optimization of design details in orthotropic steel decks subjected to static and fatigue loads

Xia, Nassif, Hwang, and Linzell

1

OPTIMIZATION OF DESIGN DETAILS IN ORTHOTROPIC STEEL DECKS 1 SUBJECTED TO STATIC AND FATIGUE LOADS 2

3 4

Ye Xia, Ph.D., Post-Doctoral Fellow 5 Rutgers Infrastructure Monitoring and Evaluation (RIME) Laboratory 6

Rutgers, The State University of New Jersey 7 96 Frelinghuysen Road, Piscataway, NJ 08854 8

Email: [email protected] 9 10

Hani Nassif*, Ph.D., P.E., Professor 11 Rutgers Infrastructure Monitoring and Evaluation (RIME) Laboratory 12

Rutgers, The State University of New Jersey 13 96 Frelinghuysen Road, Piscataway, NJ 08854 14

& International Scholar, Dept. of Civil Eng., College of Eng., Kyung Hee University 15 Phone: (732) 445-4414, Fax: (732) 445-4775 16

Email: [email protected] 17 18

Eui-Seung Hwang, Ph.D., Professor 19 Dept. of Civil Eng., College of Eng., Kyung Hee University 20

Kihung-ku, Seochun-dong 1, Yongin-si, Gyeonggi-do, 446-701, S. Korea 21 Email: [email protected] 22

23 Daniel Linzell, Ph.D., PE, Shaw Professor of Civil Engineering 24

Director, Protective Technology Center 25 231L Sackett Building, Dept. of Civil and Env. Eng. 26

The Pennsylvania State University, University Park, PA 16802-1408 27 Email: [email protected] 28

29 30

* Corresponding Author 31

32 33

34 35

36 Word count: 4942 37 Abstract: 242< 250 38 Figures & Tables: 10x250 = 2500 39 Total: 7442 40 Submission Date: 08/01/2012 41

42

TRB 2013 Annual Meeting Paper revised from original submittal.


2

ABSTRACT 1 In recent decades, orthotropic steel decks (OSDs) have been routinely incorporated in long span 2 bridges. Employment of cutouts in diaphragms (or sub-floorbeams) that the OSDs frame into is 3 the most widely used configuration to reduce stress concentration, improve fatigue performance, 4 and control crack propagation. However, the capital cost of cutout fabrication in the United 5 States is relatively high and may not be economically feasible. There is a need to study cost-6 effective modified design details without cutouts and to compare their corresponding flexural 7 and fatigue performance against current design details that utilize cutouts. 8

In this paper, alternative design details (e.g., deck ribs welded directly to the transverse 9 diaphragms using full-penetration welds) utilizing thicker deck plates, but without cutouts, was 10 investigated for potential improvements with respect to fatigue resistance and capital cost. A 11 parametric study was conducted using calibrated finite element models of a portion of the Bronx-12 Whitestone Bridge in New York City to study the effects of cutouts, deck plate thickness, and 13 other important parameters on fatigue performance. Various traffic load combinations and truck 14 types were considered using an elaborate Weight-In-Motion (WIM) database. Results detail 15 equivalent stress ranges at critical locations in the OSDs that were calculated to quantitatively 16 estimate fatigue lives for two orthotropic deck models: one containing cutouts and one with the 17 cutouts removed. Based on these comparisons, recommendations related to overall structural 18 performance are made to ensure a safe and rational design for various OSD options in long span 19 bridges. 20

21 Key Words: 22

Orthotropic steel deck 23 Diaphragm cutout 24 Parametric study 25 Deck thickness 26 Fatigue life estimation 27

28



3

INTRODUCTION 1 Orthotropic steel decks (OSDs) have been routinely incorporated in long span bridges since they 2 are lighter than traditional concrete decks. The primary advantage is to reduce the total dead load 3 carried by the main superstructure elements and substructure, resulting in potentially longer span 4 bridges (1). However, there are two major obstacles when choosing an OSD: fatigue 5 performance and overall cost. OSDs have experienced fatigue problems due to high cyclic 6 stresses and inadequate welding details. Fatigue cracking and propagation were detected on a 7 number of long span bridges and are one of the greatest threats to the integrity of orthotropic 8 steel bridge decks. In response, various designers have devised details that mitigate fatigue 9 susceptibility but are considered difficult to manufacture and, as a result, are costly. In many 10 instances, these OSD configurations require complicated welding details and costly fabrication 11 work (e.g. complicated diaphragm cutouts) that necessitate rigorous quality control procedures. 12

