Fatigue Evaluation of Cable-stayed Bridge Steel Deck Based.pdf

Fatigue evolution for cable stayed bridges

1. KSCE Journal of Civil Engineering (2017) 21(4):1400-1409
Copyright ⓒ2017 Korean Society of Civil Engineers
DOI 10.1007/s12205-016-1033-0
−1400−
pISSN 1226-7988, eISSN 1976-3808
www.springer.com/12205
Structural Engineering
Fatigue Evaluation of Cable-stayed Bridge Steel Deck Based
on Predicted Traffic Flow Growth
Zhongqiu Fu*, Bohai Ji**, Zhi Ye***, and Yixun Wang****
Received December 8, 2015/Revised April 27, 2016/Accepted June 24, 2016/Published Online August 8, 2016
··································································································································································································································
Abstract
Statistical analysis of the measured traffic flow over the Nanjing No. 3 Yangtze River Bridge from 2006 to 2010 was conducted.
The predictions of traffic flow growth model were established. Random traffic flow was simulated by Monte-Carlo method to study
dynamic impact effects under vehicle load. Considering the dynamic impact effects and wheel mark transverse distribution, the
nominal stress, hot spot stress, and notch stress in the steel bridge deck details was calculated. The results of three evaluation method
were compared. Suggestions of analysis models and fatigue evaluation were proposed. The study showed that the maximum
magnification coefficient of the dynamic impact effects was close to the suggestion of BS5400. The simplified model could be used
to analysis local stress ignoring the superimposed effects of longitudinal multi-vehicles. The evaluated service life under hot spot
stress was comparatively longer. In terms of bridge safety and convenience, notch stress for the roof weld and U rib-to-diaphragm
weld and hot spot stress for diaphragm arc gap were more suitable for fatigue evaluation. And the roof weld was most likely to crack.
Keywords: cable-stayed bridge, steel deck, fatigue evaluation, traffic flow prediction, vehicle load model
··································································································································································································································
1. Introduction
Orthotropic steel decks are widely used because of their low
weight, favourable mechanical behaviour, and rapid rate of
construction. The steel deck is complex in both its structure and
its welded connections, thus the residual stress and stress
concentration are important: fatigue damage and failure are
easily generated under long-term high traffic load (Cao et al.,
2014). Fatigue cracks, which cause severe harm, are hard to find
immediately and difficult to maintain. The fatigue behaviour of
the steel deck is complicated and influenced by many factors,
each of which is difficult to avoid in engineering practice (Xiao
et al., 2008).
Many research results concerning fatigue problems in such
steel decks are available (Zhu and Guo, 2014; Cardini and
Dewolf, 2009; Ji et al. , 2012; Zhou, 2006). The structural detail
experiments are mostly studies of local fatigue due to their
complexity. Although the precision of theoretical models and
numerical methods are discussed in many studies (Ji et al.,
2013), practical application shows that the evaluation of fatigue
damage and service life has a larger discrepancy with reality
because theoretical load models and boundary conditions differ
significantly from actual situations. Field-tests on bridges and
large segment model tests are adopted by some studies: these are
often not applicable to fatigue evaluation in real bridges due to
the limited data and appreciable differences between bridges.
The steel deck thickness of a cable-stayed bridge is usually
larger than that of suspension bridges due to the axial stress
applied (Sih et al ., 2008; Fu et al., 2015); however, measurements
show that fatigue cracks are also generated on the steel decks of
cable-stayed bridges (Chen and Cai, 2007). The Nanjing No. 3
Yangtze River Bridge, a double tower steel box girder cable-
stayed bridge with a main span of 648 m, was studied. The
measured traffic flow from 2006 to 2010 was analysed to
establish a predictive model for the fatigue load and different
methods were adopted to evaluate the fatigue damage and
service life of this steel bridge.
2. Measured Traffic Flow Load Model
2.1 Traffic Flow Prediction
It is generally believed that fatigue damage to bridges is caused
by larger vehicles. With reference to the British bridge design
standard BS 5400 and data from the charging and weighing
system used on the Nanjing No. 3 Yangtze River Bridge, traffic
with a gross vehicle weight exceeding 50 kN was analysed to
TECHNICAL NOTE
*Associate Professor, College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China (Corresponding Author, E-mail: fumi-
[email protected])
**Professor, College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China (E-mail: [email protected])
***Doctoral Candidate, College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China (E-mail: [email protected])
****Graduate Student, College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China (E-mail: [email protected])

2. Fatigue Evaluation of Cable-stayed Bridge Steel Deck Based on Predicted Traffic Flow Growth
Vol. 21, No. 4 / May 2017 −1401−
obtain the traffic flow spectrum for fatigue design. The average
daily traffic flow change on the Nanjing No. 3 Yangtze River
Bridge in July and August from 2006 to 2010 is shown in Fig. 1.
