Transactions on the Built Environment vol 32, © 1998 WIT Press, www.witpress.com, ISSN 1743-3509
Dynamic load factor in composite highway
bridges
C.C. Spyrakos
Department of Civil Engineering, Laboratory for Earthquake
Engineering, National Technical University ofAthens,
Zografos 15700, Athens, Greece
Abstract
In most design codes the amplification of load and deformation level caused by
traffic on bridges is considered with the dynamic load factor (DLF). The purpose
of this study is to investigate the validity of current AASHTO code practices in
accounting for vehicle-bridge interaction, since there are numerous experimental
and analytical studies in the literature that either contradict or support AASHTO
practices.
In this study, the DLF is evaluated both experimentally and analytically
for a commonly used bridge system. Bridges were instrumented and
measurements were taken for test vehicle (prototype truck provided by the West
Virginia Department of Transportation). The dynamic strains and accelerations
recorded were compared with the ones recommended by the AASHTO code. In
addition, extensive studies were performed with analytical models of increasing
degree of complexity and detailed simulation of interacting bridge-vehicle
systems.
Some of the conclusions include: I) DLF greatly depends on the
traveling path of the vehicle and that AASHTO code recommendations are not
conservative for all paths of the vehicle. II) Pit of pot holes located at the
approach cause more severe impact effects than when they are located near the
middle of the bridge deck. Ill) The magnitude of DLF is less on concrete deck
than that developed on steel stringers. IV) High modes of vibration can
significantly affect the bridge response for load design levels. V) Maximum
strains and displacements due to impact are greater in bridges with seat
abutments than in bridges with integral abutments.
Transactions on the Built Environment vol 32, © 1998 WIT Press, www.witpress.com, ISSN 1743-3509
212
Structures Under Shock and Impact
1. Introduction
The dynamic load allowance or DLF specified in AASHTO [1] is given by
an empirical formula with span length as the sole variable. The DLF
increases as the span length decreases obtaining a maximum limit of 0.03.
Primary parameters that affect the magnitude of DLF include: bridge span
length, number of spans, vehicle to superstructure weight ratio, number of
vehicles on bridge, number of vehicle axles, vehicle suspension system,
vehicle speed, natural frequency ratio (vehicle to superstructure), initial
oscillation of vehicle at approach, size and variation of bridge deck
irregularities (roughness) and vehicle braking force. The United Kingdom
specifies a constant impact limit of 0.60 and the Japanese code uses an
upper limit of 0.35 to 0.40 depending on the type of construction (Thomas
[2]). A survey of dynamic allowance for highway bridge design loading
revealed significant divergence for spans of 164 feet (12.5 m) and longer
depending on the jurisdiction.
The AASHTO specification is generally less conservative
compared to the Ontario Highway Bridge Design Code (OHBDC)
regarding the dynamic allowance for traffic loading. The AASHTO
specification does not incorporate the flexural fundamental frequency of
the structure into the dynamic design process. The OHBDC suggests
avoiding bridge designs with fundamental frequencies in the range of 2 to 5
Hz, because of high dynamic response when bridge and vehicle frequencies
match. If this frequency range cannot be avoided, the OHBDC established
0.45 as the maximum dynamic load allowance (OHBDC [3]).
It should be noted that there is extensive literature that either
supports or contradicts the DLF variation as specified by AASHTO. A
representative study that supports the AASHTO specifications is the work
by Schilling [4]. Schilling has presented extensive data on average impact
factors for highway steel bridges determined from stress traces and
deflection measurements. He obtained 40 values for the impact factor
ranging from 0.03 to 0.31 through stress traces and 41 values from the
deflection measurement ranging from 0 to 0.52 and concluded that the
deflection test gave higher impact factors than the stress traces. The values
of impact factors that he obtained for cantilever or suspended girder
bridges ranged from 0.45 to 0.52. Among the studies that contradict
AASHTO, one should mention the research performed by Csagoly,
Campbell and Agarawel [5] who carried out investigations for the Ontario
Ministry of Transportation and Communication (MTC) to determine the
dynamic response on a number of continuous bridges. In this study, field
vibration tests were performed using MTC test vehicles to measure bridge
deflection and natural frequencies. The investigation showed that only one
out of eleven bridges tested exhibited an impact value smaller than
AASHTO's maximum value.
