FATIGUE OF DEFORMED WELDED WIRE REINFORCEMENT Wilast Amorn, University of Nebraska, Omaha, NE Amgad Girgis, Ph.D., University of Nebraska, Omaha, NE Jeremy Bowers, E.I., HGM Engineering Company, Omaha, NE Maher K. Tadros, Ph.D., P.E., University of Nebraska, Omaha, NE

FINAL REPORT

ABSTRACT The use of welded wire reinforcement (WWR) as an alternative to traditional mild steel reinforcing bars has many advantages. WWR has a higher yield strength and higher quality control, and results in significantly lower construction labor costs. However, many designers are still reluctant to use WWR as an alternative to mild steel reinforcing bars, due to unavailability of fatigue design guidance in the American Association of State Highway and Transportation Officials (AASHTO) Bridge Design Specifications. This paper reports on an extensive cyclic testing program on deformed high strength WWR. Based on this testing, a conservative stress range formula similar to the existing one for mild reinforcing bars is presented for possible adoption in the AASHTO LRFD Specifications. The Unified Fatigue Approach, an alternative format to fatigue provisions for all materials, is also discussed. In addition, full monotonic axial tensile stress- strain relationships are presented.

1. Keywords: Welded, Wire, Reinforcement, Fabric, Fatigue, Cyclic

1

INTRODUCTION Welded wire reinforcement (WWR) has many advantages over traditional mild reinforcing steel. WWR boasts higher yield strength, higher quality control, and significantly lower construction labor costs. However, many designers are reluctant to use WWR as a structural reinforcement alternative to mild steel reinforcing bars, due to a lack of fatigue design guidance in the American Association of State Highway and Transportation Officials1 (AASHTO) Specifications. The need for this guidance is more pressing now than ever. The National Bridge Inventory (NBI) has over 600,000 bridges nationwide in their database. At an average of 5000 square feet of deck surface and 15 pounds of steel per square foot, there are over 22 million tons of steel in the NBI bridge decks. Over 30 percent of these bridges have been determined to be either structurally deficient or functionally obsolete. This estimate considers only those bridges included in the NBI database. Most of the deficiency is in the deterioration of the bridge decks. The use of WWR can greatly expedite replacement and repair efforts. The current code does not require deck reinforcement to be checked in fatigue. Fatigue must be checked only in overhangs with high moment due to live load. As technology advances and thinner decks or other innovations are used, however, fatigue will be an issue. WWR use is also continuing to increase in the precast industry. Precast bridge girder systems have been growing at a rapid pace when compared to structural steel girder bridges. WWR has been the standard product for bridge I-girders and Inverted Tee girders in Nebraska and a few other states. Several precast concrete producers in these states have reported a 30 to 40 percent savings in labor costs when WWR is used. It has been reported by a few producers that the time needed to fabricate a beam in a long-line bed has been reduced from two days to one day when WWR is used. There is a strong potential market for WWR. The code also does not require reinforcement in girder webs to be checked in fatigue. However, fatigue has never been a problem with girder webs; AASHTO limits shear capacity so that the web is not designed to crack under service loads. But as the industry shifts to the LRFD code, where significantly higher shear capacities are permitted, fatigue becomes an issue. At higher concrete strengths the section is allowed to crack at unfactored service loads with the LRFD code, making fatigue of the reinforcement an important concern. WWR also has the potential to be used in other applications in the precast industry. Consider a standard short span bridge consisting of “plank” elements. The reinforcement of an interior plank is shown in Figure 1. In the future, the reinforcement in this application could be replaced with the equivalent WWR shown in Figure 2. In this situation, the WWR will be the main tensile reinforcement and must obviously be checked for fatigue.

2

D10xD10 @ 12"x12"

# 4 (typ)

12"

D31 @ 4" (two layers) 7-#8 bars

1.5"

2'-10"

2'-10" D20 @6" for a distance to be determined

Figure 1: Plank Element with Conventional Reinforcement

Figure 2: Plank Element with Welded Wire Reinforcement

Attempts have been made to persuade Committee T10, the AASHTO Subcommittee on Concrete, to allow Grades 75 and 80 WWR to be used as auxiliary reinforcement for design of prestressed members. These attempts have been met with resistance due to a lack of evidence that the higher strength does not create excessive cracking at service loads, therefore unsafe live load cyclic stresses. When a fatigue limit is included in the AASHTO Specifications for WWR, similar to the provisions that currently exist for mild reinforcement, prestressing strands, and structural steel members, then WWR will be specified for more of these applications.

BACKGROUND Structural member fails due fatigue when cracking develops under repetitive loads that are less than static load capacity. S-N curve is usually used to present the resistance of a material to fatigue loadings, where S is a characteristic stress, often either the stress range or a function of the maximum and minimum stress, and N is the number of cycles to failure, also called fatigue life. Semi-log plots are usually used to present fatigue loading data on concrete and reinforcement steel, where stress function S is decreasing with the increase of the independent variable, fatigue life, log N, leading to a linear regression line. Three sequential stages lead to fatigue of the member. The process starts with the initiation of the cracking. This stage is followed by propagation of cracking, in which microcracking gradually takes place in the concrete or cracking grows in a steel element. Slow growth in

3

cracking is followed by a brief period of quick growth, which leads to the third stage: fracture.

Stress Range

Normal distribution is usually acceptable as representative of fatigue data. The line parallel to the mean regression line and located at distance equal to 1.96 times the standard deviation divides the area under the normal distribution curve into 95% and 5%. The equation of the lower line gives 95% confidence that any specimen will fail conservatively above that line or gives 5% confidence that the specimen will fail unconservatively below the line. As shown in Figure 3, the lower line with 95% confidence level or 95% probability of survival is commonly used.

P= 9 Me 5 % a P= n 5%

Log N Figure 3: Regression of fatigue data As explained earlier the initiation and propagation of a cracks under cyclic loading leading to the fatigue failure in reinforced (nonprestressed) bars. When the crack is propagating the stress intensity factor at the crack front is increasing to a critical value at which the bar will fracture. The stress range is the predominant factor in determining the fatigue life. Minimum stress is also significant factor. Tilly1 summarizes the factors that are influencing the fatigue life and distinguished between the important factors and the minor factors that are affecting the fatigue life. Variable that are important are the following: 1- Stress range 2- Minimum stress 3- Geometry of deformation on a bar 4- Radius of bends 5- Welding 6- Corrosion Factors that have minor effects on fatigue strength 4

1- Bar size 2- Bar orientation 3- Yield strength 4- Chemical composition 5- Other Tilly also concluded that the type of bar is not an important factor that affecting the fatigue life. The endurance limit is the limiting stress range below which the specimen will have long-life and maybe able to sustain virtually unlimited number of cycles. Above this limit the specimen will sustain only finite-life. One to two million cycles is the life beyond which the specimen assumed to sustain long life. In some studies five million cycles is recommended.