The traffic flow on the Nanjing No. 3 Yangtze River Bridge in
the next 20 years was predicted according to traffic flow data for
vehicles over 50 kN from 2006 to 2010. A non-linear regression
model for the traffic flow was established. The daily traffic flow
models for trucks are shown in Eqs. (1) to (5), where Q is a daily
traffic flow and t is years from 2006. The former four equations
were established on the basis of polynomial regression while the
last used a logarithmic regression. A comparison of the five
models is shown in Fig. 2, among which Q
A is the measured
traffic flow for loads over 50 kN from 2006 to 2010. As seen, the
regression curves can simulate the trend of traffic flow and its
dense distribution over the first five years. After 2010, the
regression curves change independently only the curve for Q
F
increases slowly over time, which coincides with the trend of
measured traffic flow.
(1)
(2)
(3)
(4)
(5)
Figure 3 shows the comparison of daily traffic flows (vehicles
exceeding 50 kN) from 2006 to 2010 obtained by measurement
and the mathematical model. Among which the daily traffic flow
calculated by curve Q
B coincided with measured data the best.
The combined regression method was adopted to describe the
growth in traffic flow. Combining Eqs. (1) and (5), a predictive
model of traffic flow for vehicles over 50 kN was established
(see Eq. (6)). Fig. 4 shows the traffic flow curve for the Nanjing
No. 3 Yangtze River Bridge obtained by the combined predictive
model: the traffic flow increased rapidly from 2006 to 2025 and
then slowed down gradually from 2025 to 2070. After 2070, the
traffic flow tended to saturation.
(6)
2.2 Measured Vehicle Load Model
MATLAB™ was programmed to sort the vehicle data according
to axle type and the axle load and numbers thereof were obtained
(see Fig. 5). Based on traffic flow data for vehicles over 50 kN in
the August of 2006 and 2010, the predictive model was applied
to predict the traffic flow in August 2030 and the vehicle counts
Q
B5.42t
4
–168.34 t
3
927.09t
2
– 2024.17 t3090+++=
Q
C135.84t
3
867.51t
2
– 1991.67 t3090++=
Q
D68.75t
2
–937.5 t3090++=
Q
E662.5t3090+=
Q
F1911.57t3090+ln=
Qt()
5.42t
4
–168.34 t
3
927.09t
2
– 2024.17 t3090+++
1911.57lnt3090+
11000
⎩
⎪
⎨
⎪
⎧
=
0t≤4<
4t70≤<
t70>
Fig. 1. Daily Traffic Flow Change
Fig. 2. Traffic Flow Predictive Model
Fig. 3. Comparison of Traffic Flow
Fig. 4. Daily Traffic Flow Curve: Predictive Model
Table 1. The Vehicle Number of the Nanjing No.3 Yangtze River
Bridge
Axle number August 2006 August 2010 August 2030
2 58488 68653 127630
3 48573 99114 138250
4 103 11423 8885
5 4 202 160
6 1 20 17
7198
Total 107170 179421 274950

3. Zhongqiu Fu, Bohai Ji, Zhi Ye, and Yixun Wang
−1402− KSCE Journal of Civil Engineering
for all types were predicted (see Table 1). It can be seen that six-,
and seven-axle vehicles accounted for a small proportion overall
thus their influence was ignored in the subsequent fatigue damage
analysis.
The axle load of all types of vehicles over 50 kN was analysed
according to the axle load data from August 2010 as taken from
the weighing system on the Nanjing No. 3 Yangtze River Bridge.
The number of different axle loads from three-, and four-axle
vehicles is shown in Fig. 6. The probability distribution not only
follows the common unimodal probability density function but
also shows features of bimodality.
According to the axle load data, the equivalent axle load for
each category of vehicle was obtained: these were summed to get
the equivalent total weight and Eq. (7) shows the equivalent axle
load (Józef, 2010).
(7)
Where, f
i is the relative frequency of vehicle i in that category,
W
ij is the load of axle j of vehicle i, and W
ej is the equivalent load
of axle j in a certain category.
Compare the equivalent axle load of vehicles of all kinds from
August 2006 to August 2010 (see Fig. 7), the average equivalent
axle load in each year were used as the calculated equivalent axle
W
ej f
iW
ij
3()∑
[]
1
3
---
=
Fig. 5. Statistical Analysis Procedure: Vehicle Types and Axle Loads
Fig. 6. Axle Load and Corresponding Frequency Diagram: (a)
Three-axle Vehicles, (b) Four-axle Vehicles
Table 2. Calculated Equivalent Axle Load (kN)
Category First axle Second axle Third axle Fourth axle Fifth axle Total weight
Two axles 35.45 87.70 123.15
Three axles 45.92 76.47 141.44 263.83
Four axles 41.38 79.24 123.70 125.98 370.30
Five axles 39.96 72.47 97.83 100.10 110.72 421.08
Fig. 7. Comparison of the Equivalent Axle Load of Vehicles of All
Kinds: (a) Two-axle Vehicle, (b) Three-axle Vehicle, (c) Four-
axle Vehicles, (d) Five-axle Vehicles
Table 3. The Calculated Equivalent Vehicle Model
Number of axles Sketch
2
3
4
5

4. Fatigue Evaluation of Cable-stayed Bridge Steel Deck Based on Predicted Traffic Flow Growth
Vol. 21, No. 4 / May 2017 −1403−
load (Table 2). Fig. 7 shows that the average equivalent axle load
was reasonable.