The OSD system was developed in Germany in the early 1950’s and utilizes close ribs 13 and diaphragm cutouts to maintain rib continuity when they passed through the diaphragm webs 14 (1). Previous research related to OSD performance has focused on OSDs with diaphragm cutouts 15 mainly because of optimized stress distributions and the lack of stress concentrations that are 16 perceived to result. These studies investigated various cutout geometry parameters and it was 17 concluded that curved cutouts and increased cutout heights would significantly improve the 18 fatigue resistance of the OSD system (2, 3). Other OSD system parameters, like the geometry 19 and size of the diaphragm/floorbeam, rib, and bulkhead were also analyzed to optimize the 20 designs (4). However, when compared against other countries, the capital cost of cutout 21 fabrication in the United States is relatively high. Hence, alternative technologies are highly 22 desired to technically prevent fatigue cracks and economically reduce the overall cost. 23

OSDs having thicker deck plates are gradually being accepted due to better fatigue 24 resistance despite the increase in weight. Mizuguchi et al. (2004) proposed a new rib-to-deck 25 detail for OSDs having a deck plate that was 1.5 times thicker and closed ribs that were 26 approximately 1.5 times larger when compared against details used for most OSDs (5). The new 27 details were used in a number of new bridges in the New Tomei Expressway that connects 28 Tokyo and Nagoya. Additionally, Xiao et al. (2008) showed that the use of a thick deck plate 29 (5/8 in.) could improve the fatigue durability of rib-to-deck joints (6). However, both of these 30 studies, as well as other available literature, are based on deck configurations containing cutouts. 31 It can reasonably be expected that improved OSD fatigue performance can be realized by 32 increasing the deck plate thickness when cutouts are not employed. 33

To reduce labor and the overall cost of fabrication, an alternative design detail for OSD 34 that utilized a thicker deck plate (3/4 in.), but without cutouts, was considered as one of the 35 design options for the Wittpenn Bridge on Route 7 in New Jersey (7). This option might, or 36 might not, be an overall improvement with respect to fatigue resistance and capital cost. To assist 37 with assessing if this type design change would be beneficial, this paper analytically compared 38 the fatigue resistance at critical locations of OSDs with and without cutouts by examining 39 another long span structure for which OSDs with cutouts have been considered, the Bronx-40 Whitestone Bridge. 41 42



4

1

(a) Bronx-Whitestone Bridge with an OSD 2 37' 0'’

2' 2'’ × 13 = 28' 2'’ 1' 5½’’ 1' 3’’

0.86%345678910111213141516

Lane 1 Lane 2 Lane 3

x

GirderFloorbeam

z

Diaphragm Rib

7’’ 1’ 7’’

With cutout

Without cutout 3 (b) OSD configurations with and without cutout (8) 4

IntermediateDiaphragmFloorbeam

63

Floorbeam 64

With cutout

Without cutout

5 (c) OSD finite element model 6

FIGURE 1 Bronx-Whitestone Bridge and OSD finite element model 7



5

1 FINITE ELEMENT MODEL 2

The preliminary deck design that contained diaphragm cutouts for the Bronx–Whitestone Bridge, 3 as shown in FIGURE 1a, is similar to orthotropic decks on most other bridges in the United 4 States. Both the deck and diaphragm plates are 5⁄8 in. thick. The 5⁄16 in. thick ribs were spaced 5 transversely at 26 in. on center and supported by floorbeams, which were spaced 19 ft. 9 in. on 6 center (see FIGURE 1b). Fillet welds were used for the rib-to-diaphragm connections and 7 complete-penetration groove welds were used for the deck plates. Bulkheads were located inside 8 the ribs and were connected by complete-penetration welds. 9

For this study, an alternate OSD design was introduced based on the Bronx–Whitestone 10 Bridge that eliminated the cutouts. In order to facilitate comparison between models, the optional 11 design, and subsequent model, maintains the global geometric configuration and material 12 properties, eliminates the cutout on the diaphragms and increases the thickness of the deck plate. 13

A detailed finite element (FE) model was developed using ABAQUS (9) to determine the 14 stresses at various critical locations and to assess the fatigue life for various OSD configurations. 15 FIGURE 1c shows two OSD details, with and without diaphragm cutouts. The structure was 16 modeled using shell elements containing 5 integration points in the thickness direction. Instead 17 of utilizing a FE model that was transversely symmetric to reduce computational time, the whole 18 transverse deck system was modeled since the applied loads were anti-symmetric. An AASHTO 19 HS20 fatigue truck with a 15% impact factor was used for the applied loads. Spacing between 20 the fatigue truck’s middle and rear axis was conservatively chosen as 14 ft following AASHTO 21 specifications. The tire pressure area was assumed to be rectangular and 20’’ in width and 10’’ in 22 length following AASHTO specifications (10). 23

24

FE Model Validation 25 To validate the FE model select results from field tests of Bronx-Whitestone Bridge were 26 examined (8). One quasi-static, crawl test (<5 mph traveling speed) with the where the test 27 vehicles’ right wheel was positioned directly over the centerline of Rib 3 (see FIGURE 1c) was 28 selected for comparison. The overall geometry and weight of the test truck was similar to that of 29 the AASHTO H-15. Strain gauges were installed on the deck, floorbeams, ribs and diaphragms 30 at selected positions. Details of the field test are given in the report by Connor and Fisher (8). 31

