Fatigue life of girders with trapezoidally corrugated webs: An experimental study

International Journal of Fatigue 64 (2014) 22–32

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Fatigue life of girders with trapezoidally corrugated webs: An experimental study B. Kövesdi ⇑, L. Dunai }egyetem rkp. 3, H-1111 Budapest, Hungary Budapest University of Technology and Economics, Department of Structural Engineering, Mu

a r t i c l e

i n f o

Article history: Received 9 October 2013 Received in revised form 23 January 2014 Accepted 20 February 2014 Available online 3 March 2014 Keywords: Corrugated web girders Stress concentration Fatigue tests Fatigue detail category

a b s t r a c t Corrugated steel plate has been increasingly used in the last 20 years for beam webs in hybrid and composite bridges. Girders with corrugated webs have many advantages over traditional structures with flat webs, but due to the new structural layout, there are still many design questions that need to be solved. In cases with girders with trapezoidally corrugated webs, the determination of the fatigue life is rather difficult because of the complex stress field in the flanges, and the fatigue detail category has also not been elucidated. This topic has gained importance in Hungary related to a highway bridge on the Tisza River designed and constructed between 2006 and 2011. There are only a small number of investigations dealing with the fatigue behaviour of corrugated web girders in the literature. The aim of the current tests published in this paper is the analysis of the fatigue behaviour of the corrugated web girders under pure bending and combined bending and shear. Furthermore, a proposal for the fatigue detail category is developed based on the test results to support the bridge design. The tests were completed to study the effect of the corrugation profile, the normal stress ratio, the effect of the combined normal and shear stresses and the weld size on the fatigue life. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Corrugated steel plate has been used in many fields for a long time because of its favourable properties. For the last 20 years, it has been increasingly used as a beam web. This structural layout has spread also spread to bridge construction, especially in hybrid and composite bridges. The first hybrid bridge with trapezoidally corrugated webs was built in France in 1986 (Pont de Cognac bridge). Because of the great number of advantages of this structural layout, it has quickly spread, especially in Japan [1], where numerous hybrid bridges have been built or are still under construction with corrugated webs. Because of the features of corrugation, the application of corrugated steel webs has numerous advantages. Because of the corrugation profile, the normal stiffness of the web in the longitudinal direction is smaller than in the case of the usual I-girders with flat webs. Therefore, the prestressing of the flanges can be more efficient. The resistance against buckling – locally and globally – increases, so the number of stiffeners or diaphragms may be significantly reduced. In comparison to flat webs, there is a high bending stiffness in the transverse direction, which

⇑ Corresponding author. Tel.: +36 1 463 1998; fax: +36 1 463 1784. E-mail address: [email protected] (B. Kövesdi). http://dx.doi.org/10.1016/j.ijfatigue.2014.02.017 0142-1123/Ó 2014 Elsevier Ltd. All rights reserved.

allows reduction of the number of cross frames in box girder bridges. Because of the increased stiffness, the web thickness may be reduced. Therefore, the dead load of the structure may be smaller, leading to easier and faster building processes especially in cases of incremental launching. The economical design of bridges requires the usage of slender structures. To avoid local or global plate buckling, numerous stiffeners are used, which are relatively expensive, and they may reduce the fatigue life of the structure. Corrugated webs increase the buckling strength of the structure. Therefore, the number of the stiffeners can be reduced, which can have a positive effect on the fatigue behaviour of the structure. The Móra Ferenc bridge at the M43 highway over the Tisza River was designed and constructed with corrugated steel webs in Hungary between 2006–2011. The completed bridge can be seen in Fig. 1. It is an extradosed highway bridge with three spans (90 m + 180 m + 90 m). The bridge has a hybrid superstructure with prestressed reinforced concrete flanges and corrugated steel webs. The bridge superstructure is a box cross-section with 3 cells and varying web depth. The bridge erection was started in 2008 and finished in 2011. Despite this girder type often being used in bridges in the last 20 years, there are only a few investigations available in the literature dealing with the fatigue behaviour of these structures.

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Fig. 1. Móra Ferenc M43 highway bridge on the Tisza river [2].

The existing experimental, analytical and numerical investigations were analysed, and it was concluded that the applicability of the previous experiments are strictly limited because the test results can be used only for special corrugation profiles and the stress ratios analysed in the previous experiments. Given the lack of research results on the fatigue life of corrugated web girders, there are no recommendations in the standards [3]. Because of these facts, an experimental research program was designed and executed at the Budapest University of Technology and Economics, Department of Structural Engineering on six large-scale test specimens to investigate the fatigue life of girders with the same corrugation profile as used in the Móra Ferenc highway bridge. The current paper investigates the experimental research program and the test results.