The equivalent vehicle models are shown in Table 3 according
to the calculated equivalent axle load for each type, as well as the
relative references and wheelbases. The axle load of vehicle
models differs to some extent from standards abroad of china.
The total weight of fatigue vehicle model stipulated in the
standards is larger.
3. Dynamic Response of a Girder to Random
Traffic
3.1 Finite Element Model
The Nanjing No. 3 Yangtze River Bridge is cable-stayed with
double towers, and has a 648 m main span, a 257 m side span,
and a 215 m high tower. The steel box girder was 3.2 m deep,
37.2 m across its full width, and 15 m along its standard span.
The horizontal centre distance between cables was 32.8 m.
Based thereon, the bridge model of the Nanjing No. 3 Yangtze
River Bridge was established by using ANSYS software are
shown in Fig. 8.
It was a hybrid finite element model with Shell63 elements
embedded into the full bridge model at mid-span (Fig. 8). The
Shell63 element model was 14 m long. Local refinement was
carried out at vehicle wheel loading positions, the gridding size
of which was 0.01 m × 0.01 m. Other parts of girder and tower
were simulated by Beam4 elements and Link10 cable element.
The boundary conditions considered six degrees of freedom on
the tower and pier restraints. The Beam4 element and Shell63
element of the steel box girder are connected with all degrees of
freedom coupling. Master-slave coupling was adopted for the
girder and tower according to the design data. The vehicle load
was simulated by Mass21 elements, which acted as mass-spring
model running across the bridge, and connected the mass
element and main girder through a Combine14 element.
The elastic modulus of steel is 2.0 × 10
5
MPa, and the Poisson's
ratio is 0.3. The steel bridge deck pavement layer using Solid45
element simulation, thickness is 50 mm. The elastic modulus of
pavement is 2000 MPa and Poisson's ratio is 0.25. Steel bridge
deck and pavement layer grid size are 0.2 m. The mesh size of
pavement along the thickness direction is 0.05 m. The mesh of
the pavement layer and the steel bridge panel is locally refined to
the size of 0.01 m at the position of wheel loading. According to
the related research, the shear stress of the steel bridge deck and
the paving layer is relatively low, only about 1 MPa (Qian et al.,
2004). So the steel bridge deck and the pavement layer are
connected by conode without considering the slip between the
two.
3.2 Random Traffic Flow
The traffic flow passing the bridge was random. Random
numbers can be generated by the Monte-Carlo method to simulate
random traffic flow (Sun et al., 2010). The effects of real traffic
formed the fatigue vehicle load spectrum: the proportion of
vehicles of all kinds was verified according to Table 1 based on
the traffic flow data from August 2010. It was assumed that the
vehicle spacing followed a lognormal distribution, the average
and standard deviation of which were 4.828 m and 1.116 m
under common running conditions, and 1.561 m and 0.280 m
under dense running conditions. The correspondence between
traffic flow and proportion of vehicles was established along
with the vehicle spacing, by MATLAB™ (see Fig. 9). Fig. 9
shows that vehicles with two, three, and four axles account for
the most traffic in each lane of the vehicle load spectrum.
Combining this random traffic flow, and the fatigue vehicle load
model, gave the fatigue load spectrum.
3.3 Dynamic Response of the Girder
Taking the vehicle load as a moving load, the analysis of the
three-dimensional model was conducted with the fatigue vehicle
Fig. 8. The FEM Model of the Nanjing No. 3 Yangtze River Bridge
Fig. 9. Traffic Flow in Each Lane of the Bridge
Fig. 10. Time History Curves: Main Girder: (a) Mid-span Bending
Moment, (b) Axial Force at the Quarter-span

5. Zhongqiu Fu, Bohai Ji, Zhi Ye, and Yixun Wang
−1404− KSCE Journal of Civil Engineering
load spectrum, where the calculated vehicle speed was 80 km/h.
The time history curve of girder internal force is shown in Fig.
10 and the bridge crossing time under random traffic flow was
160 s.
The internal force caused by dynamic load was larger than that
caused by static load thus magnification factors were applied to
describe the stress change caused by dynamic load. The
magnification factor, β, is the vertical dynamic enhancement
coefficient caused by passing vehicles where β= 1 + μ, and μ is
the dynamic impact coefficient. It showed that the time history
curves of bending moment consisted mainly of several large
bending moment cycles and the dynamic response of the
bending moment oscillated with a small amplitude around the
static response curves. The bending moment in the main girder,
at mid-span was positive, with a maximum of 4.93 × 10
7
N m
and the maximum amplitude thereof was 1.20 × 10
7
N m. At the
quarter-span, the bending moment was usually positive, but
sometimes negative: the magnification factor for internal force
was 1.23, close to the suggested value of 1.25 in BS 5400. The
bending moment in the main girder at the main tower was
negative (its maximum value was -5.56 × 10
7
N m and the
maximum amplitude was 6.8 × 10
6
N m). The change in bending
moment was the main factor influencing its stress amplitude.