Stress ranges at bottom ribs from testing and the FE model were compared in FIGURE 2 32 as the testing truck crawled over the sensor area. In the figure, the horizontal axis signified the 33 rear wheel position of the test truck. The OSD bottom ribs were subjected to tensile stresses and 34 the plotted stress ranges were predominantly in the longitudinal direction, which was consistent 35 with results from the installed sensors. As also observed in the figure, estimated stresses from the 36 finite element model matched well with those from in the field. Slight disagreement was 37 observed when the testing truck just approached the sensor area because the FE model 38 considered a limited portion of the bridge. Stress ranges estimated from FE model at other 39 locations, e.g. deck and diaphragms, also showed good consistence with measurements from 40 field test. 41



6

1 (a) Rib 3 (Figure 1b) longitudinal strain (b) Rib 8 (Figure 1b) longitudinal strain 2

FIGURE 2 Comparison between field testing and FE analysis stress ranges 3 4

Evaluation of Structural Performance 5 To simplify examining the performance of OSDs with and without cutouts for various types of 6 truck loads and axle configuration, an influence surface was generated by moving a unit load 7 over all possible locations on the OSD surface and completing a number of static analyses. The 8 resulting surface was used to quantify the influence of different truck locations on the stress 9 pattern within different OSD cutout details. 10

1020

30

020

4060

0

2

4

6

8

Longitudinalposition (ft) Transverse position (ft)

7.07

Max

imum

Stre

ss (k

si)

1020

30

020

40600

2

4

6

8

Longitudinalposition (ft) Transverse position (ft)

6.87

Max

imum

Stre

ss (k

si)

11 (a). As built geometry with cutout (b). Alternative geometry without cutout 12

FIGURE 3: Stress envelope of AASHTO HS20 at bottom of Rib 6 13 between Floorbeams 63 and 64 (see FIGURE 1b ) 14

FIGURE 3(a) and (b) show the stress envelope of AASHTO HS20 for maximum 15 principle stresses at the bottom of Rib 6 between Floorbeam 63 and 64 (see FIGURE 1c) for the 16 as built geometry that contained cutouts as well as the alternative geometry without the cutouts. 17 The position of truck was defined relative to its rear axle location. The figure indicates that the 18 the maximum principle stress in the bottom rib was slightly higher in an OSD with cutouts than 19 in one without cutouts. It is reasonable to conclude from these findings that the configuration of 20 the diaphragm cutout have more localized effects near the diaphragm than in the bottom of rib 21

0 20 40 60-1

0

1

2

3

4

Longitudinal position (ft)

Stre

ss R

ange

(ksi) ← Rib 3

TestingFE model

0 20 40 60-1

0

1

2

3

4

Longitudinal position (ft)

Stre

ss R

ange

(ksi) ← Rib 8

TestingFE model



7

between floorbeams. Moreover, FIGURE 3 also illustrates that local stresses induced by the 1 wheel loads were essentially negligible when the load was more than 2 ft. away transversely 2 from the location of interest. Therefore, it was established that truck loads in the adjacent lane 3 have negligible effects on local stresses generated in the deck plate, diaphragms, and rib walls. 4

Floorbeam 64

IntermediateDiaphragm

I : deck-rib-diaphram zoneII : rib-diaphragm zoneIII: butterfly zoneIV: rib bottom zone

I

II

III

IVII

I

IIICutout crack

Root-weld crack

Cutout crack Root-weld crack

Weld toe crack

Cutout crack

5 a). As built geometry with cutout 6

Floorbeam 64

IntermediateDiaphragm

I : deck-rib-diaphram zoneII : rib-diaphragm zoneIII: butterfly zoneIV: rib bottom zone

I

IV

II

I

Deck fatigue crack

IIIII

III

Root-weld crack

Root crack

Root-weld crack

Toe crack

7 b). Alternative geometry without cutout 8

FIGURE 4: Critical positions and typical fatigue cracks in representative OSD rib 9 10

PARAMETRIC STUDY 11 Based on the aforementioned preliminary analyses and the literature (1, 6), the most sensitive 12 OSD locations to stress concentrations and possible fatigue damage are the zones around the 13 welded connections between the longitudinal rib, transverse diaphragm and the deck plate (deck-14 rib-diaphragm) along with the welded connections between the rib wall and diaphragm web (rib-15 diaphragm). The highest tensile and compressive stress occurs at the bottom of the rib and at the 16 “butterfly”, which are positioned in the lower and higher portions of the cutout as shown in 17 FIGURE 4a. This figure is a magnified view of a single rib between two diaphragms. Critical 18 locations for fatigue cracks in this figure are classified as follows (10): 19

