Dynamic and fatigue response of a truss bridge with fiber reinforced polymer deck

International Journalof Fatigue

International Journal of Fatigue 29 (2007) 1475–1489

www.elsevier.com/locate/ijfatigue

Dynamic and fatigue response of a truss bridge with fiber reinforced polymer deck Methee Chiewanichakorn

a,*

, Amjad J. Aref b, Sreenivas Alampalli

c

a KPFF Consulting Engineers, 6080 Center Drive, Suite 300, Los Angeles, CA 90045, United States Department of Civil, Structural and Environmental Engineering, State University of New York at Buffalo, Buffalo, NY 14260, United States Bridge Program and Evaluation Services Bureau, New York State Department of Transportation, 50 Wolf Road, Albany, NY 12232, United States b

c

Received 16 June 2006; received in revised form 26 October 2006; accepted 29 October 2006 Available online 12 December 2006

Abstract Lighter fiber reinforced polymer (FRP) decks are gaining popularity among bridge owners as an alternative to replace old deteriorated heavy concrete bridge decks to increase the live load capacity of old steel superstructures requiring minimal repairs. This is more attractive in case of old truss bridges, which are relatively in good condition, but are not designed to current live loads and cannot be easily rehabilitated to improve their capacities. Replacing the heavy concrete decks on these bridges will extend their service life by reducing the dead load and thus increasing the live load capacity. When an FRP deck is used in such cases, a system level approach should be used to evaluate the bridge condition for all possible failure mechanisms. Dynamic and fatigue response is one such issue requiring careful evaluation. This paper studies the behavior of a truss bridge, where an FRP deck replaced an old deteriorated concrete deck, using experimentally validated finite element (FE) models. FE models were employed to conduct dynamic time-history analyses with a moving AASHTO fatigue truck over the bridge. The results were used to evaluate the effects of the rehabilitation process on the remaining fatigue life of the structure. Numerical results show that the fatigue life of the bridge after rehabilitation would be doubled compared to a pre-rehabilitated reinforced concrete deck system. Based on the estimated truck traffic that the bridge carries, stress ranges of the FRP deck system lie in an infinite fatigue life regime, which implies that no fatigue failure of trusses and floor system would be expected anytime during its service life.  2006 Elsevier Ltd. All rights reserved. Keywords: Fatigue; Fiber reinforced polymer; Concrete; Dynamics; Bridge deck

1. Introduction Several bridges throughout the United States on county and state highway systems are deteriorated. In order to satisfy current live load requirements and extend the service life of the bridge, structural strengthening is necessary. The New York State Department of Transportation (NYSDOT) as part of their initiative to develop effective rehabilitation methods, experimented with fiber reinforced polymer (FRP) decks to replace existing deteriorated bridge decks. The first FRP deck used on a state highway bridge is located *

Corresponding author. Tel.: +1 310 665 1536; fax: +1 310 665 9070. E-mail address: mchiewanichakorn@kpff-la.com (M. Chiewanichakorn). 0142-1123/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2006.10.031

in the New York State and was built to improve the live load capacity of a 60-year old truss over Bentley Creek in Wellsburg, New York. A static failure analysis was performed to determine strength of Bentley Creek Bridge deck after rehabilitation was completed [1]. The results verified several of the assumptions made during the design phase of the deck and studied possible failure mechanisms the deck may be subjected to in its service life. Aref et al. [2] also investigated thermal behavior of this bridge by conducting temporal-thermal stress simulations. The FRP deck was exposed to heat flux approximately equivalent to heat emitted from an oil fuel fire. Fire resistance limit – the period of time from the initiation of fire until the moment that failure occurs, was determined for different scenarios. The results