The current rebar fatigue formula was developed in a research project conducted for the National Cooperative Highway Research Program by Hanson et al.2 The research report was published in 1976 as NCHRP Report 164, titled “Fatigue Strength of High Yield Reinforcing Bars.” Grade 60, #8 bars were the primary targets. Other sizes and grades were also tested. The formula was adopted without any revision in ACI documents and in the 1994 Edition of the AASHTO LRFD Bridge Design Specifications. The research was done on single bars embedded in small beams as flexural reinforcement with two-point loading applied at the rate of 250 to 500 cycles per minute. A total of 353 concrete beams were tested. However, most of the tests were done for the “finite-life” region where the number of cycles was between 10,000 and 1,000,000. The researchers concluded that the “long-life” region of 1 to 5 million cycles was the more important one for design purposes and based their conclusions of that region on Phase II of their work. The formula was, essentially, based on only the very few tests performed on #8 Grade 60 bars from “Manufacturer A” with a minimum stress of 6 ksi, and a fatigue life in excess of 2 million cycles. The researchers also reported that the fatigue limit of interest to the bridge designer is not sensitive to concrete beam dimensions, concrete material properties, bar size, steel grade, or steel metallurgy. The formula for rebar in Article 5.5.3.2 of the AASHTO LRFD Specifications3 is: r f r = 21 − 0.33 f min + 8  h

E-1

where: fr = the allowable steel stress range fmin = the minimum live load stress combined with the more severe stress from either the permanent loads or the shrinkage and creep-induced external loads; positive if tension, negative if compression (ksi). (r/h) = ratio of base radius to height of rolled-on transverse deformations; if the actual value is not known, 0.3 may be used.

5

It is worth mentioning that the European and the Japanese fatigue specifications allow for higher stress range than AASHTO LRFD specifications. A safe fatigue life for all stresses above the endurance limit is represented by E-2, developed by Hanson et al.2 r −5 −5 −5 Log N = 6.1044 − 4.07(10 ) f r − 1.38(10 ) f min + 0.71(10 ) f u − 0.0566 A s + 0.3233  E-2 h It was also found that with the decrease of the bend-to-bar diameter ratio, the reduction of fatigue becomes larger.4,5 The reinforcing bar deformations is very important in developing bond strength between the bars and the concrete. However in WWR, bond strength is essentially developed from the presence of cross wires. Stress concentrations are developed in the reinforced bars at the base of a transverse lug, the intersection of a lug and a longitudinal rip, or at brand mark locations. Fatigue fractures are usually observed to initiate in tests on bars embedded in concrete beams at these locations that are liable to stress concentrations. Studies6,7 have shown that width, height, angle of rise, and base radius of a protruding deformation affect the magnitude of stress concentration. The stress concentration factors in reinforcing bar lugs are usually in the range of 1.5 to 2.0. The same study has shown that stress concentration increase at an external notch when an axially loaded bar is tested. Several studies have also indicated that there are small differences between the fatigue strength of bars made with old or new rolls at steel mills. Fatigue strength of the bars may also be influenced by the orientation of the longitudinal rib. 8 Most fatigue experiments9 in the past were focused on testing reinforcing bars embedded in structural concrete members. MacGregor et al.10 reported fatigue tests on reinforced concrete beams containing #5, #8, and #10 reinforcing bars with yield strength of 40, 60, and 75 ksi respectively. They concluded that fatigue strength of reinforcing bars was relatively insensitive to the tensile strength of the bar metal. However, the fatigue strength of the bars was appreciably lower than that of the base metal. This difference resulted from the stress concentration at the base of the deformations and a decarburized layer on the outside of the bars. However, this investigation was performed on fatigue tests of hot rolled deformed reinforcing bars embedded in concrete beams. Pasko11 performed fatigue tests on #5 deformed reinforcing bars conforming to ASTM A615 Grade 60, welded to #3 plain transverse reinforcing. Tack welding of reinforced bars was found to reduce the fatigue strength by one third of that of non-welded bars,8 while buttwelding has been proven to have no effect on fatigue strength.7,12 Hawkins13 performed fatigue tests on plain straight wires with cross welds, cut from 6 x 6 – W2 x W2, and fatigue loading on slabs with the same reinforcement. The high stress range values resulted in fatigue fracture of the wire before the endurance limit was reached. Hawkins14 performed another extensive testing program on long-life fatigue of WWR with the goal of using WWR as a replacement for deformed bar reinforcement in bridge decks. The fatigue testing was performed on twelve concrete slabs with welded wire reinforcement, both with and without epoxy coating. The results were 20 ksi stress range and fatigue life of