2. Review of previous research 2.1. Experimental investigations The first experiments on the fatigue life of steel girders with sinusoidal corrugated webs were completed by several researchers. Harrison (1965) tested two I-girders with sinusoidal corrugated webs under four-point-bending [4]. Korashy and Varga [5] investigated 11 I-girders with partial corrugated webs under four-point-bending in 1979. In the study, waves were placed at a defined distance from each other along the girder length. The study was not limited to homogeneous girders. It was also extended to hybrid girders as well. A comparison between hybrid and homogeneous beams revealed that there were no significant differences in the fatigue life between the two girder types. The wave-stiffened beams, in which conventional transverse stiffeners were replaced by the web corrugation, displayed 25% higher fatigue strength than the conventionally stiffened beams with transverse stiffeners welded to the web alone. The wave-stiffened beams displayed 47% higher fatigue strength than the conventionally stiffened beams with the stiffeners welded to the tension flange transversely. They displayed 56% higher fatigue strength than beams with stiffeners welded to the tension flange longitudinally. In 2005, Machacek and Tuma [6] performed numerous experimental investigations on sinusoidally corrugated girders to analyse the fatigue behaviour due to shear force, patch load and moving loads of crane girders. For all test specimens, the web was sinusoidally corrugated, with a wave amplitude ±20 mm. Three series of

specimens were produced with different web thicknesses (tw = 2 mm, tw = 2.5 mm and tw = 3 mm). Under shear loading, the fatigue cracks initiated from the weld toes at web-flange or web-stiffener connections and propagated quickly to the fracture of the girder. Based on the test results, the fatigue detail categories were recommended for design of girders with sinusoidally corrugated webs under shear and transverse loading. The first fatigue analysis of girders with trapezoidally corrugated webs was completed by Ibrahim in 2001 [7]. In the experimental program, 6 specimens were tested under four-point bending. A web depth of the girder was 500 mm and the thickness 3.18 mm. The flange size was for all specimens was 150  12 mm, the corrugation depth 75 mm and the wavelength 434 mm. The bend radius between the inclined fold and the longitudinal fold was 27 mm, and the corrugation angle was 36.9°. The size of the web-to-flange fillet welds was 5 mm. The calculated stress range on the top of the bottom flange varied between 64.7 MPa and 131 MPa. All six girders failed from fatigue cracks, and failure initiated at the web-to-flange weld toe along an inclined fold and propagated in the bottom flange within the constant moment region. The point of the crack initiation was generally at the end of an inclined fold where the bend region began. Eight large-scale fatigue specimens were tested at Lehigh University in 2004 by Sause et al. [8–10]. The test girders were made of A709 HPS 485W steel and loaded under four-point-bending. The web depth of the analysed girders were 1200 mm, and the web thickness was 6 mm. The flange size was for all specimens 225  20 mm. The corrugation angle was 36.9°, and the radius of the corrugated plate was 120 mm. The inclined folds had a slope of 3:4 with 200 mm projection parallel to the flange edges and 150 mm depth of corrugation. The web to flange weld size was 8 mm. The total length of the girder was 7400 mm, and the distance between the two end supports was 7000 mm. The nominal stress range varied from 103 to 138 MPa. Each girder failed from a fatigue crack propagated in the bottom flange from the web-toflange fillet weld toe within the constant moment region. The results of the study demonstrated that I-girders with corrugated webs exhibit a fatigue life that is generally longer than that of conventional I-girders with transverse stiffeners but shorter than I-girders with unstiffened flat webs. The fatigue life of the robotically welded girders was 42% higher than the fatigue life of similar girders welded using semiautomatic GMAW. In 2006, a total of 6 specimens with trapezoidally corrugated steel webs were tested by Ibrahim et al. [11–13]. A simple