Transactions on the Built Environment vol 32, © 1998 WIT Press, www.witpress.com, ISSN 1743-3509
Structures Under Shock and Impact
213
2. Description of Conducted Research
Prior to describing the experimental part of the research, a few
issues on DLF should be clarified. The DLF can vary considerably
depending upon its definition. There are currently several definitions of the
DLF reported in the literature. Bakht has identified eight different
definitions for DLF (Bakht and Pinjarkar [6]). Both deflection and strain
responses can be used to evaluate DLF. However, it has been clearly
demonstrated by the AASHTO test [7] that, under similar conditions, the
DLF computed from deflections are always greater than the corresponding
factors measured from strains.
Different ways of calculating DLF can be explained with the help
of Figure 1, which shows typical dynamic, static and median strain
responses at the mid-span of a girder with respect to time. The dynamic
strains correspond to a vehicle travelling with normal speed and the static
strains correspond to a vehicle travelling at crawling speed. The median
strains are obtained by averaging consecutive peaks of dynamic strains.
Among Bakht's eight definitions two of them, the ones used in this study,
are discussed herein.
/ =
*J dyn ~ w j
(1)
O stat
where Sdyn = Maximum dynamic strain and Sstat - Maximum strain for a
vehicle travelling at crawling speed.
U
(J
\
Reference point
Dynamic strain
Static strainMedian strai
Max. median strain - S „
Max. static strain » S,,,,
Max. dynamic strain - S
Figure 1. Mid-span strain caused by moving vehicle load
Transactions on the Built Environment vol 32, © 1998 WIT Press, www.witpress.com, ISSN 1743-3509
214
Structures Under Shock and Impact
._.
Om
where Sm = Maximum median strain.
In both definitions DLF is expressed in terms of strains. In a
similar manner, DLF can be expressed in terms of deflections. Definition
(1) is used with static and dynamic strains obtained with strain sensors;
while definition (2) is employed in conjunction with dynamic deflections
instead of dynamic strains recorded with acceleration sensors. In this study,
definition (2) is used as follows:
j
Odyn ~ Om
,*•.
5m
where 8^ = Maximum dynamic deflection and 8m = Maximum median
deflection.
Two different bridge systems were tested: a) concrete deck-steel
stringer and b) prestressed superstructure. Three aspects were critically
considered for selecting the bridges: a) type of system, b) type of span, and
c) span length. The bridge with a concrete deck-steel stringer system on
seat abutments was selected as being one of the most common bridge
systems. The prestressed bridge with integral abutments was selected, since
this system is becoming increasingly popular. The span length of the
bridges is in the range of 100' (30 m) and are all part of the West Virginia
Highway System. A brief description of the selected bridges is given in the
following:
West Fork River Bridge: Figure 2 shows the cross-section of the bridge
along the transverse direction. The span length of the bridge is 100' (30 m)
with a concrete deck-steel stringer superstructure on seat abutments.
. Concrete Barrier Wai
32'-4"
26'. 10"
—1
1
14'. 5"
14'- 5"
I
"I /-i
y
^
/ \
/
\
(
/ \
3 5"
/ B'-B'
8'. 6"
B'-B"
3'- 5"
SECTION
Figure 2. Transverse Section of West Fork River Bridge
Transactions on the Built Environment vol 32, © 1998 WIT Press, www.witpress.com, ISSN 1743-3509
Structures Under Shock and Impact
215
The deck has a 15 degree skew angle on both sides and the stringers are
composite with the concrete deck. The width of the roadway is 30' (9 m)
including shoulders. The superstructure is supported on concrete abutments
which rests on concrete strip footings.
East Logansport Bridge: The bridge was selected because of its special
type of structural system. It is a single span bridge with a span length of
100' (30 m). The cross-section of the bridge in the transverse and
longitudinal directions are shown in Figure 3. The cross-section shows
four steel tubes and high tension prestressing steel bars in between the steel
tubes. The system is referred as prestressed bridge with integral abutments.