6

at least 1x106 for uncoated fabric for a 95% probability of survival, as well as 22 ksi and 3x106 cycles for coated fabric. Fatigue fractures always occurred at welded intersections and the results clearly showed that in many ways WWR is more desirable than deformed bars for fatigue applications because after first wire fracture alternate load paths take over through the fabric and multiple fractures have to occur before the performance of the concrete panel is severely impacted. Prior to this study, WWR was considered to have an unacceptable level of performance in deck slabs, based on work done by Bianchini and Kesler in Illinois in the 1960s. As a result, AASHTO Specifications did not allow the use of WWR in bridge decks. Hawkins then came to the conclusion in his study that the poor performance was due to the manner in which the reinforcement was manufactured at that time. Welding heat, penetration, upset time, and other process-related factors were relatively variable difficult to maintain at a given setting. In our current testing, as well as the tests reported in Reference 14, WWR were fabricated using a welder in which controls on welding heat, penetration, and upset time were excellent and constant from weld to weld in a given line and across the width of the sheet. Hawkins 14 documented the differences by making microscopic evaluations of sectioned welds and dimensional and metallurgical checks of penetrations and heat-affected zones. The results showed that stress ranges of 19 ksi for uncoated fabric and 20 ksi for epoxy coated fabric were less than the fabric’s fatigue limit for 5x106 cycles and a 95% probability of survival. For a 20 ksi stress range, the fatigue life was at least 1x106 for uncoated fabric for a 95% probability of survival and 22 ksi for 3x106 cycles for coated fabric. No systematic correlation existed between the fatigue life of the fabrics and the penetration depths at the welded intersections. Fatigue fractures always occurred at welded intersections and the results clearly showed that in many ways WWR is more desirable than deformed bars for fatigue applications because after first wire fracture alternate load paths take over through the fabric and multiple fractures have to occur before the performance of the concrete panel is severely impacted. Clearly this WWR had a long life fatigue performance as good as that for reinforcing bars per AASHTO LRFD 5.5.3.2. Hawkins’s work is highly relevant to this study. ACI committee 215 report9 summarized work that has been done in both the United States and West Germany on WWR. More variability and data scattering were noticed when the fatigue of WWR strength compared to straight unwedded bars. The fatigue strength range was found to be 13 ksi for five million cycles. Nurnberger’s study4 found the fatigue strength range for two million cycles to be 18 ksi. Prestressing steels do not appear to have an endurance limit9, 15, 16, 17. A fatigue life of 2 million cycles is sufficient for most purposes18. The current limit in AASHTO LRFD 5.5.3.3 for strand is a flat value of 18 ksi for radii of curvature in excess of 30 ft. and 10 ksi for radii of curvature not exceeding 12 ft. A linear interpolation may be used for radii between 12.0 and 30.0 ft. The strand requirements are not dependent on fmin. These limits are established partly because of the great variability in the experimental results18. Because of stress concentrations, a stress range of 11.6 ksi is recommended by the FIP Commission on Prestressing Steels19 for the anchorage-tendon system of bonded tendons.

7

Fatigue of prestressing tendons occurs by initiation and propagation of cracks similar to that of bars. Prestressed members with pretensioned strands or post-tensioned strands are usually designed as non- cracked members. In these members the strand stress range and the minimum stresses are very small for the strands to experience fatigue failure. Full-scale bridge girder tests performed by Rabbat et al. 20 show that fatigue failure occurred in prestressing strands at the mid-span cracks with minimum stresses of 142 ksi and stress range of 9 ksi at three million cycles. The stress at the bottom fiber of the girders was 6 f c' psi.

8

METHOD OF TESTING The idea of this research is to take what was learned from the NCHRP 164 study and build upon it for WWR. Therefore, this research is focused on the “long-life” region, and a formula will be developed based on specimens with a fatigue life in excess of 2 million cycles. Select specimens will be tested to 5 million cycles to confirm that 2 million cycles is a sufficient representation of the endurance limit. The endurance limit as defined earlier is the stress range below which some materials do not fail up to a quasi infinite number of cycles18. In tests conducted on bars embedded in concrete beams, fatigue fracture generally takes place close to a flexural crack initiating from a lug base or a manufacturer’s mark. It has been found that on tests conducted in air, cracks may initiate at irregularities along bar surface. That is likely to be the primary reason for test results on bars in air being lower than on bars from the same batch embedded in concrete beams. 21 Instead of testing the reinforcement embedded in concrete members, this research focuses on the WWR material itself. The authors concede that testing in concrete members would be valuable. In fact, there is some evidence that the fatigue life of prestressing tendons in beams is shorter than for comparable tendons tested in the air. In the PCA study by Rabbat et al.20, pretensioned strands that were subjected to a stress range of only 9 ksi fractured after 3 million cycles. Hanson et al.22 reports that in testing by Warner and Hulsbos23 at Lehigh University, a pretensioned strand subjected to a 20 ksi stress range failed after only 570,000 cycles. In fatigue testing of post-tensioned beams, Rigon and Thűrlimann24 discovered that the number of cycles was considerably lower for strands tested in the beam than in the air. However, 80 percent of the wire breaks occurred within the regions where the tendon was curving. Therefore, it is logical to conclude that the curves cause the low cycles Strand is subjected to fretting friction but WWR is not, a frictional stress that occurs between two adjacent wires or between the concrete and the steel at the cracked section during repetitive cyclic loading18. While the above tests indicate that there may be credence in the idea of testing the material in concrete, it can only be useful after the fatigue properties of the reinforcement itself is established. For WWR, our goal is to have results available as soon as possible so that designers can feel comfortable designing with

9

Figure 4: Testing equipment included the MTS 810 with Teststar control system.

this material. This would not have been attainable in a reasonable time frame if the test considered all of the variables that would have to be accounted for in an embedded test. The NCHRP 164 tests have shown that testing in concrete beams did not impact the developed fatigue formula. While embedded testing should be undertaken in the future, establishing a conservative fatigue formula at this time is a significant contribution to the state of the art. In order to account for metallurgical properties and diversity among WWR producers, three producers were used to supply the WWR for testing. The work done in NCHRP 164 indicates that as long as the material meets ASTM25 metallurgical requirements, mechanical properties are adequate for distinction of fatigue properties for design purposes. Strength was used for this purpose. The NCHRP 164 study went a step further and simplified the fatigue design formula for rebar by eliminating the strength factor. While this study demands that the specimens meet ASTM requirements, no independent metallurgical analysis was conducted. However, complete stress-strain diagrams were developed. As long as yield strength and ultimate elongation does not significantly impact the fatigue behaviour, a strength factor will not be included in the design formula for WWR either. The wire sizes chosen for this research were D12, D18, D20, D28, and D31.26 The selected wire sizes were chosen based on the sizes that are most commonly used in bridge products. The three producers chosen, referred to as suppliers A, B, and C, were selected to represent geographical diversity among WWR producers. Wires with and without the welded cross wire were tested. All testing was performed on MTS 810 using a Test-star control system, with an axial capacity of 55 kips. This system is shown in Figure 3. A sinusoidal constant axial stress was applied at a frequency of 2.5 cycles per second. The methodology of the testing was to vary the fr+0.33fmin value until an endurance limit appeared to be reached. The testing then continued with the established fr and changing values for fmin and fmax. It was not the goal of this research to perform tests representative of all possible situations where WWR is used. It would be impractical, within the scope of this project, to develop different fatigue formulas for individual applications. Rather, the intent was to develop a type of baseline stress limit that would be conservatively valid for most applications.

