931 were used. This is real traffic, and a
real bridge, although this traffic does not cross this par-
ticular bridge. Damage accumulated at the upstream
Figure 3. (a) Accumulated damage, D
at the upstream cover plate end for the 200 ft span and (b) numbers of vehicles.
Iatsko et al 7
cover plate end from the passage of traffic in one of the
directions (lane 1 and 2) at WIM site 931 for the year
2014 was calculated.
Span 86-W consists of eight W36 3150 rolled section
girders spaced at 8.71 ft. On average, the total length of
the beams is 66.30 ft, and the approximate average span
length is 60 ft. The cover plate size is 10" 30–15/
16" 341"–6". Based on this information, the bridge
data inputs to estimate the damage accumulation were
calculated and listed in Table 2.
Using Equations 5 and 6, and the bridge data inputs
from Table 2, the fraction of mean fatigue life expended,
, at the upstream cover plate end is 0.01. Thus, this
1 year of traffic expends 1% of the mean fatigue life of
this fatigue-prone detail. If this annual traffic was applied
to the bridge in each year of its life, then its mean life
would be (1/D
) or 100 years. For comparison, the frac-
tion of fatigue life expended, D
, determined according
to AASHTO MBE is equal to 0.008. Therefore, the cor-
responding mean fatigue life is 120 years. For this specific
case, the traffic represented by the WIM data produces
more damage than is accounted for by the procedure in
the MBE. This will not always be true.
A procedure to quantify the fatigue damage accumulated
in steel bridges using WIM data was demonstrated using
combined WIM data collected in 2014. The procedure
can be used to assess WIM site-specific damage or
bridge-specific damage. The procedure can be used for
WIM traffic data from any state. In this paper, the
Figure 4. (a) The total number of vehicles and (b) the accumulated damage, D
for all WIM sites combined at the upstream cover plate
end for the 200 ft span.
Table 2. Bridge Data Inputs for Span 86-W Bridge on Interstate
I-59/20 in Birmingham, Alabama
Section modulus (S) 702 in.
Span length (L) 60 ft
Girder distribution factor (GDF) 0.51
Dynamic load allowance (IM) 0.15
Location of upstream cover
plate end
11.0 ft
x/L of upstream cover plate end 0.2
Location of downstream cover
plate end
53.6 ft
x/L of downstream cover plate
Number of traffic lanes 4
Direction of traffic One direction only
Fraction of truck traffic (p) 0.85
Resistance factor for mean
fatigue life for E’ detail (R
Ratio of measured to calculated
stress range (P)
Average daily truck traffic
Number of lanes (n
Bridge location Birmingham, AL
8Transportation Research Record 00(0)
procedure is demonstrated using WIM data from the
state of Alabama. The following conclusions can be
1. Comparisons of accumulated fatigue damage are
more direct comparisons of the effects of heavy
vehicles on steel bridges than simple comparisons
of GVWs and numbers of vehicles.
2. WIM site-specific damage gives a way to compare
the effects of the traffic streams along different
3. The use of WIM data for calculation of accumu-
lated fatigue damage at specific fatigue-prone
details avoids the use of a standard fatigue truck.
This approach is best suited for bridges near the
WIM site.
4. By using the procedure presented here, the dam-
age (D
) calculated at a specific fatigue-prone
detail in a particular bridge is equal to the per-
centage of the mean life expended.
5. Analysis of accumulated damage caused by legal
loads, permit loads, and illegal loads allows com-
parisons of the relative damage from different
vehicle categories. This approach can also be
applied to compare the effects of the vehicles bro-
ken down by other classification schemes such as
the total number of axles.
6. From the analysis of WIM data from the state of
Alabama, 17% of vehicles that are illegally over-
weight create more than 40% of the total fatigue
The Alabama Department of Transportation provided funding
for the research presented here and that support is gratefully
acknowledged. The authors thank the ALDOT technical staff
for their advice, discussion, and constructive comments. Special
thanks are due to Randy Braden and Kevin Perdue for provid-
ing access to the WIM and permit databases.
Author Contributions
The authors confirm contribution to the paper as follows: study
conception: J.M. Stallings, A.S. Nowak; data processing: O.