As its name implies, the abutments are compressed along with the
superstructure by prestressing bars and the steel tubes are compressed
along with the abutment. The prestressing bars which are supported by
cross-supports as shown in Figure 3, follow a curved path in order to
increase the effectiveness of prestressing. The concrete abutments are
supported on spread footings. A mechanical hinge is provided at the joint
between the abutment and the footing in order to allow rotation of the
abutment when prestressing is applied. Precast deck slabs are placed on the
steel tubes and connected to the tubes by shear connectors.
1/2" Thick Stee* lute
** Steel connecting flange
Presstressing bars
SECTION
Precast concrete deck
Figure 3. Transverse Section of East Logansport Bridge
In this study, a test vehicle was run on the bridges and the response
of the bridges was recorded over a period of time at specific locations using
strain and acceleration sensors. Accelerometers were selected by
considering the following parameters: a) frequency range of vibration, b)
acceleration range, c) mass of accelerometer, d) natural frequency of
accelerometer, e) output magnitude of accelerometer, and f) type of base
for fixing the accelerometer.
Transactions on the Built Environment vol 32, © 1998 WIT Press, www.witpress.com, ISSN 1743-3509
216
Structures Under Shock and Impact
The West Fork River bridge was tested by using both strain and
acceleration sensors. However, the East Logansport Bridge was tested
only with strain sensors. The DLF was established for different travelling
paths of the test vehicle. The DLF was evaluated when the test vehicle
traveled on either the stringer line or the center line in order to identify the
variation of DLF depending on the travelling path of vehicles.
Tests were also conducted with a hump placed at the approach of
the bridge and at mid-span. The hump was used to simulate surface
irregularities of the riding surface. Tests were performed for different
speeds of the test vehicle such as 5 mph (8 kph, mph = mile per hour, kph =
kilometer per hour), 15 mph (24 kph), 30 mph (48 kph), and 45 mph (72
kph). The 5 mph (8 kph) corresponds to crawling speed for which the
vehicle could produce static response rather than dynamic response to the
bridge. Tests were performed for several combinations of the parameters
such as vehicle speed, travelling path and hump locations. Test data was
collected over a period of time between the time the test vehicle entered the
bridge and it exited the bridge.
The DLF was evaluated for different speed and test condition. For
each DLF value, test conditions were maintained similar for both crawling
and regular speed. Table 2 shows DLF values obtained for the West Fork
River bridge at 15 mph (24 kph), 30 mph (48 kph) and 45 mph (72 kph)
using strain sensors. In Table 2 the maximum, minimum and mean values
of DLF' are presented for different speed and test conditions. Table 3
shows DLF values obtained for the East Logansport bridge at 25 mph (48
kph). According to AASHTO, the DLF values for the West Fork River
bridge and the East Logansport bridge are as follows:
/=
125 + L
125 + 100
Statistical analysis was performed on the DLF values obtained for
the West Fork River in order to establish the mean and standard deviation
of those values (Latheef, e.t, [8]). According to Table 1 the mean value of
the DLF when the test vehicle travels on the stringer with 45 mph (72 kph)
and no hump is 0.14. This value is much less than the AASHTO prescribed
value 0.22. This implies that when the vehicle wheels travel on the stringer
without any pits or pots on the riding surface the DLF value could be less
than the AASHTO prescribed value. However, according to Table 1 when
the test vehicle travels on the concrete deck (center line) without placing
the hump the mean DLF value is 0.35, which is more than the AASHTO
prescribed value. The results in Table 1 show that whenever the test
Transactions on the Built Environment vol 32, © 1998 WIT Press, www.witpress.com, ISSN 1743-3509
Structures Under Shock and Impact
217
vehicle travels on the concrete deck the DLF value is greater than both the
values corresponding to travelling on the stringer as well as the ones
specified by AASHTO. In addition, when the hump is placed at the
approach of the bridge, it creates larger dynamic amplification compared to
the amplification observed when the hump is placed at mid-span.