APPLICATION OF RESULTS There are two different ways to apply the results of this testing to the codes. The first uses the current code format, and the second is called the Unified Fatigue Approach. The formula for the WWR is similar to the current formula for rebar3,9,27 and takes into account two conditions: 1) wire with no cross weld in the high tension zone, and 2) wire with cross weld in the high tension zone. To allow for rapid implementation, the scope of this project was limited to deformed wire.

10

Current Code Format Following the previously discussed current code format, the proposed formula is expressed as follows: f wwr = A + Bf min

E-3

where: fwwr = the allowable steel stress range for straight deformed WWR (ksi) fmin = the same parameter as expressed above in LRFD Equation 5.5.3.2-1 A,B = constants obtained from the S-N curves of the fatigue experiments. Constant A will include effects due to deformation geometry and bar sizes. Unified Fatigue Approach An alternative approach can be broadly applied to other material fatigue limitations in the codes. Therefore, using this new approach, code restrictions on fatigue can be consolidated into one section for all materials commonly used in bridge construction. Consider the current fatigue equation for rebar (AASHTO LRFD 5.5.3.2), as discussed above: f r = 24 − 0.33 f min E-4 This simplification makes the r/h=0.3 assumption, a common practice for bridge designers. Define: f f y = max and x = min E-5 fy fy where fmax and fmin are the material’s maximum and minimum stress, and in this case, the stress in the steel. Using this definition, with grade 60 steel, the rebar fatigue equation can be written as: f max − f min = 24 − 0.33 f min E-6 f max f min 24 f − = − 0.33 min E-7 fy fy fy fy y = 0.67 x + 0.4 E-8 The same approach can be applied to concrete, straight strand, and bent strand. For straight strand and bent strain, where fy = 243 ksi, the current code equations (AASHTO LRFD 5.5.3.3) are:

f r = 18 for straight strand, and f r = 10 for bent strand Using the unified approach, the equations become:

11

E-9 E-10

y = 1.0 x + 0.07 for straight strand, and y = 1.0 x + 0.04 for bent strand

E-11 E-12

The current fatigue limit for concrete (AASHTO LRFD 5.9.4.2.1) states that “For service load limit analysis, concrete compressive stress due to 50% of effective prestress, 50% of dead load, plus 100% of live load shall be limited to 0.4f’c.” If f’c is used in place of fy, in the above discussion, the concrete fatigue limit can be written as: 0.5 f min + f r = 0.4 f 'c 0.5 f min f max − f min 0.4 f 'c + = f 'c f 'c f 'c y = 0.50 x + 0.40

E-13 E-14 E-15

Following this approach, the proposed fatigue formula for WWR is

y = K1 x + K 2

E-16

where K1 and K2 are constants to be determined from testing, and will be similar to those for rebar and strand. This method has the advantage of unifying all of the code’s fatigue provisions into one, easy to understand section.

TEST RESULTS Figure 5 shows a plot of steel stress versus number of cycles for WWR with cross weld. The testing range for the specimen is shown as a line connecting the two end values. An arrow indicates the testing was stopped, and the specimen could have reached a higher number of cycles. Figure 6 shows the same plot for WWR without cross weld. Figure 7 shows a plot of fr + 0.33fmin versus number of cycles for the specimens with cross welds. The data points are compared to the 23.4 ksi limit for mild reinforcement, and this limit is shown on the graph. The points on the left side of the graph that did not meet 2 million cycles represent the trial and error process to determine the appropriate range. The points below the 2 million mark did not reach the endurance limit because the fr + 0.33fmin was too high. Also shown on the graph is a similar satisfactory limit for WWR with cross weld. The 16 ksi limit for WWR with cross weld falls between the Grade 270 straight and bent strand limits. Figure 8 shows the same plot for WWR without cross weld. A similar satisfactory limit is shown on this graph. For simplicity, the 24 ksi limit can be combined with the rebar limit of 23.4 ksi. Figures 9-11 show a typical stress strain relationship for each of the three suppliers. It is important to note that all three suppliers provided steel with Fy greater than 75 ksi. Some test 12

results show that yield stress is below 80 ksi, as shown in Figure 11. It is possible to have WWR with a yield stress of 80 ksi for WWR, for which case the recommendations herein would still be valid. When high strength WWR is specified. Codes require that the high strength material (higher than Grade 60) shall test at a strain of 0.35% 60 B 12 A 12 C 12 B 20 A 28

Steel Stress (ksi)

50

B 18 A 18 C20 A 20 B 28

Note: Indicates that the specimen could have achieved a higher number of cycles if the test had not been stopped

40

30

20

10

0 100,000

1,000,000

2,000,000

5,000,000 10,000,000

# of Cycles

Figure 5: Steel Stress vs. Number of Cycles-WWR with Cross Weld

13

40 35

B 12 C 12 C 18 A 28

Steel Stress (ksi)

30 25 20

A 12 A 18 B 18

Note: Indicates that the specimen could have achieved a higher number of cycles if the test had not been stopped

15 10 5 0 100,000

1,000,000

2,000,000

5,000,000

10,000,000

# of Cycles

Figure 6: Steel Stress vs. Number of Cycles-WWR with No Cross Weld 45 40

fr + 0.33fmin (ksi)

35 30 25 20 16 ksi

15 10

B 12 A 12 C 12 B 20 A28

5 0 100,000

B 18 A 18 C 20 A 20 B 28

Note: Indicates that the specimen could have achieved a higher number of cycles if the test had not been stopped.

1,000,000

2,000,000

5,000,000

# of Cycles

Figure 7: fr+0.33fmin vs. Number of Cycles-WWR with Cross Weld

14

10,000,000

30

fr + 0.33fmin (ksi)

25

24 ksi

20

15

B 12 C 12 C 18 A 28

10

5

Note: Indicates that the specimen could have achieved a higher number of cycles if the test had not been stopped.

A 12 A 18 B 18

0 100,000

2,000,000

1,000,000

5,000,000

10,000,000

# of Cycles

Figure 8: fr+0.33fmin vs. Number of Cycles-WWR with No Cross Weld

100

Stress (ksi)

80

60

40

20

0.35 0 0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

Strain (%)

Figure 9: Typical Stress-Strain relationship for supplier “A”.