1) I: deck-rib-diaphragm connection zone, fatigue Category C; 20 2) II: rib-diaphragm connection zone, fatigue Category C; 21 3) III: butterfly zone, fatigue Category A in FIGURE 4a and no welding in FIGURE 4b; 22 4) IV: rib bottom zone, no fatigue category defined. 23



8

Maximum principle stresses at adjacent elements of critical locations are extracted to 1 evaluate the structural performance. For instance, maximum stresses of the deck-rib-diaphragm 2 zone (I) is defined as the maximum value of maximum principles stresses of deck, rib, and 3 diaphragm components as circled in FIGURE 4. Note that the butterfly zone (III) of OSD 4 without cutout in Figure 4b, which involves no welding, indicates the exact location as that of the 5 OSD with cutout in Figure 4a for comparison purposes between both OSD types. 6

The most critical parameters affecting stress magnitudes at these locations were identified 7 to be the deck plate thickness, diaphragm thickness and rib thickness (2, 6). Therefore, the 8 following parameters were selected for further study with emphasis being placed on determining 9 to what extent these items influenced stresses at the critical locations listed above: 10

1) Deck plate thickness: ½, 5/8, ¾, 7/8 and 1 in.; 11 2) Diaphragm thickness: ½, 5/8, ¾ in, 7/8 and 1 in. ; 12 3) Rib thickness: ¼, 5/16, 3/8 in, and 1/2 in. ; 13 14

Effect of Deck Plate Thickness 15 A ½ in. deck plate has been used for decades for OSDs to reduce total deck weight. Current 16 existing orthotropic decks were mostly designed using a 5/8 in. thickness. However, 3/4 in. 17 thickness has been recently employed. Hence, the two OSD designs were analyzed with deck 18 plate thicknesses of ½, 5/8, ¾, 7/8 and 1 in. 19

20 (a) Stress comparisons, locations I and II (b) Stress comparisons, locations III and IV 21

FIGURE 5: Maximum stresses for various deck thicknesses 22 FIGURE 5a shows maximum stresses at the deck-rib-diaphragm zone (I) and rib-23

diaphragm zone (II), highlighted in FIGURE 4a using red circles, with various deck thicknesses 24 for the OSD geometries with and without the cutouts. In addition to showing the maximum stress, 25 weight increase percentages were also calculated by using the 5/8 in. thickness as a baseline. The 26 total weight values that were estimated accounted for the entire deck system, including the deck 27 plate, ribs, diaphragms, rib stiffeners, diaphragm flanges, and floorbeams. In FIGURE 5, analysis 28 cases are denoted using both a roman numeral (for the critical location as listed above) and the 29 OSD cutout detail (“with” or “without” cutout). For instance, Case “I-W” examines the stresses 30 at critical area “I” for the OSD “with” a cutout. 31

As shown in FIGURE 5 (a), the two most critical locations (I and II) were examined and 32 both were initially defined as fatigue Category C according to AASHTO. For location I with the 33 cutout, I-W, peak stress decreased sharply when deck plate thickness increased from ½ to 3/4 in. 34



9

When the deck plate thickness increased from 5/8 to ¾ in., the maximum stress for I-W 1 decreased by 16.81% from 6.48 to 5.39 ksi while the total weight per span increased by only 2 8.15%. Increasing the deck plate thickness from ¾ to 1 in. resulted in limited reduction in 3 maximum stresses. This was because stresses in deck plates decreased but those in the 4 connection area (e.g. to the adjacent diaphragm) did not decrease appreciably. Hence the 5 maximum stress would shift to an adjacent location when deck plate thickness was larger than ¾ 6 in. A similar trend was observed for I-W/O where, with a very similar weight increase, 7 maximum stress decreased by 29.16% from 7.29 to 5.16 ksi, when the deck plate thickness 8 increased from 5/8 to ¾ in. Note that this stress reduction was more pronounced than the stress 9 reduction at the same location for the OSD design with cutouts. 10

Location III contained no welding but had some observed stress concentrations (see 11 FIGURE 4a). As shown in FIGURE 5b, peak stresses in case III-W were 12.84 ksi while stresses 12 in the same location for the geometry without the cutout were considerably less, 4.92 ksi. 13 Location IV was at the bottom of the ribs and yielded relatively high stresses due to localized 14 moment. The stresses in this area were not as sensitive to cutout geometries or deck thickness as 15 the aforementioned locations. 16

17 (a) Stress comparisons, locations I and II (b) Stress comparisons, locations III and IV 18

19 (c) Stress comparisons, locations I and II (d) Stress comparisons, locations III and IV 20

FIGURE 6 Maximum stresses for various diaphragm and rib thicknesses 21

22



10

Effect of Diaphragm Web Thickness 1 Diaphragm thickness has varied between 1/2 and 3/4 in. for most current OSD bridge designs. It 2 was observed from FIGURE 6a and 6b, which examine peak stresses for various diaphragm 3 thicknesses, that the thicker the diaphragm, the lower the peak stresses in all critical locations. 4 Greater stress changes as a result of increased diaphragm thickness changes were observed at 5 location III area but limited effects were observed at locations I, II and IV. 6