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showed that FRP bridge decks are sensitive to the effect of elevated temperatures. FRP deck approached the fire resistance limit at early stages of fire incident under all cases of fire scenarios. One other aspects of interest were the effects of the rehabilitation process on the dynamic characteristics of the entire structure and fatigue life ofthe bridge. By reducing self-weight of the deck, dynamic characteristics of the structure would be different and therefore needed further investigation. There have been several studies on dynamic response in terms of fatigue reliability assessment of different types of bridges. Numerical analyses were employed to estimate the expected response and to establish appropriate locations for fatigue monitoring instrumentation for a tied-arch bridge [3]. For structural health monitoring purposes, Li and Ko [4] developed a methodology and strategy for fatigue damage assessment and life prediction of bridge-deck sections of existing bridges. Based on the proposed model, an analytical approach for evaluating the fatigue damage and service life of bridge-deck sections that utilizes strain history data from structural health monitoring system and the continuum damage mechanics fatigue model were recommended. Tsiatas and Palmquist [5] employed fracture mechanics to predict the remaining fatigue life of several actual bridges with welded cover plate ends and compared with the current AASHTO bridge fatigue guidelines. It was found that fatigue lives of actual steel highway bridges as determined using fracture mechanics far exceed the remaining safe fatigue life predictions made with current AASHTO guide specifications. Hence, an adjustment factor was introduced to close a gap between values obtained by the AASHTO specifications and fracture mechanics. Chan et al. [6] developed finite element model of a large suspension steel bridge - namely ‘‘Tsing Ma Bridge’’ and performed fatigue stress analysis. The critical locations in the bridge main span were identified by the numerical results. In addition, a local stress analysis of a typical weld connection was carried out to obtain the hot-spot stresses in the region. Those results were used to provide a basis for evaluating fatigue damage and prediction the remaining life of the bridge.

This paper focuses on the study of dynamic responses of FRP deck system in comparison to a generic reinforced concrete deck system after the completion of rehabilitation process. 3D-finite element analysis procedures were employed to perform dynamic fatigue simulations on both deck systems. Predicted load-induced fatigue lives were determined based on numerical results and fatigue resistance formulae provided by AASHTO-LRFD specifications. 2. FRP bridge superstructure Bentley Creek Bridge is a highway bridge located on State Route 367 in Chemung County, New York. It was originally built as a single simple-span, steel truss bridge with reinforced concrete slab. Due to the results of a recent updated load rating, the new rating reflected additional dead load from asphalt overlays, steel corrosion on trusses and floor system, and the poor deck condition, New York State Department of Transportation decided to rehabilitate this bridge by replacing the reinforced concrete slab with fiber reinforced polymer (FRP) deck to prolong the structure’s service life as well as satisfying new load rating requirements. The bridge has a length of 42.7 m and a width of 7.3 m curb-to-curb with 27 skewed supports. The floor system was made up of steel transverse floor-beams at 4.27 m center-to-center spacing with longitudinal steel stringers. Figs. 1 and 2 illustrate the plan and elevation views of Bentley Creek Bridge, respectively. Fig. 2 also shows a detailed section of floor-beam with FRP deck. 3. Finite element model and verifications Finite element model of Bentley Creek Bridge was developed using the pre-processor package called MSC PATRAN [7] and the analysis was performed using a general purpose finite element analysis package, ABAQUS [8]. Entire bridge was modeled from North to South abutments. Fig. 3 demonstrates a three-dimensional model of the bridge. Modeling method used in this study is described herein.

Fig. 1. Bentley Creek Bridge plan view [1].

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Fig. 2. FRP deck geometry of Bentley Creek Bridge.

Fig. 3. Finite element model of Bentley Creek Truss Bridge.

3.1. Geometry modeling Webs of transverse floor-beams were modeled using four-node shell elements (S4R5), while flanges were modeled using eight-node solid elements (C3D8). Each

joint of truss members was connected using structural bolts and steel plate, which provide some rigidity to individual truss members. Hence, a three-dimensional beam element (B31) was employed to model trusses with appropriate cross-section properties.

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There were two different decks considered in this study. First, a generic old non-composite reinforced concrete deck was modeled by eight-node solid element (C3D8) with a total thickness of 240 mm. Reinforcements were not considered in this study. Second, FRP deck panels were made up of two main components – faceskins and core, as depicted in Fig. 4. Top and bottom faceskins were modeled by solid-composite elements. This type of element is basically a typical eight-node solid element (C3D8) with specified orthotropic material properties, for instance – lamina thickness, fiber orientation and stacking sequences. Core component was modeled using composite shell element, i.e., shell element with orthotropic material properties. It must be noted that data from FRP deck bridge field test were used to verify finite element model in this study. Based on the experimental results reported by Alampalli and Kunin [9], composite action was not developed between FRP deck and steel floor system. Hence, interface elements were introduced between FRP deck and floorbeams. In order to mimic a non-composite behavior, orthotropic properties with weak in-plane transverse stiffness and high vertical stiffness were imposed to the interface elements. 3.2. Materials modeling The FRP deck panels were fabricated as a sandwich type construction. Top and bottom faceskins were constructed