Iatsko, A. Ramesh Babu; analysis and interpretation of results:
J.M. Stallings, A. Ramesh Babu, O. Iatsko, A.S. Nowak; draft
manuscript preparation: O. Iatsko, J.M. Stallings, A. Ramesh
Babu. All authors reviewed the paper and approved the final
version of the manuscript.
Data Availability Statement
The traffic data that support the findings presented in this paper
are available from the corresponding author on reasonable
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with
respect to the research, authorship, and/or publication of this
The author(s) disclosed receipt of the following financial sup-
port for the research, authorship, and/or publication of this
article: The research shown in this article has been funded by
Alabama Department of Transportation.
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10 Transportation Research Record 00(0)
... To conduct the research, firstly, the traffic data sources at 35 highway locations involving 15 provinces in China were collected through weigh-in-motion (WIM) systems or existing research, and the fatigue load spectrum of the corresponding locations were derived or obtained; Secondly, based on the linear cumulative damage theory [22][23][24], the fatigue damage of the typical representative vehicles for the 35 locations and the standard vehicle was calculated. After obtaining the equivalent coefficients, i.e., the ratio of fatigue damage between typical the representative vehicles and the standard fatigue vehicle, the mathematical relationship with the gross vehicle weight is given based on the statistical analysis. ...
... The fatigue damage equivalence criterion is the theoretical basis for the study of the bridge fatigue load model. In the following discussion, the derivation of fatigue load spectrum, the calculation of vehicle fatigue damage, and the definition of equivalent coefficient and equivalent heavy vehicle flow follow the unified fatigue damage theory [22][23][24][25][26]. The definition of fatigue damage is not unique [27], so it is necessary to explain it here. ...
... Finally, the equivalent fatigue damage (EFD) of the standard vehicle can be calculated according to the basic theory (Formula (3)) of the linear cumulative fatigue damage [22] ...
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Reasonable fatigue load should be determined before bridge fatigue analysis. However, the design frequency calculation method of the standard vehicle does not always make sense when the standard vehicle load model that is provided by existing standards is adopted, as the weights (equivalent coefficients) variation of different vehicle types are not considered from the perspective of damage equivalence. The method through direct damage calculation is workable but the process is usually laborious and time-consuming. To solve this problem, the traffic data of 35 highway sites involving 15 provinces in China were collected and the fatigue load spectrum were derived. The equivalent coefficients of each vehicle type at all of the 35 locations were calculated directly and the relationship with the corresponding gross vehicle weight was obtained formulaically through statistical analysis. Therefore, the design frequency of the standard vehicle can be calculated by the product of the actual frequency for a certain type of vehicle and the corresponding equivalent coefficient. The effectiveness of the proposed method was verified from the perspective of damage equivalence compared with the existing-standard method, and its flexibility and applicability for complex traffic conditions such as China were also demonstrated. In addition, three grades for the design frequency were put forward as references in relevant project design.
... This study considers bridges with spans -defined as the distance between (intermediate) supports -ranging between 1 m and 100 m and influence line lengths ranging between 1 m and 300 m and the measurements were performed on bridges with the same range of influence line length. Iatsko et al. [67] demonstrate that relatively few, relatively heavy -overloaded -trucks provide the largest contribution to the fatigue damage in actual traffic. The axle and vehicle weights in the current measurements were therefore selected as the upper values according to legislation: 100 kN axle load for short influence lines, 1200 kN vehicle load for the longest influence lines (representing a condition with multiple vehicles present on the influence line) and 500 kN vehicle load for influence lines in between. ...
Full-text available
This paper presents a probabilistic framework to derive the safety factors for fatigue of steel and composite steel concrete road bridges. Engineering models are used for the design and the safety factor is derived in such a way that the design meets the target reliability set by international Eurocode and ISO standards, estimated using measured data and advanced probabilistic models. Engineering model uncertainties and dynamic amplification factors are established through comparison of measurements and models. The value of visual inspections is quantified based on observations from practice and expert opinions. The safety factors are derived for Eurocode’s Fatigue Load Model 4 and Eurocode’s tri-linear S-N curve. The study shows that the safety factors for fatigue as currently recommended by the Eurocodes need to be raised.