15

6.00

6.50

7.00

100

Stress (ksi)

80

60

40

20

0.35 0 0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

6.50

7.00

7.50

8.00

Strain (%)

Figure 10: Typical Stress-Strain relationship for supplier “B”.

100

Stress (ksi)

80

60

40

20

0.35 0 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50

Strain (%)

Figure 11: Typical Stress-Strain relationship for supplier “C”. 16

PROPOSED EQUATION AND RECOMMENDATIONS As discussed above, there are two different ways to apply the results of this testing to the current design code. The first is using the current code format, and the second is the Unified Fatigue Approach. Current Code Format If the current code format is used, the new fatigue formula for WWR is then: f wwr = A + Bf min

E-17

where: fwwr = the allowable steel stress range for straight deformed WWR (ksi) fmin = the same parameter as expressed above in LRFD Equation 5.5.3.2-1 A,B = constants obtained from the S-N curves of the fatigue experiments. Constant A will include effects due to deformation geometry and bar sizes. From the above test results, the proposed fatigue equation for WWR with a cross weld in the high stress region is: f wwr = 16 − 0.33 f min

E-18

For WWR with no cross weld in the high stress region, the proposed formula is: f wwr = 24 − 0.33 f min

17

E-19

DESIGN EXAMPLES Example 1 – WWR as primary tension reinforcement As discussed in the introduction, WWR has the potential to be used as the main tensile reinforcement in some applications. One possibility is the previously discussed plank elements. This example will demonstrate the use of the proposed fatigue limits for this application. System Description: This 20 ft. span bridge comprises of ten 2 ft.–10 in. wide plank elements that span in the direction of traffic. A cross section of the element is shown in Figure 2 and is shown again below. The planks are connected and act together in shear. A 2 in. composite overlay is placed. The bridge is 28 ft. 4 in. wide. The bridge is designed for its own weight and HL-93 as specified by AASHTO Bridge Design Specification. D10 x D10 @ 12" x 12"

D31

D31 2" 12.43"

D20 @ 6" for a distance to be determined

12.5" 4" 4"

1.5"

D31 @ 4" (two layers) 34"

Figure 12: Plank Element with Welded Wire Reinforcement

Materials Cast-in-place overlay Concrete strength, f’c = 4 ksi Thickness = 2 in. Precast plank Concrete strength at 28 days, f’c = 6 Concrete weight, wc = 0.150 kcf Overall plank length = 20.5 ft Design span = 20 ft

ksi

18

Clear cover to reinforcement = 1.25 in. Loads Dead load Weight of 2 in. overlay = (2/12)(34/12)(0.150) = 0.071 k/ft Weight of plank element = (12.5/12)(34/12)(0.150) = 0.443 k/ft Total dead load = 0.071+0.443 = 0.514 k/ft Live load Design live load is HL-93 which consists of: 1. Design truck 2. Design lane load of 0.64 k/ft

Bending Moment Moment due to self-weight of plank and overlay at mid-span 2 ( 0.514 )(20 ) M DL = = 25.70 k − ft 8 Moment due to live load, HL- 93 loading at mid-span MLL = 76.90 k-ft (calculated by a commercial computer program) Total moment at mid-span MTT = MDL+MLL = 25.70+76.90 = 102.60

k-ft

Cross Section Properties Modulus of elasticity, Ec: 1.5 For cast-in-place overlay = 33,000(0.150 ) 4 = 3,834 ksi For precast plank = 33,000(0.150 )

1.5

6 = 4,696 ksi

3,834 = 0.82 4,696 29,000 Modular ratio between WWR and plank material = = 6.18 4,696 Uncracked Composite Section: Modular ratio between overlay and plank material =

Table 1: Uncracked Composite Section Properties

Overlay Plank

∑ ybc

Area (in2) 55.76 425 463.76

yb (in.) 13.50 6.25

Ayb (in3) 752.80 2656.30 3,172.88

A(ybc-yb)2 2290.40 300.50

I (in4) 18.59 5533.85

7.09 Ig = moment of inertia of the gross composite section = 8,143 in4

Cracked Section: kd = distance of the neutral axis from the extreme compression fiber Icr = moment of inertia of the cracked section 19

I+A(ybc-yb)2 2309.00 5834.40 8143.40

The neutral axis distance from the extreme compression fiber, kd, can be determined by setting the first area moment about the neutral axis = 0. Precast section kd = 3.27 in. Composite section kd = 3.96 in. The moment of inertia of the cracked section: Precast section Icr = 1,782 in4 Composite section Icr = 2,514 in4 Check if section cracks at total loading: Modulus of rupture =

7.5 6,000 = 0.581 ksi 1,000

Bottom fiber stress due to total load, assume section to be uncracked:

f bot =

(102.60 )(12 )(7.09 ) = 1.072 ksi ≥ 0.581 ksi My = Ig 8,143

Therefore, the section cracks under total load, and the cracked section properties must be used in the computation of stress in the steel. The stress in steel is then calculated for both dead loading and total loading: Total load: fs = n

My (102.60 )(12 )(12.43 − 3.96 ) = 25.635 ksi = (6.18)x I cr 2,514

Dead load only applied to precast section: fs = n

My (25.70 )(12 )(10.43 − 3.27 = (6.18)x I cr 1,782

)

= 7.658 ksi

The stress range is:

f r = 25.635 − 7.658 = 17.977 ksi The main tensile reinforcement, WWR in this application does not have a weld in the high stress region. The actual stress range is compared to the allowable stress range as follows: Max. f r = 24 − 0.33 f min = 24 − 0.33(7.658) = 21.473 ksi Actual f r = 17.977 < Max. f r = 21.473 ksi OK

20

Therefore, this reinforcement is acceptable under the proposed fatigue limitation for WWR. Determine the extension of WWR with cross weld from beam ends using stress range for WWR with a cross weld in the high stress region f r = 16 − 0.33 f min

Determine moments corresponding to this stress limit n

M TT y M y M y − n DL = 16 − (0.33)n DL I cr I cr I cr

 102.60  M TT =   M DL = 3.99 M DL  25.70  (6.18) x

3.99 M DL (12 )(12.43 − 3.96 ) M (12 )(10.43 − 3.27 ) − (0.67 )(6.18)x DL = 16 2,514 1782 M DL = 20.07 k − ft

Determine a distance x from the support

(0.5)(0.514)(x )(20 − x ) =

20.07 x = 5.32 ft , or 5.82 from beam end (5.82)(12) = 12 Number of D20 @ 6 in. = 6 Provide welded cross wires for 11 spaces @ 6 in. per space at beam end. Based on shear design, additional non-welded wire was not found to be required. 20.5 ft 2"