It was noticed that by increasing the diaphragm thickness from 3/8 to ¾ in. the maximum 7 stress for I-W decreased by 5.48% from 6.48 to 6.13 ksi while the total weight per span increased 8 by only 0.89%. In similar fashion, stresses for I-W/O decreased by 3.38% from 7.29 to 7.04 ksi 9 with a weight increase of 1.32% (see FIGURE 6a). Therefore, increasing the diaphragm 10 thickness appeared to be an efficient and economical way to reduce maximum stresses, 11 especially for OSDs with cutouts. There was a more pronounced effect on maximum stresses for 12 OSDs without cutouts than those with cutouts because diaphragms were more integrally 13 connected to the deck and longitudinal ribs when compared to a design that had the cutouts. Peak 14 stresses in locations II and IV decreased by less than 1 ksi with a maximum increase in the 15 diaphragm thickness. Around the butterfly (III) in OSDs with the cutout, a significant stress 16 decrease was observed due to the diaphragm thickness increase. A 3/4 in. thick diaphragm 17 yielded somewhat better results when compared to a 5/8 in. diaphragm, but the 5/8 in diaphragm 18 would be easier to weld. 19

Tension

TensionCompression

Compression

Peak value-6.73 ksi7.35 ksi4.61 ksi

-3.19 ksi

20 a). As built geometry with cutout 21

Compression Tension

Compression

Peak value-4.58 ksi4.46 ksi

-2.72 ksi3.25 ksi

Tension

22 b). Alternative geometry without cutout 23

FIGURE 7 Diaphragm web horizontal stress contours 24



11

It appears from the finding discussed above that using an OSD design without cutouts 1 was effective for reducing peak stress values at a number of critical locations. These findings are 2 substantiated by FIGURE 7, which plots horizontal stress (S11) contours in the diaphragm web 3 for OSDs with and without cutouts when the right rear truck wheel is placed between Rib 3 and 4 Rib 4 from FIGURE 1b. Various symbols are used to identify critical stress magnitudes, senses 5 and locations in the contours in the figure, with and denoting maximum compressive and 6 tensile stresses, respectively, while and representing the stresses of interest in the web plate. 7 In FIGURE 7a, which is for the OSD design with the cutouts, the peak compressive stress occurs 8 at the butterfly location (III) and the two peak tensile stresses occur at the butterfly (III) and 9 deck-rib-diaphragm location (I), respectively. In FIGURE 7b, which is for the OSD design 10 without the cutouts, the peak compressive stress occurred at rib-diaphragm location (II) and the 11 two peak ensile stresses happened at deck-rib-diaphragm (I) and rib-diaphragm (II) locations. 12 These results indicated that: 1) the stress distribution inside the diaphragm webs depend on live 13 load position; 2) maximum compressive stress at location III was due to the wheel load 14 traversing the center of the side lane; and 3) using an OSD design without a cutout was effective 15 in reducing maximum principal stress magnitudes. 16 17 Effect of Rib Wall Thickness 18

The influence of rib wall thickness was considered by examining four different values: ¼, 5/16, 19 3/8 and ½ in. Increasing the rib wall thickness from 5/16 to 3/8 in. decreased the maximum stress 20 for I-W by 2.59% from 6.48 to 6.31 ksi while the total weight per span increased by 4.74% (see 21 FIGURE 6c). It was observed that stress reduction trends caused by rib thickness variations 22 followed similar trends to those previously discussed for diaphragm thickness variations (see 23 FIGURE 6d). One difference was that, at critical locations, the efficiency with which an increase 24 in rib thickness decreased critical stresses, which was quantified by comparing the stress 25 decrease percentages against weight increase percentages, was much lower than that for 26 increases in the deck and diaphragm thicknesses. 27

There are many reasons for high stresses around diaphragm cutouts and adjacent to OSD 28 decks and ribs. When live loads act on deck plates away from the floorbeam of interest the deck 29 plate bends in a transverse direction. As a result, the longitudinal ribs distort out of plane, 30 especially near their bottom flanges. 31

Based on the previously discussed results, the following recommendations can be made: 32 • The deck components demonstrate similar trends in behavior as thickness parameters 33

were varied. It appears that an increase in the thickness of the deck plates and the 34 diaphragm webs generate better results than that for increases in rib wall thickness when 35 efficiency is measured as a function of the reduction in maximum stresses in critical areas 36 coupled with the corresponding increase in weight. 37

• In addition to lower anticipated capital costs, OSD designs without a cutout have lower 38 stress ranges than those with a cutout at most locations except the deck-rib-diaphragm 39 connections. The capacity at these deck-rib-diaphragm locations is appreciably improved 40 by increasing the deck plate thickness from 5/8 to ¾ in. 41