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supported test arrangement was used, and the girders were subjected to four-point bending. The tested girders had a 3 mm thick and 500 mm depth web with a yield strength of 324 MPa. The corrugation amplitude was 75 mm, and the wavelength was 434 mm. The inclined folds had a slope of 3:4 with a 100 mm projection parallel to the flange edges. The flanges were made from 150  12.5 mm steel plate with a yield strength of 379 MPa. Bearing stiffeners with 11 mm thickness were placed at the ends of the girders and under the load application points. The total length of the girder was 6076 mm, and the distance between the two end supports was 5859 mm. The web to flange weld size was 5 mm. All fatigue cracks occurred in the tension flange at the constant bending moment zone. The cracks initiated at the weld toe of the web-to-flange fillet weld in the inclined folds where the bend region began. The fatigue crack then propagated perpendicular to the direction of the longitudinal stress in the tension flange and through the flange thickness. The cracks also continued to propagate upward for a short distance in the corrugated web. The investigations revealed that corrugated web girders had 30–50% longer fatigue life than stiffened flat-web plate girders with stiffeners cut short from the tension flange. It was also observed that the corrugated web girder fell between the fatigue categories of the stiffened and unstiffened flat-web girders. Furthermore, the researchers reported that the start-stop point of the welding process results in a high stress concentration that can reduce fatigue life. Experimental investigations have been performed on hybrid bridges with corrugated steel webs and concrete flanges in Japan [14]. The aim of the tests was to analyse the fatigue behaviour of the connection between the web plates at the elongation cross-section. A new connection type was proposed to reduce the stress concentration and to improve the fatigue life of this structural detail. The cross-section shape for the experiment was selected based on the Koinumarukawa bridge. The geometry of the tested box girders and the corrugated steel plates were the same as in the real bridge construction, and to avoid the size effect, a full-size model was built in the laboratory. The fatigue tests revealed that up to 60 million cycles, no fatigue cracks occurred. 2.2. Evaluation of the previous investigations and the new research aims From previous studies, 57 tests are available in the literature investigating the fatigue behaviour of girders with corrugated webs. Of these, 55 were conducted on steel girders and two on hybrid girders with concrete flanges. From the 55 experiments, 35 involved sinusoidally corrugated webs and 20 trapezoidally corrugated webs. Among the 35 tests, 10 focused on fatigue failure due to shear force. In addition, 10 specimens were loaded with patch load, and 13 tests involved analysing the fatigue behaviour due to normal stresses caused by the bending moment. Finally, two tests were conducted to determine the fatigue behaviour of crane girders due to transverse wheel force. From the 20 previous tests with trapezoidally corrugated webs, all the experiments were focused on the fatigue behaviour under pure bending. The influence of the normal stress ratio due to the bending moment was analysed previously with two different corrugation profiles and girder depths. The previous test results can be used only in limited way for new bridge design because the corrugation profile and some geometric parameters, which have important effects from the point of view of fatigue, are different. Considering the relatively large scatter in the fatigue behaviour of such complex structures, and the different structural arrangements in the actual problem, it was decided to execute a new experimental research program on 6 large scale test specimens. Comparing to the relative small number of the previous tests, the

results of the current research program on 6 specimens can give significantly new information on the fatigue behaviour of the corrugated web girders. It is important to underline that the geometry of the specimens is different from the previously tested ones. Major parameters (as corrugation angle, corrugation depth and weld size) which have influence on the fatigue behaviour are different from that values which were applied in the previous research programs. The main aim of the current investigation is the determination of the fatigue behaviour of the corrugation profile applied in the Móra Ferenc bridge in Hungary, therefore the geometrical properties are similar to the erected bridge structure with minor modifications. Furthermore, the combined loading situation of bending and shear have not been investigated until now for corrugated web girders. Therefore, this study is also aimed performing tests to analyse this effect on fatigue life. Furthermore in the tests extended strain gauge measurements are carried out and documented in details. These results can give a background for numerical model development and verification for researchers working on this topic. 3. Experimental program 3.1. General In the context of the current experimental study, 6 large-scale test specimens were tested in the Structural Laboratory of the Budapest University of Technology and Economics to analyse the fatigue behaviour of the trapezoidally corrugated web girders. The research program has 3 different parts, which are related to the three different research aims. For the corrugation profile, all tested girders were the same, but the test layout, the loading situation, the applied stress range and the weld size were varied. Two test specimens were investigated under four-point-bending to analyse the effect of the longitudinal stress ratio. The second aim of the tests is the analysis of the combined loading situation under bending and shear. Therefore, four specimens were loaded under three-point-bending. Furthermore, the investigations were extended by the analysis of the weld size effect on fatigue behaviour. Of the 4 specimens loaded with combined bending and shear, two specimens were welded with a weld size of 6 mm and two specimens with a weld size of 3 mm. Each specimen was loaded at first using a static load. The purpose of the static tests was the determination of the static response of the girder by measuring the deflection and stresses at different locations. After the static loading, all the fatigue tests were executed with monotonic cyclic loading followed by load fluctuation between Fmin and Fmax. The minimum load was set to 10 kN for all specimens, and different stress ratios were analysed by varying the value of Fmax. The applied loads are summarised in Table 1. 3.2. Test specimens The test specimens were large scale I-girders with a total length of 7150 mm and a span of 6750 mm. The girders have a 6 mm thick and 500 mm depth web, made of cold formed steel plates. The flange width was 225 mm, and the thickness was 20 mm. In cases Table 1 Test program – applied loads. Specimen

Fmin (kN)

Fmax (kN)

DF (kN)

Loading

Weld size

(1) (2) (3) (4) (5) (6)

10 10 10 10 10 10

210 240 240 230 240 220

200 230 230 220 230 210

4-Point-bending 4-Point-bending 3-Point-bending 3-Point-bending 3-Point-bending 3-Point-bending