D20 @ 6"

D20 @ 6"

14"

12" 20 ft (f r+0.33 f x

min

) x

16 ksi

24 ksi

uncracked under full load cross weld allowed

cross weld not allowed

21

cross weld allowed

Figure 13: Stress range diagram Example 2 –Design of Highway Bridge Deck System Description: The bridge deck cross section shown in Figure 14 consists of four NU1100 (Nebraska University 1100 mm (43.3 in.)) girder lines, spaced at 12 ft on centres. The deck is 8.5 in. thick cast-in-place (CIP) concrete, including a 0.5 in. sacrificial wearing thickness and 8 in. structural thickness. The slab is continuous and composite with the girders. It is subjected to slab weight, traffic barrier weight of 0.400 k/ft/side, a future wearing surface of 25 psf, and a live load = HL-93 as specified by AASHTO Bridge Design Specification. The haunch over the girder top flange is required to be a minimum of 1 in. along the girder length. 46' - 4" 1

2

29" 8.5" 1 5' - 2"

12'

2 12'

12'

5' - 2"

NU 1100

Figure 14: Example 3 Cross Section

Specified Materials: Slab concrete strength at 28 days, f’c = 4 ksi, weight, wc = 0.150 kcf. Clear concrete cover to reinforcement = 1.0 in. at the bottom and 2.5 in. at the top. It is the practice of the Nebraska Department of Roads (NDOR) and that of several other state highway agencies to invoke the Empirical Design Method wherever it is applicable. The Empirical method would be valid for this condition. However, because of its empirical nature a prescribed amount of steel (#5 @12” each way bottom and #4@12” each way top) is prescribed without calculations. The validity of the method with WWR has not been established. The method cannot be used for precast slabs and for other practical applications. For this reason, the AASHTO-LRFD strip method will be used to design this deck. It is expected to give larger reinforcement content than that by the Empirical Method. But, it will illustrate the procedure for design of deck slabs of general conditions. The primary transverse strip is designed for an axle load of 32.0 k. the axle consists of two wheels 6 ft apart. The tire contact area of each wheel is determined according to AASHTO to be 20 in. the direction of the slab span by 12 in. the direction of traffic. Use detailed analysis

22

which takes into account non-prismatic effects according to the thicknesses shown in Figure 15, a wheel load width of 28 in. at the mid-thickness of the deck, and a support width of 6 in., the web width. According to Article 4.6.2.1.3 of AASHTO, the distribution width for the positive moment is (26 + 6.6 S) in. where S is spacing in feet, or (26+ (6.6)(12))/12 = 8.77 ft. The corresponding strip width for the interior negative moment design is (48 + 3.0 S), or 7.00 ft. One lane loading and a multiple presence factor of 1.2 are used in the analysis. The design section for negative moment is at a distance of 1/3 of the beam flange width from the centerline of the support but not to exceed 15 in. Beam flange width/3 = 48.2/3 = 16.1 > 15 in. Therefore the design section for negative moment is at 15 in. from the centerline of the beam. The most critical positive moment section for this deck was found to be section 1 and the most critical negative moment section was section 2. The critical placement of truck load for interior span is shown in Figure 16. Slab thickness 8"

12" 4" 21" Web width

Average top flange thickness + 1" haunch

40" 6"

24"

Figure 15: Slab thickness variation used in the detailed analysis model 1

16 k 1.5' 29"

20"

16 k

2

6' 4.5' 20"

8.5" 14"

15"

6' 5' - 2"

1 12'

Figure 16: The critical placement of truck load

23

2

Table 2: Bending Moments (k-ft/ft) Using Detailed Analysis

Section

1 2

CIP Slab MCIP 0.432 -0.823

Unfactored Load moments Wearing Live Load Barrier Surface Plus impact Mws Mb MLL 0.102 0 (-0.704) 6.752 -0.194 0 (0.460) -7.045

Strength I Mu 12.509 -13.649

Fatigue moments Min. 0.534 -1.017

Max 5.598 -6.301

The table shows a maximum factored positive moment = 12.509 k-ft/ft, and negative moment of 13.649 k-ft/ft. The load factors, per AASHTO are 1.25 for deck and barrier weight, 1.5 for wearing surface and 1.75 for live load. The minimum and maximum moments shown in the table reflect a fatigue load factor of 0.75 as given in AASHTO. Moments due to the weight of the barrier -0.704 and 0.460 k-ft/ft on section 1 and 2 respectively are conservatively ignored. Through trial and adjustment, it has been determined that WWR Grade 75 D20 @ 5 in. for bottom main reinforcement, WWR Grade 75 D10 @ 6 in. for top main reinforcement, and WWR Grade 75 D10 @ 6 in. top and bottom for longitudinal distribution reinforcement would be acceptable reinforcement. The following calculations demonstrate the adequacy of this reinforcement.

Cross Section Properties Modulus of elasticity, Ec: 1.5 For cast-in-place = 33,000(0.150 ) 4 = 3,834 ksi Modular ratio between reinforcement and deck material =

29,000 = 7.56 3,834

Uncracked Section: Ig = moment of inertia of the gross section =

(12)(8)3 12

= 512 in 4

Check if section cracks at total loading: 7.5 4,000 = 0.474 ksi 1,000 Top fiber stress due to total load, assume Section 2(negative moment) to be uncracked: Modulus of rupture: =

f top =

(8.062 )(12 )(6 ) = 0.336 ksi < 0.474 ksi My = Ig 1728

Therefore, the fatigue need not be investigated for negative moment. Bottom fiber stress due to total load, assume section 2 (positive moment) to be uncracked:

24

f bot =

(7.286 )(12 )(4 ) = 0.683 ksi > 0.474 ksi My = Ig 512

Therefore, the section cracks under total load, and the cracked section properties must be used in the computation of stress in the steel. The moment of inertia of the cracked section is determined for the cracked transformed section properties. Cracked Section: kd = 1.76 Icr = 112 The stress in steel is calculated for both dead loading and total loading as follows: Total load: fs = n

My (5.598 )(12 )(6.75 − 1.76 ) = 22.627 ksi = (7.56)x I cr 112

Dead load: fs = n

My (0.534 )(12 )(6.75 − 1.76 ) = 2.158 ksi = (7.56)x I cr 112

The actual stress range is:

f r = 22.627 − 2.158 = 20.469 ksi Using the current code format, the stress range is compared to the allowable stress range: Max. f r = 24 − 0.33 f min = 24 − 0.33(2.158 ) = 23.288 ksi Actual f r = 20.469 < Max. f r = 23.288 ksi OK

25

2

1

D10 @ 6 in.