... These systems are used to detect and classify vehicles without interrupting the traffic flow, but require spatio-temporal readings in order to be capable of classifying vehicles appropriately [37]. The popularity of WIM systems is growing exponentially, because they have been shown to yield improved maintenance schedules, let alone their use for traffic law enforcement [38,39]. In addition, the availability of data on traffic-structure interaction can be significant for SHM strategies [40]. ...
Full-text available
The integration of weigh-in-motion (WIM) sensors within highways or bridge structural health monitoring systems is becoming increasingly popular to ensure structural integrity and users safety. Compared to standard technologies, smart self-sensing materials and systems present a simpler sensing setup, a longer service life, and increased durability against environmental effects. Field deployment of such technologies requires characterization and design optimization for realistic scales. This paper presents a field investigation of the vehicle load-sensing capabilities of a newly developed low-cost, eco-friendly and high durability smart composite paving material. The novel contributions of the work include the design and installation of a full-scale sensing pavement section and of the sensing hardware and software using tailored low-cost electronics and a learning algorithm for vehicle load estimation. The outcomes of the research demonstrate the effectiveness of the proposed system for traffic monitoring of infrastructures and WIM sensing by estimating the gross weight of passing trucks within a 20% error during an autonomous sensing period of two months.
... Miao and Chan [13] have established bridge live load models for highway bridges based on 10 years of WIM data. Iatsko et al. [14] have determined the fatigue damage condition of a typical steel bridge utilizing the WIM data collected in Alabama. Han et al. [6] conducted a series of safety assessments for typical small and mid-span bridges in China based on on-site WIM data. ...
Nowadays, the overload issue is becoming more prevalent which inevitably accelerates the degradation of bridges. Restriction on vehicle weight is a practical option to solve this issue. Under the circumstances, a reliability-based method is proposed in this paper to determine the vehicle weight limit of urban bridges. Firstly, the framework of the methodology is presented and a stochastic urban traffic model is established through the site-specific weigh-in-motion data. Then refined vehicle-bridge coupling simulation is incorporated in the framework of the method. Subsequently, reliability analysis is performed based on the probabilistic density evolution method, and uncertainties in both the load and the structural resistance are taken into account. Finally, the vehicle weight limits for 75 urban bridges in Nanjing, China were investigated as a case study. The results showed that the proposed method can obtain more reasonable vehicle weight limits, hich would effectively increase the reliability of urban bridges and provide references for policymakers.
Full-text available
This study analysed the processes of damage formation and development in early age unloaded concrete using the acoustic emission method (IADP). These are of great importance in the context of the durability and reliability of a structure, as they contribute to reducing its failure-free operation time. Concrete made with basalt aggregate and Portland or metallurgical cement cured under different conditions after demoulding was the test material. The obtained damage values were compared with the measured concrete shrinkage, and a shrinkage strain–acoustic emission signal (resulting from damage) correlation was found. The correlation allows easy measurement of damage level in the early period of concrete hardening, and consequently can be the basis of a non-destructive method.
Full-text available
The US and European bridge design codes were developed based on a limited amount of traffic data. The design live load for AASHTO LRFD code used in the US is based on traffic data collected by Ontario Ministry of Transportation in 1970s. Eurocode was initially developed using traffic data collected within few weeks in Auxerre, France in the 1980s. An extensive Weigh-in-Motion (WIM) data can serve as a basis to verify the design live load model. The objective of this paper is to analyze and compare statistical parameters of a live load in the US and Europe using available WIM data. WIM measurements from 44 locations in 20 states around the US from 2005 till 2014, containing 118 million records are used. Also, WIM measurements from European countries (Poland, Netherlands, Czech Republic, Slovenia and Slovakia) of about 2 million vehicles are used. The statistical parameters of US are similar to Europe, and US traffic data can be used to recalibrate European bridge design code if required. Also, site-specific live load model in the US can be developed using the statistical parameters developed in this study and also can serve as basis to update national live load model in the US.