from two types of materials denoted as QM6408 and Q9100, while core component was made up of material denoted as Q6408. Each lamina was arranged in systematic manner to ensure that the required strength was achieved. Technical details of lamina thickness, fiber orientation and stacking sequence are kept confidential as per the manufacturer request. A typical bilinear stress–strain relationship of Grade 36 structural steel was used in transverse floor-beams and stringers. Modulus of elasticity used for steel is 200 GPa. Concrete was assumed to remain uncracked under the applied load. It was modeled as an elastically homogeneous material with modulus of elasticity of 26.3 GPa. The mechanical properties of all materials are summarized in Table 1. 3.3. Loading configurations Static load-tests were conducted by a team from New York State Department of Transportation by Alampalli and Kunin [9]. Three separate load cases were utilized. Two NYSDOT dump trucks (designated A and B) were used to load the bridge. Truck weights used in the testing are summarized in Table 2. Only one load case was used in finite element analysis in this study for model verification purpose. Both NYSDOT dump trucks were placed on the bridge as depicted in Fig. 5. Truck A was located over the third floor-beam which was instrumented by strain gages on web and flanges

Fig. 4. FRP deck compositions [1].

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Table 1 Material properties Structural component

Properties

Value

Floor-beam, stringer, trusses

Yield strength, fy Modulus of elasticity, Es

248 MPa (33 ksi) 200 GPa (29,000 ksi)

Concrete QM6408

Modulus of elasticity, Ec Modulus of elasticity, E Shear modulus, G Ultimate tensile strength, Xt Ultimate compression strength, Xc Ultimate shear strength, Xs

26.3 GPa (3.81 ksi) 18,479 MPa (2680 ksi) 5861 MPa (850 ksi) 310 MPa (45 ksi) 221 MPa (32 ksi) 114 MPa (16.5 ksi)

Q9100

Modulus of elasticity, E Shear modulus, G Ultimate tensile strength, Xt Ultimate compression strength, Xc Ultimate shear strength, Xs

29,724 MPa (4310 ksi) 6206 MPa (900 ksi) 621 MPa (90 ksi) 476 MPa (69 ksi) 121 MPa (17.6 ksi)

Neoprene shim Epoxy adhesive Glue Interface

Modulus Modulus Modulus Modulus

10,000 MPa (1450 ksi) 15 MPa (2.2 ksi) 0.1 MPa (0.015 ksi) 0.1 MPa (0.015 ksi)

of of of of

A B

Eshim Eepoxy Eglue Einterf

4.1. Structural damping

Table 2 Truck weights Truck

elasticity, elasticity, elasticity, elasticity,

Front axle

Rear axle

Gross weight

Left

Right

Left

Right

44 45

41 42

64 66

65 68

214 211

Unit = kN.

(see Fig. 6). Truck B was offset and placed over the second floor-beam. 3.4. Model verification results In this section, finite element results are compared with measured results obtained from load-tests. Fig. 7 shows good agreement between finite element analysis and experimental results. Gage numbers were labeled at the tips of each bar. A lack of composite action between floor-beams and FRP deck was confirmed by strain values obtained from Gages 1 to 5. Top flange strain (Gage 1) was approximate the same as strains as the bottom flange strains (Gages 4 and 5), while strains at mid-height of the floor-beam (Gages 2 and 3) are negligible. This implied that the location of neutral axis almost coincided with a geometric centroid of steel floor-beams. 4. Dynamic fatigue simulations As previously mentioned, the dynamic fatigue responses of reinforced concrete and FRP deck systems were investigated in this study. The most important factor to cause structural fatigue damage is the stress fluctuation, which mainly induced by traffic loading [10]. In order to obtain accurate and reliable stress histories, structural characteristics must be well identified.