42



12

FATIGUE LIFE ANALYSIS BASED ON WIM DATA 1 The parametric study results achieved so far are based on static analyses. As a result, the true fatigue 2 life of the OSD design components is not quantifiable based on stress ranges obtained from these 3 limited studies. Therefore, a live load simplification approach was proposed along with a more 4 precise derivation of equivalent stress ranges to convert values obtained from the live load analyses 5 performed herein into comparable fatigue service lives. 6

Fatigue stress-number of cycle (S-N) curves presented in AASHTO (10) are widely used 7 to estimate fatigue life by providing designers with an approximate relationship between stress 8 ranges and the number of stress cycles to failure. The S-N curves were developed via 9 experimental testing of typical fatigue sensitive details with results from the tests being used to 10 produce the curves within a certain confidence interval. Techniques are available to convert 11 stress ranges at certain location to equivalent stress ranges that can be used with the S-N curves 12 to more accurately estimate fatigue life cycles (11). Results can also be used to identify a 13 constant amplitude fatigue limit (CAFL) below which fatigue damage accumulation will not 14 occur under a constant amplitude loading. The current procedure for fatigue life estimation in the 15 AASHTO Specifications utilizes an equivalent stress range with the direct extension of the S-N 16 curves of slope -3 to below the CAFL. 17

18

Formulations of Fatigue Accumulation 19 The equivalent stress range fatigue life estimate using the S-N curves should be representative of 20 live induced load stress ranges within critical components. The relationship between fatigue life 21 in cycles and an equivalent stress range with consideration of damage accumulation is described 22 below. 23

To account for different stress ranges due to various truck loads, a linear damage 24 accumulation law is usually assumed (11): 25

i

i i

nTN

=∑ (1) 26

where in is the number of applied load cycles at constant stress level iS and iN is the fatigue 27 life at constant stress level iS obtained from the S-N curve. T is the fraction of life consumed by 28 exposure to the load cycles, experimentally found to be between 0.7 and 2.2. According to 29 Miner’s rule (11), when the fraction reaches 1 failure occurs. 30

For a linear S-N curve with a slope of –m, Schiling et al. (1978) stipulated that (12): 31

i

i i

i i e

nn CN N

= =∑

∑ (2) 32

eN is the computed fatigue life using the equivalent constant amplitude stress range, reS , and 33

/ me m reN C S= (3) 34

As stipulated in the AASHTO (10), m=3 and mC is the detail category constant taken 35 from AASHTO (e.g., 844.0 10mC = × ksi3 for Detail Category C and C’). Equation (3) gives the 36 linear S-N curve in log-log form by combining the above two equations and solving for reS as 37 follows: 38



13

1/3

3re i ri

i

S Sγ⎡ ⎤= ⎢ ⎥⎣ ⎦∑ (4) 1

where /i in Nγ = is the percentage of occurrence of stress range riS in the histogram. 2 The above equation is the equivalent stress range for fatigue life estimation under 3

variable amplitude stress ranges as in AASHTO (10). As a result of these simplifications, 4 Equation (3) can be written as, 5 3

3 /e reN C S= (5) 6 7

Live Load Model Based on WIM Truck Data 8 Stress ranges at locations of interest on the OSD components under an HS20 truck load can be 9 obtained using aforementioned finite element analyses. However, on an actual bridge there are 10 many vehicle configurations and weights that traverse them and it is quite difficult to simulate all 11 the load cases using FE models for an adequate fatigue assessment. To overcome these 12 limitations and also provide additional information on accumulative fatigue damage due to traffic 13 loads, a general solution to the simplification of vehicular loading on a bridge was introduced 14 herein. The objective of this approach was to find the most representative truck model(s) to apply 15 to the FE models to simulate accumulative damage caused by all possible live loads. As a result, 16 the obtained equivalent stress range and hence the estimated fatigue life could be obtained for 17 comparison between OSD designs with and without cutouts. 18

All live loads used for the solution were measured using Weigh-in-Motion (WIM) 19 systems and were simplified into limited groups based on least square estimation technique. Each 20 group could be represented by one truck model with statistically determined parameters, such as 21 axle spacing and axle load ratio. The optimized truck models were then used to more accurately 22 consider local truck traffic and estimate maximum stress values at locations of interest. The 23 larger the number of truck models used to correlate the simulations to the WIM data the more 24 accurate the simulation results. Since the most important factor that affected the maximum 25 stresses was the vehicle weight, maximum stresses due to one category of live loads were 26 proportional to truck weights from the WIM data. Other factors, such as the axle number and 27 spacing, could be simplified using the proposed approach without sacrificing necessary accuracy. 28 Trivial error was observed when more than two truck models were used for estimation of actual 29 WIM data. It was found that 12-months of truck data from the WIM system could be represented 30 using one truck model to obtain adequate stress ranges for fatigue life comparison purposes for 31 the OSD designs with and without cutouts. 32