Taking the bending moment time history as the evaluation
standard, and the fatigue behaviour of the segment at mid-span,
was unfavourable.
The calculation of axial force time history along the X-axis
showed that the dynamic response curve vibrated around the
dynamic response. The axle load amplitude in the main girder
at mid-span was larger, with a maximum value of 2.52 × 10
7
N
m. The main axle force at mid-span was tensile, and of
opposite sign to the fatigue behaviour of the steel box girder.
The dynamic response curve oscillated around the dynamic
response with a low amplitude at both the quarter-span and
main tower. Taking the axial force time history as the evaluation
standard and the fatigue behaviour of the segment at mid-span
was unfavourable.
Transforming the dynamic response of bending moment and
axial force into a stress, adding the two, we obtained the dynamic
stress time history at mid-span, quarter-span, and main tower.
The change in magnification factor β at different positions is
shown in Fig. 11. The stress in the main girder caused by the
dynamic and static responses at mid-span fluctuated and β was
between 0.8 and 1.2.
4. Local Stress Analysis
4.1 Local Model of Steel Bridge Deck
According to the analysis of internal force response in the main
girder, the mid-span segment was unfavourable, but was chosen
for local stress analysis. The magnification coefficient of 1.25,
considering dynamic impact effects as stipulated in BS 5400,
was adopted for this study of fatigue behaviour and damage. The
structure of the steel bridge deck is shown in Fig. 12. The
thickness of the deck is 16 mm on lane 3 and lane 6 in Fig. 9.
Deck thickness on other lanes is 14 mm.
Two types of calculation model were established by using
ANSYS software and the results compared. Model 1 was a
hybrid finite element model which used Shell63 elements
embedded into the full bridge model at mid-span (Fig. 8). Model
2 was a simplified model (Fig. 13). Seven U-ribs were fitted in
the transverse direction and six diaphragm distances were
adopted in the longitudinal direction. The thickness of the
diaphragm was 10 mm. The steel deck was simulated by Shell63
elements, all degrees of freedom were restrained at the diaphragm:
overall, three translational degrees of freedom around the model
were restrained. The gridding size of the simplified model was
the same as that of the hybrid element model.
According to International Institute of Welding (IIW), the
Fig. 11. Stress Magnification Factor β for the Main Beam
Fig. 12. Structure of the Steel Bridge Deck
Fig. 13. Simplified Model of Deck
Fig. 14. Positions of Fatigue Details

6. Fatigue Evaluation of Cable-stayed Bridge Steel Deck Based on Predicted Traffic Flow Growth
Vol. 21, No. 4 / May 2017 −1405−
transverse stress 1.5t (t is the deck thickness) to the weld was
adopted as the reference index for the fatigue cracks of the deck
developed vertically relative to the longitudinal direction. The
transverse stress in the deck was adopted for the deck detail at
the diaphragm section (σ
1 of detail 1). The stress in the U rib-
diaphragm weld (σ
2 of detail 2), as well as that in the diaphragm
arc gap which was weakened the most (σ
3 of detail 3), were
adopted to represent the fatigue details of the diaphragm, as
shown in Fig. 14.
4.2 Transverse Distribution Probability of Wheels
The acting length of the single wheel was 0.3 m and 0.2 m
respectively along the transverse and longitudinal direction and
that of double wheels was 0.6 m and 0.2 m, respectively. The
wheel load depended on the vehicle load model, the maximum
value of which was 140 kN (verified according to the statistical
results for traffic flow over the Nanjing No. 3 Yangtze River
Bridge). The action and effect of a single wheel were only taken
into consideration along the transverse and longitudinal directions.
Transverse distribution of wheels was generated as the vehicle
deviated from the wheel track centreline. With reference to the
wheel track data from Humen Bridge in China (Cui et al., 2010),
a distance of 150 mm along the transverse direction was assumed
as a kind of distribution. The distribution probability of wheel
tracks in all positions is shown in Fig. 15. Single wheel load and
double wheel loads consisted of the type of loads and the
position of the transverse load is shown in Fig. 16.
4.3 Stress Calculation for Fatigue Details
As seen from Fig. 17, the stress amplitude discrepancy of the
deck and diaphragm details of the two models were both less
Fig. 15. Transverse Distribution of the Wheeltrack
Fig. 16. Transverse Wheel Loads: (a) Single Wheel, (b) Double Wheels
Fig. 17. Stress Influence Lines: Different Models under Load P1: (a) Detail 1, (b) Detail 2, (c) Detail 3
Fig. 18. Stress Influence Line Under Single Wheel Load (single wheel): (a) Detail 1, (b) Detail 2, (c) Detail 3

7. Zhongqiu Fu, Bohai Ji, Zhi Ye, and Yixun Wang
−1406− KSCE Journal of Civil Engineering
than 5.0% under load P1. The results obtained by the simplified
model were reasonable and the calculation procedure was
efficient, Model 2 was thus adopted for local stress analysis.