Numerical simulation technique was employed to study dynamic characteristics, particularly structural damping, of both deck systems. In this study, the bridge was assumed to remain elastic when subjected to dynamic fatigue loading. In general, a proper amount of damping in a system cannot be determined analytically due to the fact that most formulae would not account for a significant part of the energy dissipated through friction at steel connections, and others. The damping of the system should be determined from its modal damping ratios, which account for all energy dissipating mechanisms. For the purpose of this study, Rayleigh damping was employed to incorporate structural damping mechanisms. Rayleigh damping consists of two main parts, stiffnessproportional and mass-proportional damping, which can be written as in Eq. (1): c ¼ am þ bk

ð1Þ

where m and k are a total mass and effective stiffness of the structure, respectively, a and b can be determined from Eqs. (2) and (3), when both ith and jth modes are assumed to have the same damping ratio [11]. xi and xj are the ith and jth modes of vibration, which was obtained from eigenvalue analysis: 2xi xj
xi þ xj 2
b¼f xi þ xj a¼f

ð2Þ ð3Þ

To determine a and b for Bentley Creek Bridge, an appropriate modal damping ratio f is necessary. The modal damping ratio of 0.5% was chosen for a finite element study of a suspension bridge by Chan et al. [6] and a dynamic simulation of a tied arch railway bridge by Malm

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Fig. 5. Truck positions [1].

and Andersson [12]. Therefore, the modal damping ratio of 0.5% was employed in the dynamic fatigue simulations of Bentley Creek Bridge. The first and fifth modes of vibration were assumed to contribute the same amount of energy dissipation. Therefore, a and b values for FRP and concrete deck systems can be computed using Eqs. (2) and (3) and are summarized in Table 3. In finite element analyses, a and b values were implemented as mass-proportional and stiffness-proportional damping parameters in ABAQUS [8]. 4.2. Dynamic loading patterns In dynamic fatigue simulation, a nominal fatigue truck designated by AASHTO-LRFD bridge specifications [13] was employed, which has a constant spacing of 9 m between the 145 kN axles. The dynamic load allowance

of 15% was imposed on the design truck for fatigue and fracture limit state evaluation. Lane load was not considered in this study. Assuming maximum allowable speed on Bentley Creek Bridge is 50 mph or 22.35 m/s, at a constant traveling speed, a total time for a truck to cross this bridge would be Traveling time ¼

Length 42:7 m ¼ ¼ 1:91 s  2 s Speed 22:35 m=s

To simulate a moving truck, eight discrete time instants were considered. Therefore, stepping-time increment is Dt ¼

2s ¼ 0:25 s 8 time instants

Considering a single truck travels on the right lane from south to north (see Fig. 1) and assuming a truck was off the

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Fig. 6. Location of FRP deck and girder strain gages [1].

200 EXP FEM

1.15

17

15

150 11 10 4

5

Amplification Factor

Strain (microstrain)

100

14

50 7 2

12

3

13

0 9

6 8

50

Time 1

100

t/1000 = 0.002 seconds 150

Fig. 8. Loading protocol. 0

2

4

6

8

10 . Gage No

12

14

16

Fig. 7. Finite element model verification results (both Trucks A and B).

Table 3 Coefficient of Rayleigh damping for n = 0.5% System

x1 (rad/s)

x5 (rad/s)

a

b

FRP Concrete

19.61 9.44

62.79 70.87

0.1494 0.0833

1.214E04 1.245E04

bridge at time t = 0 s, an impact time duration at each time instant was assumed to be one-thousandth of a total traveling time, i.e., 0.002 s (see Fig. 8). In finite element simulation, the same truck loading was placed on the deck at eight different locations with eight different assigned loading protocol curves (namely AMPLITUDE option) as illustrated in Fig. 9. Truck load was removed from one time instant to another.

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M. Chiewanichakorn et al. / International Journal of Fatigue 29 (2007) 1475–1489 0.50L

0.25L

0.75L

t = 0 sec A

B

t = 0.25 sec A

t = 0.50 sec A

t = 0.75 sec A

t = 1.0 sec A

t = 1.25 sec A

t = 1.50 sec A

t = 1.75 sec A

A

t = 2.0 sec

Fig. 9. Moving truck location.