6 mm 6 mm 6 mm 6 mm 3 mm 3 mm

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where the specimens were loaded under four-point-bending, the fatigue crack was expected in the middle part of the girder in the constant bending moment region. Therefore, the flange thickness was increased to 30 mm at both girder ends 600 mm from the load introduction points to reduce the normal stresses in these end zones. Under the load introduction locations, 20 mm thick stiffeners were applied. Stiffeners above the supports were welded to the web and to both flanges; however, the stiffeners at the load introduction location were cut short at one-fourth of the web depth from the lower flange to avoid disadvantageous fatigue detail. The web to flange weld size was 6 mm in the case of specimens Nos. 1–4 and 3 mm for specimens Nos. 5–6. The start-stop points of the weld toe were kept away from the fold line, so the weld was continuous in the sensitive zone. All the specimens with 3 mm weld size were loaded under three-point-bending. The used steel grade in the tests is S355 (Eurocode notation). The yield and ultimate strengths were measured, and in the case of the 20 mm thick plates, these values are 379 MPa and 517 MPa, respectively. In the case of the web plate with 6 mm thickness, the measured values were 373 MPa and 542 MPa, respectively. The geometry of the specimens are shown in Figs. 2 and 3. The corrugation profile was the same for all specimens, and the geometry is shown in Fig. 4. The fold lengths were a1 = 210 mm and a2 = 212 mm, and the projected lengths of the inclined folds were a3 = 133 mm and a4 = 165 mm. The corrugation angle was 39°, and the bending radius was 60 mm for all specimens. The geometry of the corrugation profile can be seen in Fig. 4. The test specimens were simply supported at both ends. The load was applied through a hydraulic actuator with a maximal loading capacity of 250 kN, which was applied on the girder at between 3 and 4 Hz, depending on the deflection of the girder. In the case of the three-point-bending, the load was applied at midspan as a concentrated load, and in the case of four-pointbending, the load was transferred through a supplementary girder with a span of 1.5 m. The test arrangement and the loading equipment can be seen in Fig. 5a and b. 3.3. Strain gauge measurements A large number of strain gauges were placed on the specimens to measure the stresses during the tests. This was performed to measure the following: – Normal stresses in the upper and lower flange. – Normal stresses in the web. – Geometric (hot spot) stresses at the stress concentration zones. The position of the strain gauges can be seen in Fig. 6. Strain gauges (1–5) were placed on the lower (tension) flange in the mid-

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dle of a parallel fold. Gauges (6–8) were placed on the upper (compressed) flange at the same location as gauges (1, 3 and 5). The aim of the application of these strain gauges was the determination of the normal stress distribution in the flanges far from the stress concentration zones. The strain gauges (9–22) were placed on the web along the height of the specimen in two cross-sections. The aim of these measurements was the determination of the special normal stress distribution of the corrugated web girders in the parallel and in the inclined folds of the web plate. Strain gauges (23–34) were used to measure the hot spot stresses of the analysed specimens at four typical locations, where the initiation of the fatigue cracks was expected. Note that not all the 6 specimens were analysed with such a number and arrangement of strain gauges. Specimen No. 1 was tested using all the 34 strain gauges, but the further specimens were tested by a reduced measurement. The strain gauge locations are the same as shown in Fig. 6 for all the test specimens except for specimens Nos. 4–6, where the location of the strain gauges (1–5) was moved from the middle cross-section of the parallel fold to the middle of the inclined fold to analyse the effect of the fold direction on the flange normal stress distribution. In addition, the strain measurements the deflection of the girders was also measured under the load introduction locations (Figs. 2 and 3), and the applied force was measured with a hydraulic actuator (Figs. 2 and 3). 4. Test results 4.1. Stress distribution under static tests The structural behaviour and the stress distribution of the corrugated web girders were analysed based on the strain measurements. The measured stress distributions in the flange and web plate represent the global structural behaviour of the corrugated web girders, which have not been deeply investigated in the past. In addition, the hot spot stresses were also measured and studied, and these have great importance in fatigue behaviour. This section summarises the tendencies found in the strain measurements during the static tests. 4.1.1. Normal stress measurements in the flange and web – influence of the accordion effect Measurements revealed that the normal stress distribution in the flange is different depending on the position of the analysed cross-section. Within the constant bending moment zone, the following tendency was found. In the line of the parallel folds, the normal stresses are smaller nearer the web and larger far from it. The tendency of the stress distribution between the two flange edges is nearly linear, and the difference changes between 18% and 27% for the analysed girders. Fig. 7 shows the measured

Fig. 2. Geometry of the specimen under 4-point-loading.

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B. Kövesdi, L. Dunai / International Journal of Fatigue 64 (2014) 22–32

Fig. 3. Geometry of the specimen under 3-point-loading.

Fig. 4. Geometry of the corrugation profile.