The stress indexes of details under single, or double, wheels
were extracted to analyse unfavourable loading positions of
transverse wheels. Meanwhile, a typical three-axle vehicle model
was selected based on measured data to assess the influence of
longitudinal axle spacing. The stress influence lines of details
under single wheel load with different transverse loading
positions are shown in Fig. 18.
The results show that the transverse position of load P1 (single
wheel load) and P4 (double wheel load) was unfavourable to
detail 1; while transverse load positions P3 (single wheel load)
and P5 (double wheel load) were unfavorable to details 2 and 3.
For diaphragm details in these different positions, the transverse
unfavourable load position was verified and the out-of-plane
deflection was even more unfavourable. By comparison of single
and double wheel loads, the single wheel load caused the larger
pressure under the same load and the largest transverse stress
amplitude was generated from a single wheel, which led to the
obvious local effects on the steel bridge deck.
Figure 19 shows the stress influence line for structural details
under three-axle load and single load: P1 (a single wheel load)
was adopted for transverse loading. Three obvious transverse
stress amplitudes were generated at each measurement point
under three-axle load and a stress cycle was caused by the
passing of each wheel load. The stress amplitude caused by the
rear axle was the largest, and little mutual influence between
wheels in the longitudinal direction was found. The principal
stress amplitude caused by a single-axle load conforms to that of
a three-axle load and thus the superimposed effect of multiple
longitudinal vehicles could be overlooked and the single-axle
load was adopted.
4.4 Stress Amplitude of Fatigue Details
According to each stress influence line, the rain flow counting
method (Ni et al. , 2014) was adopted to extract stress amplitudes
and cycle times. The stress amplitude of each fatigue detail was
taken to calculate the equivalent stress amplitude by Miner linear
rule. The equivalent stress calculation formula is as follows:
(8)
Where, Δσ
eq is the equivalent stress amplitude, n is the stress
cycle times, n
i is the stress cycle times corresponding to the stress
amplitude i, Δσ
i is the amplitude value corresponding to the
stress amplitude i, and n is the slope parameter of the S-N curve
(generally 3.0).
The dynamic impact effects and wheel track transverse distribution
obtained by using Eq. (8) were taken into consideration to modify
σ
eqΔ nσ
i
mΔ
i1=
n
∑
⎝⎠
⎜⎟
⎛⎞
1m⁄
=
Fig. 19. Stress Influence Line: Three-axle Vehicle: (a) Detail 1, (b) Detail 2, (c) Detail 3
Tabel 4. Modified Equivalent Stress Amplitude
Details
Vehicle type
Calculated stress amplitude (MPa) Modified equivalent
stress amplitude (MPa)12345
Detail 1
2-axle 13.50/11.48 32.71/27.80 25.92/22.03
3-axle 17.05/14.49 28.76/24.45 53.78/45.71 44.10/37.48
4-axle 15.13/12.86 30.63/26.04 50.39/42.83 50.00/42.50 51.00/43.36
5-axle 15.20/12.92 26.92/22.88 38.50/32.73 38.48/32.71 38.67/32.87 44.92/38.18
Detail 2
2-axle 10.88/9.68 24.20/21.54 22.73/20.23
3-alxe 13.86/12.34 21.41/19.05 40.07/35.66 38.80/34.52
4-axle 12.25/10.90 22.80/20.29 36.01/32.05 36.44/32.43 43.56/38.76
5-axle 11.85/10.54 20.68/18.41 29.13/25.93 31.61/28.13 32.56/28.98 42.54/37.86
Detail 3
2-axle 24.51/21.57 54.46/47.92 49.06/43.17
3-axle 24.29/21.38 42.74/37.61 79.37/69.84 73.49/64.66
4-axle 28.09/24.72 55.82/49.12 86.56/76.17 87.61/77.09 100.54/88.47
5-axle 28.53/25.11 50.48/44.42 72.51/63.81 72.03/63.39 79.88/70.29 98.27/86.47
Note: value 1/value 2, value 1 and value 2 are the stress of 14 mm and 16 mm thickness deck.

8. Fatigue Evaluation of Cable-stayed Bridge Steel Deck Based on Predicted Traffic Flow Growth
Vol. 21, No. 4 / May 2017 −1407−
the equivalent stress amplitude. BS 5400 was referred to find the
dynamic impact effects, where β = 1.25 was adopt to calculate
the wheel track modified coefficient according to the wheel track
distribution in Fig. 15. The calculated stress amplitude and modified
equivalent stress amplitude, acting on the most unfavourable
load, were obtained under a single-axle load of the typical
vehicle (see Table 4).