The objective is to present an approach for the evaluation of fatigue performance. The proposed method is a combination analytical and experimental approach. The steps include identification of critical components and details, determination of the load distribution factors and stress range, instrumentation of the bridge, measurement of strains under a control vehicle to calibrate the equipment and determine the load distribution factors, measurement of strain under normal traffic, verification of load distribution factors, verification of load range, and evaluation of fatigue performance. Critical components and details are identified on the basis of analysis and past experience. The analysis provides theoretical values of load distribution factors and stress ranges. Measurement results provide a basis for verification of the analytical values. The number of load cycles is determined from the stress record under normal traffic. For a given number of load cycles, the effective stress range is calculated and compared with the critical level. Then the remaining fatigue life is estimated as a percent of the remaining number of cycles to failure. This service of the evaluation of fatigue performance. The proposed approach is applied to an existing steel girder bridge. The superstructure consists of four plate girders and transverse floor beams. The bridge is instrumented, and the results of measurements are presented and discussed. For the considered components and details, the measured stress range and estimated number of load cycles are not critical. Some minor cracking may be expected, but in general the bridge may be considered as adequate with regard to fatigue.
Estimates of the stress intensity factor, K, are basic to the use of linear-elastic fracture mechanics in applications. Sections 1. 2 to 1. 6 have presented those K analysis techniques that have been most helpful for cracks in steel bridges. Similar analysis techniques are followed for fatigue cracking and the more rapid fracture extension. Section 1. 5 provided a brief review of the crack extension behaviors observed in bridge steels. All of these analysis and testing methods are given specific illustration in the following chapters. Refs.
As traffic volumes increase, bridges age, and maintenance budgets are cut, transportation officials often need quantitative data to distinguish between bridges that can be kept safely in service and those that need to be replaced or retrofitted. Strain gages can be utilized to evaluate fatigue damage in steel bridges using the techniques that are discussed in this paper. To evaluate fatigue damage, the cycles induced by vehicular traffic must be quantified using a cycle-counting algorithm, such as a rainflow algorithm. The amount of fatigue damage induced during the monitoring period can then be calculated using the traditional method, the effective stress range, or using a new approach based on the index stress range. One distinct advantage of the proposed method is that the relative amount of fatigue damage accumulated at different locations along the bridge can be easily compared. The advantages and limitations of both methods are demonstrated using measured data from a fracture-critical steel bridge. © 2015, American Institute of Steel Construction Inc. All rights reserved.
A fatigue-live-load model is developed for steel girder bridges. The database for the model is obtained by weigh-in-motion (WIM) measurements. Five bridge structures were selected for testing to determine the site-specific truck parameters' and component-specific stress spectrum. The database includes 22,000 truck files, each consisting of gross vehicle weight (GVW), axle weights, and axle spacing. Stress cycles were measured at the midspan of all bridge girders and results are presented as cumulative distribution functions. The WIM measurements confirm that truck bads are strongly site-specific. The results also indicate a significant variation in stress spectrum between girders. A three-axle truck is proposed to represent the truck traffic. For sites with 10- and 11-axle trucks, an additional four-axle truck is proposed. The developed fatigue live load model is verified using fatigue-damage analysis to compare the model with measured results.
Thesis (M.S.)--Auburn University, 2002. Abstract. Vita. Includes bibliographical references (leaves 197-198).
Fatigue Evaluation of Steel Bridges
  • M D Bowman
  • G Fu
  • Y E Zhou
  • R J Connor
  • A A Godbole
Bowman, M. D., G. Fu, Y. E. Zhou, R. J. Connor, and A. A. Godbole. NCHRP Report 721: Fatigue Evaluation of Steel Bridges. Transportation Research Board, Washington, D.C., 2012.
A Fatigue Primer for Structural Engineers. National Steel Bridge Alliance
  • J W Fisher
  • G L Kulak
  • S Smith
Fisher, J. W., G. L. Kulak, and S. Smith. A Fatigue Primer for Structural Engineers. National Steel Bridge Alliance, American Institute of Steel Construction, 1998.
Fatigue Load Spectra for Steel Girder Bridges
  • J A Laman
  • A S Nowak
Laman, J. A., and A. S. Nowak. Fatigue Load Spectra for Steel Girder Bridges. Department of Civil and Environmental Engineering, University of Michigan, 1992.