4.3. Analytical results Dynamic time-history analyses of Bentley Creek Bridge subjected to a moving fatigue truck was conducted for reinforced concrete and FRP deck system. Total time duration of 10 s were considered with 2 s of truck traveling time and 8 s of free structural vibration, which was considered to be sufficient for predicting its fatigue life based on dynamic responses. Two main components, i.e., trusses and floorbeams, were expected to be potentially vulnerable to fatigue damage and failure. This bridge has two main trusses, East and West trusses. Fig. 10 shows truss element numbers, which will be referred throughout this paper. To distinguish between East and West truss members in this study, letters ‘‘E’’ and ‘‘W’’ will be placed in front of member numbers. For instance,

member ‘‘E022’’ represents one of the bottom chord members on an east truss. For FRP deck system, Fig. 11 illustrates dynamic responses of seven different members on the west truss. Two of those are the critical members of all, which had thick box around each plot. Those members are ‘‘W028’’ and ‘‘W057’’. Although maximum response of two members are small than those of members ‘‘W340’’ and ‘‘W354’’, their stress ranges or stress fluctuations are more important in governing their fatigue life of the system and not peak stress values. For reinforced concrete deck system, stress history in Fig. 12 indicates higher fluctuations and slower rate of decay compared to FRP deck system. The critical members of the west truss for reinforced concrete deck system are ‘‘W004’’ and ‘‘W009’’, which are not the same set of members as FRP deck system.

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DETAIL B DETAIL A U5

U3

U3

U1

L0

U1

L2

L1

L3

L4

L4

L5

L3

L2

L0

350

329

322

118

135

124 132 301

L1

205

121

116 108

319

105 201

203

307

209

347

333

220

304

336

315

233

343

223

102

235 004

001

022

009

006 007

211

012

033 024

019

031

042

040 036

037

DETAIL A 351

330

131

323

140

143 125

205

314

128

117 354

233

204

340

110 326

226

344 337

316 308

229

113

311 214

202 109

235 049

046

051 054

043

028

015 048

013

025

018

057 217

030

060

055

DETAIL B Fig. 10. Truss element numbers.

5. Fatigue life predictions Fatigue life of Bentley Creek Bridge can be evaluated based on fatigue resistance formulae (Eqs. (4) and (5)) specified in AASHTO-LRFD design specifications. The code considers the design life to be 75 years, which appears in Eq. (5):  13 A 1 ðDF Þn ¼ P ðDF ÞTH N 2

ð4Þ

where A n (ADTT)SL (DF)TH

y¼

A 3 nð365ÞðADTTÞSL ðDF Þn

ð5Þ

constant taken from Table 5 (MPa3) number of stress range cycles per truck passage taken from Table 6 single-lane ADTT as specified in Article 3.6.1.4 in AASHTO-LRFD constant-amplitude fatigue threshold taken from Table 7 (MPa)

1 when ðDF Þn P ðDF ÞTH 2 ð6Þ

and ðADTTÞSL ¼ p  ADTT

and N ¼ ð365Þð75ÞnðADTTÞSL

In this study, a number ‘‘75’’ in Eq. (5) was replaced by an unknown variable ‘‘y’’ representing a fatigue life in years. Eqs. (4) and (5) can be rearranged into Eq. (6):

ð7Þ

where, (ADTT)SL is the number of trucks per day in one direction averaged over the design life, (ADTT) is the number of trucks per day in a single-lane averaged over the design life, and p is fraction of truck traffic in a single lane – taken as 1.0 in this study. New York State Department of Transportation has monitored traffic volume over Bentley Creek Bridge in year 2002 and made a prediction for traffic volume in year 2020. This information is utilized to predict fatigue life. In 2002, an average daily traffic (ADT) was 3624 vehicles per day while ADT for year 2020 would be 5062 vehicles per

Stress (MPa)

-10

-5

0

5

-5

0

5

0

0

L0

-10

10

Stress (MPa)

10

5 Time (sec)

L1

U1

10

L2

10

W004

5 Time (sec)

W121

Stress (MPa) -10

-5

0

5

10

0

L3

U3

0

Stress (MPa)

10

W009

L5

U5

5 Time (sec)

L4

-5

0

5

10

-10

10

0

-5

0

5

10

-10 0

5 Time (sec)

L3

U3

Stress (MPa)

Fig. 11. West truss of FRP deck bridge results.