33

Fatigue Life Results Analysis 34 As presented in the previous section, systematic parametric studies were conducting using finite 35 element analysis and local stresses at the locations of interest were obtained to compare the two 36 OSD designs. Based on these results, critical locations for the OSD design with cutouts were at 37 the toe of the weld connecting the diaphragm web to the longitudinal ribs (II in FIGURE 4) and 38 in butterfly location at the diaphragm web (III). AASHTO fatigue categories for these locations 39 were C and A, respectively, as discussed earlier. To further examine and compare the OSD 40 designs, estimated stress ranges were obtained at these locations using the proposed live load 41 simplification approach (TABLE 1). The table presented the procedure of fatigue strength 42



14

calculation, and as a result, the fatigue strength at locations II controlled the fatigue service life 1 over that at locations III for OSD design with cutouts. In the table, trucks lighter than 20 kips 2 were not accounted for and stress ranges lower than 1 ksi were considered as noise. The Average 3 Daily Truck Traffic (AADT) was assumed to be 50,000 trucks based on the WIM data. 4

As for the OSD design without the cutouts, the critical location was the deck-rib-5 diaphragm (I) with a deck thickness of 5/8 in. and it would shift to the rib-diaphragm location (II) 6 when the deck thickness increased to 3/4 in. Table 2 shows a summary of the equivalent stresses 7 and further fatigue service life at various critical locations in the OSDs with and without cutouts. 8 The summary in Table 2 was performed using various deck thicknesses and the procedure 9 presented in TABLE 2. Since stress ranges for the fatigue Category A connections were low, 10 they are not listed in the table. 11

12 TABLE 1 Fatigue strength calculation using 12-months of WIM data 13

with cutout, location II with cutout, location III

riS (ksi)

Cycles (N)

Frequency ( iγ )

3i riSγ riS

(ksi) Cycles

(N) Frequency

( iγ ) 3

i riSγ

2 593993 19.60% 1.57 2 256086 8.11% 0.65 3 626731 20.68% 5.58 3 398985 12.63% 3.41 4 567263 18.71% 11.98 4 363354 11.50% 7.36 5 418062 13.79% 17.24 5 332756 10.53% 13.17 6 262272 8.65% 18.69 6 312172 9.88% 21.35 7 197613 6.52% 22.36 7 307830 9.74% 33.43 8 163617 5.40% 27.64 8 269036 8.52% 43.61 9 126252 4.16% 30.36 9 194856 6.17% 44.97

10 55186 1.82% 18.21 10 156170 4.94% 49.44 11 14405 0.48% 6.33 11 128781 4.08% 54.26 12 3528 0.12% 2.01 12 112401 3.56% 61.49 13 1370 0.05% 0.99 13 79945.6 2.53% 55.60 14 476 0.02% 0.43 14 92046 2.91% 79.96 15 182 0.01% 0.20 15 72614 2.30% 77.58 16 122 0.00% 0.16 16 44181 1.40% 57.29 20 194 0.01% 0.51 20 35215 1.11% 89.18

>20 32 0.00% 0.16 >20 2424 0.08% 20.72 Effective stress range

3 1/3( )re i riS Sγ= ∑ 5.46 ksi Effective stress range

3 1/3( )re i riS Sγ= ∑ 8.93 ksi

Fatigue category C Fatigue category A Fatigue life in cycles, N 2.70E+07 Fatigue life in cycles, N 3.51E+07

14



15

TABLE 2 Fatigue life comparison using 12-months of WIM data 1

Parameters Deck

thickness (in)

Critical location

Fatigue category

Equivalent stress range

(ksi)

Fatigue life in cycles

Fatigue life in years

with cutout

5/8 II C 5.46 2.70E+07 54 5/8 III A 8.93 3.51E+07 70 3/4 II C 5.02 3.47E+07 69 3/4 III A 8.71 3.78E+07 76

without cutout

5/8 I C 5.76 2.31E+07 46 3/4 II C 4.98 3.56E+07 71

Figure 8 shows a comparison of fatigue life for the OSD designs with and without cutouts 2 as a function of deck plate thickness. This result is consistent with the stress distribution in 3 FIGURE 5a, with the OSD detail design having a thicker deck plate (3/4 in.) and no cutout 4 producing slight improvement in fatigue life. Increasing the deck plate thickness would help to 5 extend the fatigue life by reducing the vehicular bending moment for both design options. When 6 compared to the OSD designs with the cutout, those without the cutout benefited less from an 7 increase of deck thickness above 7/8 in. This was mainly because no cutout geometry was more 8 integrated and stiffer than this design. Hence, it suffered more from local stress concentrations 9 caused by out-of-plane motions and distortion inducing secondary stresses. 10