D10 @ 6 in.

29" 8.5"

D20 @ 5 in. D10 @ 6 in.

1 5' - 2"

12'

Figure 17: Reinforcing WWR details

26

2

Example 3 – High shear; WWR as web reinforcement System Description: Two 120 ft. spans, four NU1100 girder lines, spaced at 12 ft. o.c. Figure 18 shows a cross section of this system. The deck is 8 in. thick, and a future wearing surface of 2 in. is considered.

46' - 4" 29" 7.5"

5' - 2"

12'

12'

12'

5' - 2"

NU 1100

Figure 18: Example 1 Cross Section

The system is simple span for member self-weight and slab weight, and continuous for the future wearing surface, barrier weight, and live load. The haunch over the girder lines is ignored for the structural analysis but included for weight calculations. For the sake of the example, several simplifying assumptions are made. Most notably, the studied section for shear is at a location dv away from the support, and dv is assumed to be 0.72h. The considered section is therefore at 0.72h = 0.72(43.3+7.5) = 36.576 in. ~ 36 in. from the interior support. The shear force at the critical section due to each stage of loading is summarized below: Simple Span: Self Weight: 0.724 k/ft. – V36 = 41.27 k Slab Weight: 12 ft. x 8/12 x 0.150 kcf = 1.2 k/ft - V36 = 68.4 k Continuous: Future wearing surface: 12 ft. x 2/12 x 0.150 kcf = 0.3 k/ft - V36 = 21.6 k Barrier: 0.4 k/ft. x 2 barriers / 4 girders = 0.2 k/ft - V36 = 14.4 k Live Load: HL93 Loading; V36 = 163.04 k

27

Totals: VDL = 41.27 + 68.4+21.6 + 14.4 = 145.67 k VDL+LL = 145.67 k + 163.04 k = 308.71 k The shear reinforcement chosen for this section is two sheets of WWR 4x4-D24xD24 Therefore, As = 1.44 in2/ft. For the purpose of the example, θ and β are assumed. θ = 30.5º, β = 2.59 The shear stress in the reinforcement can be calculated by rearranging terms in AASHTO LRFD Equation 5.8.3.3-4. fy is replaced with fs, the stress in steel, and Vs is shear force minus shear taken by concrete. α is 90º for vertical stirrups. Fundamentally, this equation finds the stress in the steel using the equilibrium of the compression struts and the tension tie of the bottom reinforcement. Therefore, the equation looks like: fs =

sVs Av d v cot ϑ

From this, the upper and lower stress values can be determined and compared to the cyclic loading limit. fupper is calculated using VDL+LL and flower is calculated using VDL only. Therefore, the upper and lower cyclic stress values are calculated as:

f upper =

(12" )(308.71 − 49.17) = 35.39 ksi (1.44 in 2 )(36" ) cot(30.5°)

f lower =

(12" )(145.67 − 49.17) = 13.16 ksi (1.44 in 2 )(36" ) cot(30.5°)

The calculated stress range, therefore, is:

f r = 35.39 − 13.16 = 22.23 ksi As shear reinforcement, WWR in this application does not have a weld in the high stress region. Therefore, using the current code format, the stress range is compared to the allowable stress range: f r ≤ 24 − 0.33 f min

22.23 ksi ≤ 24 − 0.33(13.16 ) = 19.66 ksi, try a larger steel area The stress range for this example exceeds the allowable stress range for the reinforcement. Reinforcement is changed to two sheets of D28 at 4 in. Therefore, As = 1.68 in2/ft. θ = 30.5º, β = 2.59. In the same way as above, the upper and lower stress limits are calculated:

28

f upper =

(12" )(308.71 − 49.17) = 30.33 ksi (1.68 in 2 )(36" ) cot(30.5°)

f lower =

(12" )(145.67 − 49.17) = 11.28 ksi (1.68 in 2 )(36" ) cot(30.5°)

The stress range is:

f r = 30.33 − 11.28 = 19.05 ksi In the same way as before, the stress range is compared to the allowable stress range:

19.05 ksi ≤ 24 − 0.33(11.28) = 20.28 O.K. Therefore, this reinforcement is acceptable under the proposed fatigue limitation for WWR.

NOTATION A = area of cross-section of the precast section As = area of non-pretensioning tension reinforcement Av = area of transverse reinforcement a = depth of the compression block b = width of the compression face of a member DC = dead load of structural components and non-structural attachments DW = load of wearing surfaces and utilities d = distance from extreme compression fiber to centroid of the tensile force dv = effective shear depth Ec = modulus of elasticity of concrete f’c = specified compressive strength at 28 days fbot = the bottom tensile stresses fmax = maximum stress level fmin = minimum stress level fr = stress range fr = modulus of rupture of concrete fs = stress in steel under service loads fwwr = the allowable steel stress range for straight deformed WWR fy = yield strength of reinforcing bars h = over all depth of a member I = moment of inertia about the centroid of the non-composite precast member Icr = moment of inertia of cracked section Ig = moment of inertia of gross concrete section about centroidal axis IM = dynamic load allowance kd = distance of the neutral axis from the extreme compression fiber Mb = unfactored bending moment due to weight of barriers

29

Mc = flexural resistance of the barriers at its base MCIP = unfactored bending moment due to weight of cast-in-place slab MDL = unfactored bending moment due to total dead loads MLL = unfactored bending moment due to total live loads MTT = unfactored bending moment due to total live loads Mu = factored bending moment Mws = unfactored bending moment due to weight of future wearing surface n = modular ratio Rw = transverse resistance of the barrier r = radius of gyration of gross cross-section S = center-to-center spacing of beams s = spacing of rows of ties T = total dead load and live load thrust in the structure VDL = shear force at section due to unfactored total dead loads VLL = shear force at section due to unfactored total live load Vs = shear resistance provided by shear web reinforcement Vu = factored shear force at the section WWR = Welded wire reinforcement yb = distance from centroid to the extreme bottom fiber of the non-composite beam ybc = distance from centroid to the bottom of beam of the composite section β = factor indicating ability of diagonally cracked concrete to transmit tension φ = strength reduction factor