5 Time (sec)

L4

-10

-5

0

5

W354

Stress (MPa)

10

10

W028

L2

5 Time (sec)

L1

U1

-10

-5

0

5

10

10

W340

Stress (MPa)

0

L0

5 Time (sec)

10

W057

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Stress (MPa)

-10

-5

0

5

10

0

Stress (MPa)

0

5 Time (sec)

10

W004

L1

U1

5 Time (sec)

L0

-10

-5

0

5

L2

10

W121

-10

-5

0

5

10

0

L3

U3

0

L4

10

W009

L5

U5

5 Time (sec)

-5

0

5

10

0

L4

-10

10

L3

U3

-10

-5

0

5

10

0

5 Time (sec)

Stress (MPa)

Stress (MPa)

Fig. 12. West truss of concrete deck bridge results.

5 Time (sec)

-10

-5

0

5

Stress (MPa)

10

Stress (MPa)

W354

10

W028

L2

5 Time (sec)

0

5

10

-10

-5

L1

U1

10

W340

Stress (MPa)

10

0

5 Time (sec)

L0

10

W057

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day. The number of trucks was approximately 7.6% of given ADTs. Hence, the average daily truck traffic (ADTT) for trucks only would be 275 and 384 in years 2002 and 2020, respectively. Since a fraction of truck traffic in a single lane (p) was taken as 1.0, (ADTT)SL would be equal to 275 and 384 in years 2002 and 2020, respectively (see Eq. (7)). The number of stress range cycles per truck passage, n, in Eq. (5) was obtained directly from finite element analysis results. The difference between n-values from FEM and code-specified n-values will also be discussed in this paper.

Situation

Detail

Base metal: Of unpainted weathering steel, all grades, designed and detailed in accordance with FHWA (1990) Base metal at ends of partial-length cover plates: Wider than the flange without end welds Base metal: At net section of riveted connections

B

E0

Table 5 Detail category constant, A

Components and details susceptible to load-induced fatigue cracking have been grouped into eight categories, called detailed categories, by fatigue resistance. Parts of detailed categories specified in AASHTO-LRFD Bridge Design Specifications [13] that are relevant to connection types of Bentley Creek Bridge trusses and floor-beams Table 4 Detail categories for load-induced fatigue

category Plain members

Built-up members Mechanically fastened connections

10

Constant, A · 1011 (MPa3)

B D E0

39.3 7.21 1.28

5 0 -5 -10 5 Time (sec)

5 0

Stress Range (MPa)

5 0 -5 -10 5 Time (sec)

10

200

100

0 0

5 Time (sec)

0

10

20 W057

0

10

10

10

W028

15

15

W057

15 10 5 0

5 10 Stress Range (MPa)

300 W057 No. of Cycles

0

300 W028 No. of Cycles

Stress Range (MPa)

Stress (MPa)

D

Detail category

20 W028

Stress (MPa)

5.2. Fatigue life of truss members Fig. 13a and d illustrate stress history of selected critical members, i.e., W028 and W057 on west truss of FRP deck system. As mentioned previously, a main cause of fatigue failure is not stress amplitudes, but rather stress ranges. Stress range history of members W028 and W057 are plotted in Fig. 13b and e, respectively. Both members were categorized in detailed group E 0 , with a constant-amplitude fatigue threshold of 17.9 MPa (see Table 7). Their stress ranges are greater than half of a constant-amplitude fatigue threshold. Hence, their fatigue lives can be determined using Eq. (6) with number of cycles (n) obtained from dynamic analyses. Since these members were subjected to many levels of stress ranges at different number of cycles, frequency distribution method was used to group different stress-range levels. In this paper, stress-range levels were grouped at an increment of 1 MPa. Histograms were plotted to show stress-range versus number of cycles as demonstrated in Fig. 13c and f. Only those stress ranges that

5.1. Classification of fatigue connections

General condition

are summarized in Table 4. Every joint was riveted connection that falls into detailed category D in Table 4. Bottom and top chord members and a vertical member at mid-span were rolled sections which can be grouped in detailed category B. All other diagonal members were built-up members and were categorized into group E 0 .

0

5 Time (sec)

10

200

100

0 0

Fig. 13. Response history of critical members on west truss of FRP deck.