Fig. 5. (a) Loading under four-point-bending. (b) Loading under three-point-bending.

normal stresses under a 230 kN load level for specimen No. 2 in a cross-section within a parallel fold. Strain was measured at 8 points within the cross-section, with 5 strain gauges placed in the lower flange and 3 in the upper flange. The reason for this phenomenon can be explained by the structural characteristics of the corrugated web. In the cross-section of the parallel folds, the interlock between the upper and lower flanges are better than in the cross-section with an inclined fold. Therefore, the web contribution in the load bearing is more dominant in the cross-section with a parallel fold than in a cross-section with inclined folds. More details on this observations can be found in Kövesdi et al. [15]. This behaviour is also shown by the strain measurements in the web. The measured normal stress distribution in an inclined and in a parallel fold can be seen in Fig. 8. The diagram shows the wellknown ‘‘accordion effect’’ that is typical for the corrugated web girders and that indicates that the longitudinal stresses are

relatively small in the web and dominant in the flanges. Furthermore, the diagram indicates that the normal stresses in the inclined folds are smaller than in the parallel folds. The previous two factors are in correlation with each other, and this results in the difference in the normal stress distribution in the flanges. Line (a) in Fig. 7 represents the calculated normal stress under the applied bending moment with the assumption that only the flanges are taken into account in the inertia calculation, and the web part is neglected. This assumption is based on the so-called ‘‘accordion effect’’ and its consideration is also recommended by the Eurocode 3 (EN1993-1-5 [16]) in the design of girders with corrugated webs. In the line for the inclined folds, the normal stresses are approximately the same along the whole flange width in the constant bending moment zone, and the stresses are just slightly smaller than the calculated value represented by line (a) in Fig. 7. This indicates that the measurements prove the assumption that the normal stresses in the flange of a corrugated web girders

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Fig. 6. Position of the applied strain gauges.

hw [mm]

500

400

300 inclined fold parallel fold

200

100

s [MPa] 0 -80

-60

-40

-20

0

20

40

60

80

100

Fig. 8. Longitudinal normal stresses in the web along the depth.

Fig. 7. Nominal stress distribution in the flanges – specimen No. 2.

can be calculated neglecting the web part from the inertia calculation. The stresses in the cross-section with a parallel fold are smaller nearer the web, but the largest stress can be determined using the above-mentioned assumption. To determine the average stresses in the flange with a parallel fold, an effective cross-section with a small web part can be taken into account. The effective crosssection is calculated based on the stress measurements, and it is

presented in Fig. 9. The effective web is 3/20 of the whole web depth for the girder with the analysed geometry, but it is also dependent on the stiffness ratio of the flange, web plates and the corrugation profile.

4.1.2. Geometric (hot spot) stresses at the flange and web connection The geometric (hot spot) stresses have major importance in the fatigue behaviour of a girder because it measures the local stress concentration in the area, which is sensitive for fatigue. The hot spot stress includes all stress raising effects of a structural detail,

B. Kövesdi, L. Dunai / International Journal of Fatigue 64 (2014) 22–32

3 hw 20

hw

3 hw 20

28

Fig. 9. Equivalent cross-section for the nominal stress calculation.

excluding the stress concentrations due to the local weld profile itself [17]. The structural hot spot stress approach is recommended for welded joints where there is a no clearly defined nominal stress distribution due to the complicated girder geometry, which is the case for corrugated web girders. The hot spot stress can be determined on the basis of stresses of reference points and by an extrapolation to the weld toe. Therefore, the hot spot stresses are measured on each specimen at four different locations with three strain gauges placed behind each other in the distance of 8, 18 and 28 mm from the weld toe. The four measured locations along the web and the strain gauges can be seen in Figs. 6 and 10. Location (1) is the edge of the inclined fold at the beginning of the bending radius of the corrugation profile. Location (2) is placed in the middle of the flange plate close to the inclined web. Location (3) is at the same position as (1) but in the inner side of the corrugation profile. Location (4) is at the same position as location (3) but on the other side of the web. The hot spot stress measurement locations are the same during the tests, but not all locations are measured on each specimens. Table 2 gives an overview on the measured locations for each specimen and the measured stresses. The first column shows the applied load levels in the static tests and the nominal stresses in the constant bending moment zone of the specimens. The second column shows the gauge number. No. 1 is the closest to the web, and No. 3 is the farthest from the web. Columns 3, 5, 7 and 9 show the measured stresses at the strain gauges at all four different locations. Columns 4, 5, 8 and 10 show the maximum Dr values representing the difference between the nominal stresses and the maximum measured stress concentration values. The measurements indicate that the critical point of the corrugated web from the point of view of the hot spot stresses is the fold edge on the inclined fold where the bending radius of the corruga-

Fig. 10. Strain gauges for hot spot stress measurements.