Table 1 DLF Values for the West Fork River Bridge
Mean
Max.
Hump No. of Min.
Speed & Vehicle
Value
Value
travel
option Values Value
Gage
Location path
No
15 Stringer
0.05
0.02
hump
6
0.08
line
mile/hr
Stringer
Stringer
No
30
0.04
0.03
0.02
4
hump
mile/hr
line
Stringer
Stringer
No
45
0.14
34
0.21
hump
0.06
mile/hr
line
Stringer
No
Center
45
0.24
0.46
035
8
hump
mile/hr
line
Stringer
Hump
Stringer
45
0.67
0.53
at the
0.30
16
mile/hr
line
end
Stringer
Hump
Center
45
0.79
0.46
0.28
at the
8
mile/hr
line
end
Stringer
Hump
Stringer
45
0.24
12
0.13
at the
0.18
mile/hr
line
middle
Stringer
Center
Hump
45
034
0.38
036
6
at the
mile/hr
line
middle
Stringer
Hump
Stringer
45
0.62
0.17
035
6
at the
line
mile/hr
middle
Concrete
Stand.
Deviat.
*
*
0.047
0.066
0.102
0.165
0.034
*
*
(*) The standard deviation was not established because of insufficient
number of records
Transactions on the Built Environment vol 32, © 1998 WIT Press, www.witpress.com, ISSN 1743-3509
218
Structures Under Shock and Impact
The DLF value for the concrete deck component for 45 mph (72
kph) varies from 0.17 to 0.62 with a mean value of 0.35. The West Fork
River bridge was tested for maximum speed of 45 mph (72 kph). However,
many states allow a speed limit of 65 mph (104 kph). For 65 mph (104
kph) speed the DLF values could be much higher than what we have
obtained in this study. A series of tests were also conducted for the test
vehicle traveling over the bridge off-center. The most important
observations are briefly discussed in the conclusions.
Table 2 presents the DLF values for the East Logansport bridge.
As mentioned earlier, the bridge was tested only for maximum speed of 25
mph (40 kph) because of inadequate straight approach. The DLF values
determined for this bridge are high even at 25 mph (40 kph) speed level.
The DLF values range from 0.32 to 0.48 for 25 mph (40 kph) which are
much higher than the AASHTO value of 0.22. It is expected that if the
speed level is 55 mph (88 kph) or 65 mph (104 kph) the dynamic effects
would be even higher.
Even though, both bridges have approximately the same first
natural frequency (2.93 Hz and 2.91 Hz) and the same span length, the
DLF value of the prestressed bridge (East Logansport bridge) is much
higher than the concrete deck-steel stringer bridge (West Fork River
bridge). This clearly indicates that bridges with prestressed systems may
experience large dynamic amplification which is not considered in
AASHTO specifications.
Three different vehicle models were selected to examine the
dynamic response of the superstructure. The different models were selected
to provide an increased understanding of the changes in vehicle dynamic
characteristics. In all models we assume that the vehicle does not lose
contact with the structure as it traverses the span.
The first vehicle is a roling mass traversing a simply supported
beam. The mathematical model is based on the assumption that the mass is
moving with a constant velocity. The second vehicle model is a single-axle
one-degree-of-freedom model. Springs have been added to the model to
simulate suspension forces. The third vehicle model is a two-axle four
degree-of-freedom system. In the third model the mass for the suspension
system has been lumped over the tire springs for each axle and a pitcing
force from the main body mass has been included in this model (Coffinan
[9]).
Modeling simulates a vehicle traveling on a smooth surface; i.e.,
the initial conditions for the vehicle model upon entrance to the bridge are
set equal to zero.
The DLF calculated with the models are much lower than the
experimental values (25% difference), but the fundamental frequencies
closely compare to the experimental values (up to 5% difference).