5 10 Stress Range (MPa)

15

M. Chiewanichakorn et al. / International Journal of Fatigue 29 (2007) 1475–1489 Table 6 Cycles per truck passage, n

Table 8 Predicted fatigue life (ADTTs from NYSDOT)

Longitudinal members

n

Simple span girder Trusses

1.0 1.0

Location

Detail category

Threshold (MPa)

B D E0

110 48.3 17.9

0 -5 -10 5 Time (sec)

10

10

Concrete

Infinite life Infinite life Infinite life

394 (E113) 354 (E128) Infinite life

1063 (W028) 1063 (W057) Infinite life

532 (W004) 394 (W009) 532 (W105)

75-Year (ADTT)SL equivalent to infinite life (trucks per day)

B D E0

865 1875 6525

replacing old reinforced concrete deck with light-weight FRP deck. According to AASHTO-LRFD Bridge Design Specifications, ADTT for 75 year that equivalent to infinite life of different detailed categories can be computed using Eqs. (4) and (5) and are summarized in Table 9. Therefore, by applying these values to Bentley Creek Bridge, it would yield a lowerbound limit of fatigue life of trusses. Table 10 shows fatigue lives of trusses of Bentley Creek Bridge with FRP deck system and reinforced concrete deck system based on the given ADTT from the code. Fatigue lives are 63 years and 20 years for FRP and concrete deck systems, respectively. Again, these values confirm that the rehabilitation process indeed improved fatigue life of the structure. In summary, only the west truss of FRP deck system may be susceptible to fatigue failure as shown in Tables 8 and 10. Fig. 15 illustrates a relationship between predicted fatigue 300 W004

15 10 5 0

W004

5 Time (sec)

-5 -10

0

15 10 5

5 Time (sec)

10

0

5 Time (sec)

10

10 Stress Range (MPa)

20

300

W009

0 0

100

10

W009

No. of Cycles

0

Stress Range (MPa)

5

200

0 0

20 W009

Stress (MPa)

FRP

No. of Cycles

Stress Range (MPa)

Stress (MPa)

5

Concrete

Detail category

20 W004

West truss

FRP

Table 9 75-Year (ADTT)SL equivalent to infinite life

exceed half of a constant-amplitude fatigue threshold were used to compute fatigue life. Numerical results show that an estimated fatigue life of the west truss for FRP deck system is approximately 1063 years which is equivalent to an infinite fatigue life. It must be noted that the same procedure was applied to predict fatigue life of the east truss. For reinforced concrete deck system, fatigue life was approximately half of the ones predicted for the case of FRP deck systems. Fig. 14 illustrate results of the critical elements on the west truss. It shows slower rate of decay in stress history compared to FRP deck system. Fatigue life of the west truss members for reinforced concrete deck system is approximately 394 years which is equivalent to an infinite fatigue life. However, a fatigue life of 354 years on the east truss governs in reinforced concrete deck system. Fatigue lives for truss members of FRP deck system and concrete deck system are summarized in Table 8. It must be noted that these values were determined based on ADTTs provided by New York State Department of Transportation. Although, numerical results imply an infinite fatigue life for both systems, it definitely shows that a fatigue of Bentley Creek Bridge has been prolonged by 10

Fatigue life (years) East truss

1 2 3

Table 7 Constant-amplitude fatigue threshold

0

1487

200

100

0 0

Fig. 14. Response history of critical members on west truss of concrete deck.

10 Stress Range (MPa)

20

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Table 10 Predicted fatigue life (75-year ADTT equivalent to infinite life in AASHTO) Location

Fatigue life (years) East truss

1 2 3

West truss

FRP

Concrete

FRP

Concrete

Infinite life Infinite life Infinite life

23 (E113) 20 (E128) Infinite life

63 (W028) 63 (W057) Infinite life

31 (W004) 23 (W009) 31 (W105)

required for computing fatigue life using Eq. (6). As illustrated in Figs. 13c and f, and 14c and f that the number of cycles per truck passage can be greater than 100 cycles at low stress range. The results also show that the number of cycles per truck passage decreases as stress range increases. In this particular study, only those stress ranges that exceed an infinite life limitation were used in predicting fatigue lives. At those stress-range levels, the number of cycles per truck passage is comparable to values specified by the specifications (see Table 6). These results clearly verified the values given by the code.