tion profile begins. The same observation was published by Sause et al. [8] and by Ibrahim et al. [11], and this fact is confirmed by the current test results. The highest measured stress concentration reached 124.6% compared to the measured nominal stress in the undisturbed zone in the case of four-point bending. In the case of three-point-bending, the measured maximum stress concentration is 116.4%. The typical stress concentration tendencies are presented in Figs. 11 and 12 in the case of specimens No. 1 and 6, where the stress concentrations were measured at all the four analysed locations. The test results at gauge No. 27 (gauge 2 in location 2) displayed slightly smaller stress value than gauge No. 28 (gauge 3 in location 2), which could be a measuring error. The measurements on the further specimens revealed that the tendency of the stress concentration is the same at location (2) as in the other three measured locations. 4.2. Results of the fatigue tests 4.2.1. Measured stress ranges and fatigue life The nominal stress range in the fatigue tests varied between 100.6 and 159.9 MPa depending on the loading type and specimen geometry. The stresses were measured during the fatigue tests with 5000 cycles to study the structural behaviour of the girder during its life time. The strain measurements are conducted with a 4-s long period by 50 Hz frequency. Table 3 summarises the applied forces, the applied stress ranges and the observed fatigue life times. In columns 2 and 3, the maximum and minimum applied forces and in columns 4 and 5 the normal and shear stresses measured in the undisturbed zone of the flange are presented. The normal stresses were measured on the top (inner side) of the lower flange, and the shear stresses were measured in the corrugated web plate in 50 mm distance from the web to flange weld toe. In the case of the normal stresses, the question arises for which value should be taken into account by the evaluation procedure of the fatigue assessment? One possibility is the highest normal stress in the constant bending moment zone, which is in the middle of the incline fold. The second and third possibilities are the average normal stress in the parallel fold or the normal stress at the web line because the stresses were smaller near to the parallel web fold, where the fatigue crack initiated. Because the stress distribution in the cross-section from where the crack initiated is nearer to the stress distribution of a parallel fold, it was decided to take the stresses into account that were measured in the parallel fold. To simplify the calculation, the average normal stresses were taken into account. Column 7 presents the loading cycles leading to fatigue failure. In the case of the specimens where no fatigue crack was detected, the table presents the loading cycles marked with the sign ‘‘>’’. In the cases of these specimens, the fatigue life was bigger than these values. Therefore, these results can be used as a lower approximation of fatigue life. Table 3 shows that the specimen Nos. 1–2 did not fail after more than 4 million cycles. The applied stress ratio in the cases of these specimens was the smallest (100.6 and 110.6 MPa), and these girders were loaded under a four-point-bending arrangement, which resulted in a pure bending zone in the middle of the girder, where the fatigue crack is expected. Specimens Nos. 3–4 were loaded with higher stress ratios and three-point bending. The higher stress ratio and the complex stress field caused fatigue cracking after 1.3 million cycles on both girders, which indicates the important effect of the combined loading situation on fatigue behaviour. Specimen No. 5 was loaded with the same stress range as specimen No. 3, but the weld size was smaller (3 mm). The fatigue crack was detected after 3.3 million cycles, which is almost triple the fatigue life of specimen No. 3. Specimen No. 6 was loaded with the smaller stress ratio, and no fatigue crack was detected after 15

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B. Kövesdi, L. Dunai / International Journal of Fatigue 64 (2014) 22–32 Table 2 Hot spot stress measurements – stresses in (MPa). Gauge

Location (1)

Ds (%)

Location (2)

Ds (%)

Location (3)

Ds (%)

Location (4)

Ds (%)

Specimen (1) F = 200 kN snom = 101.1 MPa

1 2 3

126.0 118.5 110.0

24.6

118.9 105.4 109.6

17.6

115.5 106.5 102.0

14.2

122.3 115.5 110.3

20.9

Specimen (2) F = 230 kN snom = 110.9 MPa

1 2 3

136.9 127.4 123.0

23.4

Specimen (3) F = 230 kN snom = 146.7 MPa

1 2 3

Specimen (4) F = 220 kN snom = 140.3 MPa

1 2 3

154.3 145.5 140.7

9.9

148.8 142.9 137.7

6.1

141.2 132.3 133.8

0.6

Specimen (5) F = 230 kN snom = 148.8 MPa

1 2 3

159.3 138.7 132.4

7.1

167.5 150.6 150.2

12.5

162.9 145.0 135.0

9.5

Specimen (6) F = 220 kN snom = 133.8 MPa

1 2 3

155.8 144.0 137.6

16.4

142.0 134.1 131.4

6.1

136.0 128.8 124.7

1.6

151.2 144.6 137.3

13.0

location (2)

location (1)

location (4)

location (3)

130

130

120

120

120

120

110

110

110

110

8

weld

10

10

8

weld

10

10

weld

web plate

130

web plate

130

web plate

web plate

normal stress [MPa]

Specimen number, and nominal stress

8

10

10

weld

8

10

10

Fig. 11. Measured hot spot stresses in specimen No. 1.

Fig. 12. Measured hot spot stresses on specimen No. 6.