Transactions on the Built Environment vol 32, © 1998 WIT Press, www.witpress.com, ISSN 1743-3509
Structures Under Shock and Impact
219
Table 2: DLF Values for the East Logansport Bridge
DLF Values
Travelling path
Hump options
Speed
0.36,0.48
Symmetric to the
No hump
25 mile / hr
cross-section
0.32,0.36
Symmetric to the
Hump at the end
25 mile / hr
0.44
cross-section
0.45, 0.47
Hump at the Symmetric to the
25 mile / hr
cross-section
middle
The observation indicates that the finite element responses are
indeed simulating the actual system but lacks in amplitude. This can be
basically explained by the fact that simple finite element models were used
to model the superstructure (Spyrakos [10]). The degree of modeling
sofistication was capable to capture overall dynamic characteristics, such
as the natural frequencies but, as expected, proved to be inadequate to
determine the response to transient loads at specific locations (Spyrakos
[11]).
3. Conclusions
The following observations and conclusions can be drawn from this study.
1.
When the test vehicle travels on the stringer line, the DLF is less
than the AASHTO prescribed value. When the test vehicle travels
on the concrete deck, the DLF is greater than the AASHTO
assigned value. This shows that the AASHTO is not conservative
for all travelling paths of the vehicle. Also, when the test vehicle
travels on the stringer line the DLF is less than when the test
vehicle travels on the center line. This behavior indicates that the
DLF value substantially depends upon the travelling path of the
vehicle.
2.
The mean value of DLF that corresponds to the case of a hump
placed at the approach is twice as much as for the case where the
hump is placed at mid-span. Thus pit or pot holes located at the
approach will cause more severe impact effects than when they are
located near the middle of the bridge deck. However, this effect
depends upon the span length of the bridge and is yet to be
investigated.
3.
The evaluated DLF of the concrete deck is less than that
corresponding to steel stringers. However, not enough data is
available in order to substantiate this result.
4.
The mean DLF value for the prestressed bridge (East Logansport
bridge) was found to be 0.40 at 25 mph (40 kph) which is much
higher than the AASHTO prescribed value. Therefore, the impact
effects could be very high for this type of systems at 55 mph (88
kph) or 65 mph (104 kph). This shows that bridges with
prestressed systems could experience higher impact effects than
non prestressed systems.
Transactions on the Built Environment vol 32, © 1998 WIT Press, www.witpress.com, ISSN 1743-3509
220
Structures Under Shock and Impact
4. References
[1] AASHTO, Standard Specifications for Highway Bridges, Washington
D.C., USA.
[2] Thomas, P.K., A Comparative Study of Highway Bridge Loadings in
Different Countries, Transportation and Road Research Laboratory,
Report 135UC, England, 1975.
[3] Ontario Highway Bridge Design Code (1979), Ontario Ministry of
Transportation and Communications, Ontario, Canada.
[4] Schilling, C.G., Impact Factor for Fatigue Design, Journal of Structural
Division, ASCE, Vol. 108, ST9, pp. 2034-2044, 1982.
[5] Csagoly, P.P., Cambell, T.I. and Agarawel, Bridge Vibrational Study,
Ontario Ministry of Transportation and Communication, Research
Report 181, Ontario, Canada, 1972.
[6] Bakht, B., and Pinjarkar, S.G., Review of Dynamic Testing of Highway
Bridges, TRB 880532, SRR-8901, pp. 1-33, 1989.
[7] AASHTO Road Test (1962), Report 4, Bridge Research Special Report
610, Highway Research Board, National Academy of Sciences,
Washington, DC.
[8] Latheef, I., Coffinan, R., and Spyrakos, C. Experimental Evaluation of
Dynamic Load Factor on Highway Bridges, Report is under progress CFC, Department of Civil Engineering, West Virginia University, 1991.
[9] Coffinan, R. L., Assessment of DLF Accounting for Super- Sub- and
Soil-structure Interaction, Problem Report, Civil Engng. Depart., West
Virginia University, Morgantown, WV, 1995.
[10] Spyrakos, C.C. Finite Element Modeling in Engineering Practice,
Algor Publishing Division, Pittsburgh, PA, 1995.
[11] Spyrakos, C.C. and Raftoyiannis, J. Linear and Nonlinear Finite
Element Analysis in Engineering Practice, Algor Publishing Division,
Pittsburgh, PA, 1997.