1500

Fatigue Life (year)

8

W028

ADTT(2002)=275, Fatigue Life=1485 ADTT(2020)=385, Fatigue Life=1063

6. Conclusions and recommendations

1000

500

ADTT(AASHTO)=6525 0

0

1000

2000

3000

4000

5000

6000

7000

ADTT (trucks/day) 1500

Fatigue Life (year)

8

W057

ADTT(2002)=275, Fatigue Life=1485 ADTT(2020)=385, Fatigue Life=1063

1000

500

ADTT(AASHTO)=6525 0

0

1000

2000

3000

4000

5000

6000

7000

ADTT (trucks/day)

Fig. 15. Fatigue life of critical members on west truss of FRP deck.

life and ADTT of two critical members. These curves were plotted based on Eq. (6). Fatigue life of these critical members approaches an infinite life regime as ADTT decreases. This figure also shows the two limit, i.e., upperbound and lowerbound. The upperbound represents the given ADTTs from NYSDOT and the lowerbound represents ADTTs given in Table 9 for an infinite life. 5.3. Fatigue life of steel floor-beams and stringers Similarly, steel floor-beams and stringers can also be categorized as fatigue-damage members. Numerical results indicate that stress range induced on these members lies within an infinite life regime. Hence, they would be well functioning without any load-induced fatigue failures.

A detailed finite element analysis was performed in this study to determine fatigue life of an old rehabilitated truss bridge when subjected to dynamic loading causes by AASHTO fatigue live load. Two different deck systems were investigated, a generic reinforced concrete and fiber reinforced polymer (FRP) deck systems. A finite element model of entire bridge system was developed. Trusses were modeled according to construction drawings. The FE model (with FRP deck system) was validated against load-test results. The numerical results agree well with experimental results. The FRP deck was replaced by a generic reinforced concrete deck in a model to simulate a pre-rehabilitated deck system. Eigenvalues or frequency analyses were performed to determine the first five natural frequencies of vibration of the systems. Assuming 0.5% damping ratio, mass and stiffness-proportional damping parameters were computed and used in the dynamic time-history analyses. Implicit dynamic time-history analyses were conducted with appropriate loading configuration for a moving design fatigue truck. Fatigue life of all truss members, floor-beams and stringers were determined based on a fatigue resistance formula in the code. It was found that this bridge would expect to have 354 years or presumably infinite fatigue life based on anticipated ADTT and new construction assumption. Therefore, the number of years that this bridge has been in service should be counted for to determine the remaining fatigue life. Most importantly, the results show great improvements in fatigue life of the bridge after the replacement of concrete deck by FRP deck. The fatigue life of FRP deck system almost doubles when compared with the reinforced concrete deck system. In addition, dynamic analyses also confirm that a number of cycles per truck passage (n) provided in the code is reasonable for simplified analysis and design of bridges for fatigue limit state.

5.4. Stress-range versus number of cycles

Acknowledgements

In this study, dynamic analysis results were used to determine number of cycles per truck passage, n, that is

The work in this paper was conducted in collaboration with New York State Department of Transportation (NYS-

M. Chiewanichakorn et al. / International Journal of Fatigue 29 (2007) 1475–1489

DOT). The views presented in this document represent those of the authors and not necessarily of the NYSDOT. References [1] Aref AJ, Chiewanichakorn M. The analytical study of fiber reinforced polymer deck on an old truss bridge. Report submitted to New York State Department of Transportation, Transportation Research and Development Bureau, and Transportation Infrastructure Research Consortium, 2002. [2] Aref AJ, Chiewanichakorn M, Alnahhal WI. Temporal thermal behavior and damage simulations of FRP deck. Report submitted to New York State Department of Transportation, Transportation Research and Development Bureau, and Transportation Infrastructure Research Consortium, 2004. [3] Roeder CW, MacRae G, Crocker P, Arima D, Wong S. Dynamic response and fatigue of steel tie-arch bridge. ASCE J Bridge Eng 2000;5(1):14–21. [4] Li ZX, Ko CJM. Fatigue analysis and life prediction of bridges with structural health monitoring data – Part I: Methodology and strategy. Int J Fatigue 2001;23:45–53.

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