Table 3 Summary of the fatigue test results. Specimen

Fmin (kN)

Fmax (kN)

Dsnorm (MPa) in the flange

Dt (MPa) in the web

N (db)

1 2 3 4 5 6

10 10 10 10 10 10

210 240 240 230 240 220

100.60 110.63 146.70 140.27 148.81 127.54

0 0 32.51 37.08 33.79 29.11

>4,486,760 >4,162,440 1,309,530 1,325,790 3,271,740 >15,000,000

million cycles. A comparison of the test results of specimens Nos. 3–4 to specimens Nos. 5–6 reveals the important effect of the weld size. The results proved that a larger weld size leads to significantly reduced fatigue life.

4.2.2. Fatigue crack initiation and crack propagation The fatigue crack initiated for all specimens from the weld toe of the tension flange to the web weld at the end of the bending radius between the inclined and parallel fold from the inclined fold

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Fig. 13. Fatigue crack initiation point and crack propagation.

120 100 80

Ds [MPa]

60 40

stresses at location 1 stresses at location 2

20

stresses at location 3

fatigue life [ cycles]

0 0

500000 1000000 1500000 2000000 2500000 3000000 3500000

-20 -40 -60 Fig. 14. Stress history at the characteristic points of specimen No. 5.

side. This is the most sensitive point of the corrugated web girders to fatigue, as also observed by several researchers ([8,11]). This crack initiation point is called as S-point in the literature, and it

is a characteristic point of the corrugated web girders. A typical crack pattern is shown in Fig. 13. The fatigue crack initiated in the case of the specimens Nos. 3–4 from the S-point in the second inclined fold measured from the middle of the specimen. In the case of the specimen No. 5, the fatigue crack initiated from the S-point of the middle inclined fold, as shown in Fig. 13. During the fatigue tests, the stress history measured on the strain gauges near to the S-point were evaluated. Using the strain measurements, the crack initiation and propagation could be followed. A typical stress history is presented in Fig. 14 in the case of the specimen No. 5. Strain gauges (locations 1–4) were placed at the crack initiation areas. The strain measurements revealed that the stresses were almost constant until 2.4 million cycles. After that, the longitudinal stress decreased at location 1 with a high slope until the crack reached the plate surface and led to the fatigue damage. The fatigue crack initiated in the inner side of the flange plate, and therefore, it was undetectable without strain measurements. The measured stresses in the stress concentration zone indicate the start of the crack initiation (2.4 million cycles for specimen No. 5) and the stress redistribution in the girder during fatigue life.

Fig. 15. Typical crack pattern of the trapezoidally corrugated web girders.

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Fig. 16. Fatigue life of trapezoidally corrugated web girders – fatigue detail category.

Table 4 Statistical evaluation of the test results. Specimen number Middle value of the fatigue strength (xm) Standard deviation (Stdv) Reduction factor (k)

20 127.1 MPa 12.74 MPa 2.3

The crack propagated initially in the inner side of the tension flange, and when it reached the flange surface, it propagated perpendicular to the direction of the principal stress in the tension flange (3–5° from the longitudinal axis of the girder). The principal stress and its direction were measured on the tension flange of specimen No. 3 at four different locations with 3 directional (rosetta) strain gauges. The crack propagation was nearly perpendicular to this direction. After the crack reached the flange surface, the propagation became very rapid, going to the flange edge, and the crack propagation continued upward for a short distance in the web, as shown in Fig. 13. 4.2.3. Crack pattern and crack initiation point in the flange plate The crack pattern presented in Fig. 15 shows a typical high cycle fatigue crack. The same crack pattern is observed for all specimens. There is an initial defect or stress concentration zone at the web to flange weld toe, which initially propagated in the flange plate. The crack pattern has a plastic zone with smooth surface between the web and the nearer flange edge, from where the crack initiated. At the other side of the flange, the crack pattern has a rough surface that is related to the fatigue fracture. 5. Evaluation of the test results In the EN1993-1-9 [3], there is no standard design fatigue detail category for corrugated web girders. The relevant fatigue detail category is expected to be lower than girders with flat webs that

are classified in the detail categories of 125 or 112, depending on the welding process, and it can be higher than the fatigue detail category of the flat web girders with transverse stiffeners, which are classified in the fatigue detail category 80 in the EN1993-1-9 [3]. The fatigue detail category of the corrugated web girders may be between these values depending on the corrugation angle and corrugation profile. The stress ratios and the cycle numbers leading to fatigue failure are presented in Fig. 16 for all test specimens. In this diagram, the current and the previous test results found in the literature are also evaluated. In the first step of the evaluation, only the test results of the specimens loaded by four-point bending are evaluated. The characteristic fatigue detail category is determined based on the test results according to the IIW recommendations [17]. To determine the fatigue detail category, the mean value of the fatigue strength (xm) and the standard deviation (Stdv) are determined by 2 million cycles. Table 4 summarises the calculation results and the reduction factor based on the number of specimens. Based on the statistical evaluation and on the number of the evaluated test specimens, the characteristic S–N curve of the analysed structural detail can be determined by Eq (1).

xk ¼ xm  k  Stdv ¼ 127:1  2:3  12:74 ¼ 97:75 MPa

ð1Þ

The calculated characteristic fatigue strength is 97.75 MPa, which can be classified into fatigue detail category 90. On this basis, the corrugated web girders with the analysed corrugation profiles (a < 39°) loaded by pure bending can be considered to be in fatigue detail category 90. In the second step of the evaluation process, the effect of the combined loading situation on the fatigue detail category was studied. The fatigue crack initiated and propagated in the tension flange. Therefore, the equivalent stresses are calculated at the tension flange inner side. Table 5 summarises the measured normal and calculated shear stresses and the fatigue life for specimens Nos. 3–6.