5. Fatigue Damage Evaluation
5.1 Fatigue Stress Calculation
The equivalent stress amplitude was calculated by the nominal
stress, hot spot stress, and notch stress methods, taking both the
bridge pavement and wheel track distribution into consideration.
The most unfavourable load was applied to the model. The out-
of-plane deflection was unfavourable to the fatigue behaviour of
diaphragm details. The nominal stress was got from the hybrid
finite element model (Fig. 8). And the position of nominal stress
is shown in Fig. 14. According to the characteristics of the
fatigue details, the Solid95 element was selected to establish
detail models for hot spot stress and notch stress calculations.
The boundary conditions of these detail models were obtained by
sub-model interpolation within the simplified model (Model 2 in
Fig. 13). The interpolation boundary should not be affected by
stress concentration. The 1 mm hot spot stress method (Ya and
Yamada, 2008), which takes the stress at a position 1 mm from
the surface was adopted. The size of fatigue detail gridding was
1 mm. A circular simulated hole with a radius of 1 mm, as
recommended by the IIW was adopted and secondary refinement
of elements around the notch reduced the detail gridding to
0.3 mm. Only the influences of the weld geometry were considered
in finite element model. The material properties were the same
material with the deck. The weld cross-section was simplified to
be triangular with the weld leg size of 6 mm. The Solid95
tetrahedron element were adopt. The mesh size of weld is 0.01
m. The welding is bonded together with the top plate, the
diaphragm and the U rib by glue operation.
Considering the dynamic impact effects at β = 1.25, wheel
track influence, and an unfavourable loading position, the fatigue
stress amplitudes are shown in Table 5. As the nominal stress
model was not applicable to the calculation of detail 2 and the
gap stress model was not applicable to the non-welded position
of detail 3, the nominal stress of detail 2 and notch stress of detail
3 were omitted from Table 5. In order to compare the three types
fatigue stress, the nominal stress value was also listed. The peak
value under 1-axle vehicle load was adopted because of the
vehicle load was the same with the other two fatigue stresses.
5.2 S-N curve
The S-N curves of the deck and diaphragm details based on the
nominal stress were proposed in EuroCode 3, BS 5400, and by
the IIW respectively. FAT144, an S-N curve of deck details based
on simplified girder theory (Cui et al., 201), was adopted for
detail 1 and the corresponding failure probability was 2.28%. In
EuroCode 3, diaphragm details of different types were classified.
FAT100, proposed by EuroCode 3, was used for the nominal
stress S-N curve of detail 2 and FAT140 was used for detail 3: the
failure probability of both was 5.0%.
The fatigue strength curve FAT104, evaluated by the 1 mm hot
spot stress method, was measured (Jong and Boersma, 2004)
through fatigue tests and the corresponding failure probability
was 2.28%, which was more conservative. Therefore, the FAT100
curve proposed by the IIW was adopted for the hot spot fatigue
strength curve here. The FAT225 curve provided by the IIW,
Table 5. The Equivalent Fatigue Stress Amplitude with Different Evaluation Methods (MPa)
Details
Nominal stress 1 mm hot spot stress notch stress
14 mm deck 16 mm deck 14 mm deck 16 mm deck 14 mm deck 16 mm deck
Detail 1 41.68 35.43 61.92 52.63 156.43 132.97
Detail 2 36.56 31.08 53.57 47.67 171.64 152.76
Detail 3 69.44 61.11 93.77 82.52 -
Fig. 20. S-N Curves for Different Evaluation Methods: (a) S-N Curves, (b) Fatigue Stress on S-N Curves

9. Zhongqiu Fu, Bohai Ji, Zhi Ye, and Yixun Wang
−1408− KSCE Journal of Civil Engineering
which was conservative, was adopted for the fatigue strength
curve for the notch stress analysis. The corresponding failure
probability of FAT225 was 2.28%.
The S-N curves of deck and diaphragm details based on
nominal stress, hot spot stress, and notch stress methods are
shown in Fig. 20. The notch stress is the largest one while the
nominal stress is the smallest one the in the three. And for the
details, the fatigue stress of detail 3 is the largest one while the
one of detail 2 is the smallest.
5.3 Damage Evaluation of Fatigue Details
The three types of evaluation methods were run to calculate
the accumulated damage from 2006 to 2010, and service life
prediction for all details considering the increases in traffic flow
was undertaken. Among which the traffic flow was obtained by
the predictive model of daily average flow (Eq. (6)) proposed
herein. The stresses were respectively: nominal stress (Model 1
in local stress calculations), hot spot stress, and notch stress.
Miner linear damage accumulation theory was used to calculate
the extent of damage and the service life of all details. The
accumulated damage over the five years corresponding to
different fatigue evaluation methods is shown in Table 6.