REFERENCES 1. Tilly, G. P.,” Fitigue of Reinforced Bars in Concrete: A Review,” Fatigue of Engineering Materials and Structures, Vol. 2, Pregamon Pres, Oxford, pp.251-268 2. Hanson, J.M., Somes, N.F., Helgason, T, Corley, W.G., and Hognestad, E., “Fatigue Strength of High Yield Reinforcing Bars,” NCHRP Report 164, National Cooperative Highway Research Program, Transportation Research Board, Washington, D.C., 1976, 90 pp. 3. AASHTO LRFD, 2005 and Interim Bridge Design Specifications, Second Edition, American Association of State Highway and Transportation Officials, Washington, D.C. 4. Nurnberger, U.,” Fatigue Resistance of Reinforced Steel,” Proceedings Int. Ass. Bridge Struct. Eng. Colloq., Lausanne. 1982, IABSE, Rep., Vol. 37, pp. 213-220. 5. Pfister, J. F. and Hongestad, E.,” High Strength Bars as Concrete Reinforcement, Part 6: Fatiguer Tests,” Journal, PCA Research and Development Laboratory, Vol. 6, No. 1, Jan. 1964, PP. 65-84. 6. Jhamb, I.C., and MacGregor, J.G., “Stress Concentrations Caused by Reinforcing bars deformations,” Abeles Symposium: fatigue of Concrete, American Concrete Institute, SP-41, 1974, pp. 168-182. 7. Derecho, A. T. and Munse, W. H.,” Stress Concentration at External Notches in Members Subjected to Axial Loadings,” Bulletin No 494, Engineering Experiment Station, University on Illinois, Urbana, January 1968, 51 pp.

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8. Burton, K. T. and Hognestad, E.,” Fatigue Test of Reinforcing Bras-Tack Welding of Stirrups,” ACI Journal, Proceedings, Vol. 64, No. 5, May 1967, pp.244-252. 9. ACI Committee 215, “Considerations for Design of Concrete Structures Subjected to Fatigue Loading,” ACI Manual of Concrete Practice 1998 Part 1, American Concrete Institute, Farmington Hills, MI. 10. MacGregor, J.G., Jhamb, I.C., and Nuttall, N., “Fatigue Strength of Hot Rolled Deformed Reinforcing Bars,” ACI Journal, March 1971, pp. 169-179. 11. Pasko, T.J., “Effect of Welding on Fatigue Life of High-Strength Reinforcing Steel Used in Continuously Reinforced Concrete Pavements,” Report No. FHWA-RD-7232, Federal Highway Administration, Washington, D.C., November 1971. 12. Sanders, W. W., Hoadley, P. G. and Munse, W. H.,” Fatigue behaviour of Welded Joints in Reinforcing Bars for Concrete,” The Welding Journal, Research Supplement, Vol. 40, No. 12, 1961. pp. 529-s to 535-s 13. Hawkins, N.M. and Heaton, L.W., “The Fatigue Properties of Welded Wire Fabric,” Report SM 71-3, University of Washington, Seattle, WA, September 1971. 14. Hawkins, N.M. and Takebe, Y., “Long Life Fatigue Characteristics of Large Diameter Welded Wire Fabric,” Report SM 87-1, University of Washington, Seattle, WA, January 1987. 15. Edwards, A.D. and Picard, A., “Fatigue Characteristics of Prestressing Strands,” Proceedings ICE, Institute of Civil Engineers, London, Vol. 53, 1972, pp.323-336 16. Harajli, M.H., and Naaman, A.E., “Static and Fatigue Tests of Partially Prestressed Beams,” ASCE Journal of the Structural Division, 111(7); 1602-18, 1985. 17. Ekberg, C.G., Walther, R.E., and Slutter, R.G., “Fatigue Resistance of Prestressed Concrete Beams in Bending,” ASCE Journal of the Structural Division, July 1957, Paper No. 1304, pp. 1-17. 18. Naaman, A., Prestressed Concrete Analysis and Design, Techno Press 3000, Ann Arbor, Michigan, 2nd Edition, pp. 59-62. 19. FIP Commission on Prestressing Steels and Systems, “Report on Prestressing Steels: Types and Properties,” FIP, Wexham Spring, England, August 1976, 18 pp. 20. Rabbat, B.G., Kaar, P.H., Russell, H.G., and Bruce, R.N., “Fatigue Tests of Pretensioned Girders with Blanketed and Draped Strands,” PCI Journal, Vol. 24, No. 4, July-Aug. 1979, pp. 88-114. 21. Kong F. K. Hand book of Structural Concrete, McGraw-Hill (1983) 22. Hanson, John M., Hulsbos, Cornie L., and Van Horn, David A., “Fatigue Tests of Prestressed Concrete I-Beams,” ASCE Journal of the Structural Division, Vol. 96, No. ST11, Nov. 1970, pp.2443-2464. 23. Warner, R.F., and Hulsbos, C.L., “Fatigue Properties of Prestressing Strand,” PCI Journal, Vol. 11, No.1, Jan-Feb. 1966, pp 32-52. 24. Rigon, Claudio and Thűrlimann, Bruno, “Fatigue Tests on Post-Tensioned Concrete Beams,” Bericht Nr. 8101-1, Institut fűr Baustatik und Konstruktion, Eidgenőssische Technische Hochschule, Zűrich, Aug. 1984, 77 pp. 25. “Standard Specification for Steel Welded Wire Reinforcement, Deformed, for Concrete.” ASTM A497/A497M-02, American Society for Testing and Materials International, West Conshohocken, Pa., 2002, 5 pp. 26. “Structural Welded Wire Reinforcement Manual of Standard Practice”, Wire reinforcement Institute, 6th Edition, 2001, Hartford, CT, 36 pp.

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27. “Bridge Design Manual,” Precast Prestressed Concrete Institute, Chicago, Illinois, 1997, 1200 pp.

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