11 FIGURE 8 Fatigue life comparison for OSD with and without cutout 12

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CONCLUSIONS AND SUGGESTIONS 14 A parametric study was performed that examined the influence of various parameters, including 15 deck plate thickness, on stress ranges generated at critical locations under applied traffic load for 16 two OSD design options on the Bronx-Whitestone Bridge, one containing cutouts in the 17 transverse diaphragms that accommodated the deck ribs and one that did not use cutouts and 18 directly welded the ribs to the diaphragms webs. A general solution for simplifying vehicular 19 loads on a bridge was also introduced to facilitate fatigue life analyses by estimating 20 accumulated damage under applied live loads. Overall fatigue performance was compared for the 21



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original OSD design, that which used the cutouts, and the alternative design that did not utilize 1 cutouts. The main conclusions from the study are summarized as follows: 2

• Increasing the deck plate thickness and the diaphragm web thickness were found to 3 significantly improve the fatigue resistance of both OSD systems while simultaneously 4 keeping weight under control. However, increases in the diaphragm web thickness were 5 found to have limited effect on the fatigue resistance. 6

• As for the OSD design with cutouts, the component most sensitive to fatigue damage was 7 the toe of the weld connecting the diaphragm web to the longitudinal ribs (II in FIGURE 8 4a). It was also observed that, for this design, an increase of deck plate thickness 9 improved the fatigue performance by decreasing the detrimental in-plane moments in the 10 deck components. 11

• For the OSD system without cutouts, the critical location was identified to be at the rib-12 deck-diaphragm zone (I) for a deck plate thickness of 5/8 in. but the critical location 13 shifted to rib-diaphragm zone (II) when the deck plate thickness increased to 3/4 in. 14 Therefore, an increase in deck thickness did not only relieve the bending moment due to 15 traffic loads but also enhanced the fatigue resistance, especially at the rib-deck-16 diaphragm connections. 17

• For the designs and parameters that were examined, the OSD design that had a thicker 18 deck plate without cutouts had optimal overall fatigue performance. 19 20

ACKNOWLEDGEMENTS 21

Advice and suggestions from Prof. Ben T. Yen in Lehigh University to the first author are 22 acknowledged. The help of Dr. Yingjie Wang and graduate student Dan Su is also acknowledged. 23 24 REFERENCES 25

1. Chen, W. F., and L. Duan. Bridge engineering handbook. CRC Press, 2000. 26 2. Connor, R. J. Influence of cutout geometry on stresses at welded rib-to-diaphragm 27

connections in steel orthotropic bridge decks. In Transportation Research Record: 28 Journal of the Transportation Research Board, No. 1892, Transportation Research Board 29 of the National Academies, Washington, D.C., 2004, pp. 78-87. 30

3. Abdou, S., W. Zhang, and J. W. Fisher. Orthotropic deck fatigue investigation at 31 Triborough Bridge, New York. In Transportation Research Record: Journal of the 32 Transportation Research Board, No. 1845, Transportation Research Board of the National 33 Academies, Washington, D.C., 2003, pp. 153-162. 34

4. Oh, C. K., K. J. Hong, D. Bae, H. Do, and T. Han. Analytical and experimental studies on 35 optimal details of orthotropic steel decks for long span bridges. International Journal of 36 Steel Structures, Vol. 11, No. 2, 2011, pp. 227-234. 37

5. Mizuguchi, K., K. Yamada, M. Iwasaki, and S. Inokuchi. Rationalized steel deck 38 structure and large model test for developing new type of structure. In Proc., Int. 39 Orthotropic Bridge Conf., ASCE, CD-ROM, Reston, VA, 2004, pp. 675-688. 40

6. Xiao, Z. G., K. Yamada, S. Ya, and X. L. Zhao. Stress analyses and fatigue evaluation of 41 rib-to-deck joints in steel orthotropic decks. International Journal of Fatigue, Vol. 30, 42 No. 8, 2008, pp. 1387-1397. 43



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7. New Jersey Dept. of Transportation. Design and Fabrication of Orthotropic Deck Details. 1 Request For Proposals (and addendum), Project No. 2011-14, Bureau of Research, New 2 Jersey, 2011. 3

8. Connor, R. J., and J. W. Fisher. Results of Field Measurements Made on the Prototype 4 Orthotropic Deck on the Bronx-Whitestone Bridge New York City, NY. ATLSS Report 5 04-03, 2004. 6

9. ABAQUS Standard User’s Manual Version 6.12. Hibbit, Karlsson and Sorensen Inc., 7 Pawtucket, RI, 2012. 8

10. AASHTO. Load Resistance and Factor Design, Bridge Design Specifications, 5th 9 Edition. America Association of State Highway and Transportation Official, Washington, 10 D.C., 2010. 11

11. Miner, M. A. Cumulative Damage in Fatigue. Journal of Applied Mechanics, Vol. 12, 12 1945, pp. A159-A164. 13

12. Schilling, C. S., K. H. Klippstein, J. M. Barsom, and G. T. Blake. Fatigue of welded steel 14 bridge members under variable amplitude loading. NCHRP Report 188, Transportation 15 Research Board, Washington, D.C., 1978. 16

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