As seen from Table 6, for detail 1, the fatigue life by hot spot
stress method was the largest one and the life was over 100
years. The life of notch spot stress method was the smallest while
the evaluation showed that the result was close to the nominal
stress method life. For detail 2, the fatigue life by the notch stress
method was the smallest and the results obtained by nominal
stress method and hot spot stress method were both over 100
years. For detail 3, the evaluation difference of nominal stress
method and the hot spot stress method was small with about by
2.5% difference. Generally, the service life found by the hot spot
stress method was the biggest one. For the safety of the bridge,
the fatigue maintenance should be based on the most unfavourable
evaluation results. Therefore, the notch stress method was
suggested for details 1 and 2. Due to the small difference of
evaluation results between the two methods for detail 3, the hot
spot stress method is suggested considering the briefness and
convenience.
The damage (Table 6) was not proportional to the service life
prediction because the increase of traffic flow was taken into
consideration. However, the accumulated damage and fatigue
life prediction over the five years showed that detail 1 was the
easiest to crack of the three details. According to Table 6, the
fatigue lives of detail 1, detail 2, and detail 3 in the bridge deck of
the Nanjing No. 3 Yangtze River Bridge were respectively: 69
years, 79 years, and 79.1years.
6. Conclusions
Taking the increase of traffic flow over the Nanjing No. 3
Yangtze River Bridge into consideration, the dynamic response
and fatigue damage condition of the steel bridge deck under
traffic load were analysed. The following conclusions were drawn:
1. The predictive function for traffic flow growth was estab-
lished according to the measured traffic flow over the first
five years after opening the bridge to traffic. The statistics
showed that vehicles with 2, 3, 4 and 5 axles accounted for
the biggest proportion. Taking vehicles exceeding 50 kN
into consideration, the equivalent axle load of vehicles of all
kinds was obtained to establish an equivalent vehicle load
model.
2. The analysis of the dynamic time history of random traffic
flow based on the Monte-Carlo method showed that the
change in amplitude of the bending moment and axial ten-
sion in the mid-span section of the steel box girder was the
biggest and most easily caused fatigue damage. The maxi-
mum value, 1.23, of the magnification coefficient of the
bending moment dynamic impact effects was generated in
the quarter-span, which was close to the suggested value of
1.25, as proposed by BS 5400.
3. The local stress on the diaphragm at the mid-span showed
that the results from the hybrid element model, considering
the full-bridge boundary conditions, differed by 5% from
those obtained by a local simplified model. The principal
stress peak under a single axle load coincided with that
under a multi-axle load thus the superimposed effects of lon-
gitudinal multi-vehicles could be overlooked and a single
axle load adopted when it came to local stress calculation.
4. Nominal stress, hot spot stress and notch stress methods
were used for the fatigue evaluation in the diaphragm sec-
tion and the service life predicted by the hot spot stress
Table 6. Damage Degree and Service Life Corresponding to Different Methods
Details
Evaluation
method
Damage degree from 2006 to 2010 Maximum
lane
Life
(year)Lane-1 Lane-2 Lane-3 Lane-4 Lane-5 Lane-6
1
Nominal 0.0278 0.0291 0.0279 0.0287 0.0319 0.0256 5-lane 86.3
Hot spot 0.0113 0.0137 0.0130 0.0108 0.0152 0.0128 5-lane 161
Notch 0.0438 0.0431 0.0435 0.0450 0.0472 0.0427 5-lane 69
2
Nominal 0.0179 0.0194 0.0211 0.0176 0.0212 0.0191 5-lane 134
Hot spot 0.0099 0.0086 0.0127 0.0093 0.0110 0.0118 3-lane 168
Notch 0.0406 0.0410 0.0428 0.0401 0.0402 0.0415 3-lane 78.9
3
Nominal 0.0345 0.0356 0.0399 0.0381 0.0359 0.0355 3-lane 79.1
Hot spot 0.0357 0.0337 0.0336 0.0397 0.0301 0.0323 4-lane 81

10. Fatigue Evaluation of Cable-stayed Bridge Steel Deck Based on Predicted Traffic Flow Growth
Vol. 21, No. 4 / May 2017 −1409−
method was the biggest one. In terms of bridge safety and
calculation convenience, the notch stress should be evalu-
ated at roof welds and the U-rib-to-diaphragm weld: the hot
spot stress was better evaluated at diaphragm arc gap below
the U-rib.
5. The fatigue damage calculation in the diaphragm section
showed that the roof weld was most likely to crack among
the structural details considered here. Taking traffic flow
growth into consideration, the fatigue life of the diaphragm
roof weld in the mid-span section was 69 years, for the U-
rib-to-diaphragm weld it was 79 years, and in the diaphragm
arc gap below the U-rib it was 79.1 years.
Acknowledgements
The authors appreciate the support of The National Natural
Science Fund (No.51278166 and No.51478163); The Fundamental
Research Funds for the Central Universities (2015B17414).
References
Cao, V. D., Sasaki, E., Tajima, K., and Suzuki, T. (2014). “Investigations
on the effect of weld penetration on fatigue strength of rib-to-deck
welded joints in orthotropic steel decks.” Int. J. Steel. Struct, Vol. 15,
No. 2, pp. 299-310, DOI: 10.1007/s13296-014-1103-4.