Table 5 Evaluation of the combined loading situation. Specimen

Fmin (kN)

Fmax (kN)

Dsnorm (MPa) in the flange

Dt (MPa) in the flange

Dsequ (MPa) in the flange

N (db)

3 4 5 6

10 10 10 10

240 230 240 220

146.70 140.27 148.81 127.54

0.98 0.94 0.98 0.89

146.71 140.28 148.82 127.55

1,309,530 1,325,790 3,271,740 >15,000,000

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The results indicate that the calculated shear stresses are small, almost negligible at the flange inner side. Therefore, there is only a minor influence between the evaluation based on the pure normal stresses and that based on the equivalent stresses. The diagram in Fig. 16 shows that the points of the specimens Nos. 3–4 are very close to the S–N curve of the previous test results under pure bending. On this basis, it can be concluded that the combined loading situation for the corrugated web girders can be taken into account also with pure normal stresses as well as the equivalent stresses calculated in the tension flange inner side. This conclusion is only valid for the analysed M/V ratio. To generalise this conclusion, further investigations would be needed studying different M/V ratios. The test results demonstrate that the shear stresses measured or calculated in the web panel are not needed to take into account in the fatigue analysis of the trapezoidally corrugated web girders. However, because of the small number of the test results and the small shear stresses, further investigations are needed to draw a strict conclusion. In the third part of the evaluation process, the effect of the weld size on the fatigue life is analysed. Specimens Nos. 5–6 resulted in larger fatigue life with a weld size of 3 mm than specimens Nos. 3– 4 with a weld size of 6 mm. These results indicate that the weld size has a major influence on the fatigue life of corrugated web girders. Therefore, the minimal required weld size is recommended in the design. The effect of the weld size on the fatigue behaviour can be analysed by the hot spot stress theory, which is an ongoing research field in this area.

Based on the fatigue test results, the corrugated web girders with the investigated corrugation profile can be classified into fatigue detail category 90 with pure bending loading. The current measurements prove that the combined loading situation has a significant influence on the fatigue life of corrugated web girders, and this should be taken into account in the fatigue design process. Furthermore, the test results highlighted the importance of the weld size from the point of view of fatigue design. Using a smaller weld size resulted in the fatigue life of the analysed girders being longer. Therefore, the usage of the minimal required weld size is recommended for this design. Further possible research in this field involves the determination of the fatigue detail category based on the hot spot stresses and the determination of a fatigue detail category that takes the corrugation profile and the corrugation angle into consideration, which would make it possible to extend the fatigue design of corrugated web girders for all possible corrugation profiles. Acknowledgments The financial support provided by the NIF Zrt., and the test specimens produced by Rutin Ltd. are gratefully acknowledged. The work reported in the paper has been developed in the framework of the ‘‘Talent care and cultivation in the scientific workshops of BME’’ project. This project is supported by the grant TÁMOP4.2.2.B-10/1–2010-0009, which is gratefully acknowledged. References

6. Summary and conclusions The paper presents an experimental research study on the fatigue behaviour of trapezoidally corrugated web girders. The test program was conducted to support the design of the new Móra Ferenc bridge at the M43 highway over the Tisza River in Hungary. Six large-scale test specimens were investigated under static and repeated loading. The aim of the tests was the analysis of the fatigue behaviour of the corrugated web girders and the determination of their fatigue detail category. In the tests, the fatigue life of the analysed girders were determined under pure bending and under combined bending and shear. Furthermore, the effect of the weld size on the fatigue behaviour was also investigated. The results of the static measurement indicated typical structural behaviour for the corrugated web girders. The well-known ‘‘accordion effect’’, which is typical for this girder type was observed for the analysed girder geometry. The normal stress distributions in the flange and web plates were analysed in a detailed manner. The effect of the bending moment and the shear force on the flange stress distribution was measured and evaluated on the test specimens, and a detailed evaluation can be found in [15]. This paper focuses mainly on the fatigue behaviour of the tested girders. The hot spot stresses were also measured at 4 locations along the girder length. The most sensitive point of the corrugated web girders from the fatigue point of view was determined based on the hot-spot measurements. The stress concentrations were measured and evaluated during the tests. The highest measured stress concentration reached 124.6% compared with the measured nominal stress in the undisturbed zone of the flange in case of four-point bending and 116.4% in the case of three-point bending.

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