Cardini, A. J. and Dewolf, J. T. (2009). “Long-term Structural health
monitoring of a multi-girder steel composite bridge using strain
data.” Struct. Health Monit., Vol. 8, No. 1, pp. 47-58, DOI: 10.1177/
1475921708094789.
Chen, S. R. and Cai, C. S. (2007). “Equivalent wheel load approach for
slender cable-stayed bridge fatigue assessment under traffic and
wind: Feasibility study.” J. Bridge. Eng., Vol. 12, No. 6, pp. 755-
764, DOI: 10.1061/(ASCE)1084-0702(2007)12:6(755).
Cui, B., Wu, C., Ding, W. J., and Tong, Y. Q. (2010). “Influence of
acting position of vehicle wheels on fatiguestress range of steel
deck.” Jounal for Architecture and Civil Engineering, Vol. 3, No. 27,
pp. 19-23. (in Chinese)
Fu, Z. Q., Ji, B. H., Yang, M. Y., Sun, H. B., and Hirofumi Maeno
(2015). “Cable replacement method for cable-stayed bridge based
on sensitivity analysis.” J. Perform Constr Fac, Vol. 29, No. 3, pp.
04014085-1-8, DOI: 10.1061/(ASCE)CF.1943-5509.0000460.
International Institute of Welding (IIW). “Recommendations for Fatigue
Design of Welded Joints and Components.” Paris, 2008.
Ji, B. H., Chen, D. H., Ma L., Jiang, Z. S., Shi, G. G., Xu, H. J., and Zhang,
X. W. (2012). “Research on stress spectrum of steel decks in
suspension bridge considering measured traffic flow.” J. Perform
Constr Fac, Vol. 26, No. 1, pp. 65-75, DOI: 10.1061/(ASCE)
CF.1943-5509.0000249.
Ji, B. H., Liu, R., Chen, C., Maeno, H., and Chen, X. F. (2013). “Evaluation
on root-deck fatigue of orthotropic steel bridge deck.” J. Constr.
Steel. Res., Vol. 90, pp. 174-183, DOI: 10.1016/j.jcsr.2013.07.036.
Jong, F. B. P. D. and Boersma, P. D. (2004). “Maintenance philosophy
and systematic lifetime assessment for decks suffering from fatigue.”
2004 Orthotropic Bridge Conference, California, USA, pp. 359-375.
Józef, J. (2010). “Determination of equivalent axle load factors on the
basis of fatigue criteria for flexible and semi-rigid pavements.” Road
Mater. Pavement Des, Vol. 11, No. 1, pp. 187-202, DOI: 10.3166/
RMPD.11.187-202.
Ni, Y. Q., Ye, X. W., and Ko, J. M. (2014). “Modeling of stress spectrum
using long-term monitoring data and finite mixture distributions.” J.
Eng. Mech, Vol. 138, No. 2, pp. 175-183, DOI: 10.1061/(ASCE)
EM.1943-7889.0000313.
Qian, Z. D. and LUO, J. (2004). “Pavement stress analysis of orthotropic
steel deck.” Journal of Traffic & Transportation Engineering, Vol. 4,
No. 2, pp. 10-12. (in Chinese)
Sih, G. C., Tang, X. S., Li, Z. X., Li, A. Q., and Tang, K. K. (2008).
“Fatigue crack growth behavior of cables and steel wires for the
cable-stayed portion of Runyang bridge: Disproportionate loosening
and/or tightening of cables.” Theor. Appl. Fract. Mech., Vol. 49,
No. 1, pp. 1-25, DOI: 10.1016/j.tafmec.2007.10.008.
Sun, S. J., Xu, J. W., Han, W. S., and Mei, K. H. (2010). “Whole rigidity
characteristic of T-beam bridge under random traffic flow.” Journal
of Traffic & Transportation Engineering, Vol. 10, No. 5, pp. 23-29.
(in Chinese)
Xiao, Z. G., Yamada, K., Ya, S., and Zhao X.L. (2008). “Stress analyses
and fatigue evaluation of rib-to-deck joints in steel orthotropic
decks.” Int. J. Fatigue, Vol. 30, No. 8, pp. 1387-1397, DOI: 10.1016/
j.ijfatigue. 2007.10.008.
Ya, S. and Yamada, K. (2008). “Fatigue durability evaluation of trough
to deck plate welded joint of orthotropic steel deck.”J. Jpn. Soc. Civ.
Eng., Vol. 64A, No. 64, pp. 603-616.
Zhou, Y. E. (2006). “Assessment of bridge remaining fatigue life through
field strain measurement. “J. Bridge. Eng., Vol. 11, No. 6, pp. 737-
744, DOI: 10.1061/(ASCE)1084-0702(2006)11:6(737).
Zhu, J. S. and Guo, Y. H. (2014). “Numerical simulation on fatigue
crack growth of orthotropic steel highway bridge deck.” Journal of
Vibration & Shock, Vol. 33, No. 14, pp. 40-32.