- Email: [email protected]
Research on fatigue performance of CFRP reinforced steel crane girder
Composite Structures 154 (2016) 277–285
Contents lists available at ScienceDirect
Composite Structures journal homepage: www.elsevier.com/locate/compstruct
Research on fatigue performance of CFRP reinforced steel crane girder Qing-Rui Yue, Yun Zheng, Xuan Chen, Xiao-Gang Liu ⇑ National Engineering Research Center for Steel Construction, Central Research Institute of Building and Construction CO. Ltd. MCC, Beijing 100088, China
a r t i c l e
i n f o
Article history: Received 7 April 2016 Revised 5 July 2016 Accepted 25 July 2016 Available online 26 July 2016 Keywords: CFRP reinforcement Steel crane girder Fatigue performance Stress intensity factor
a b s t r a c t The fatigue performance of CFRP reinforced steel crane girders was comparatively studied by experimental research. In addition, the stress concentration behavior and the stress intensity factor were also discussed to analyze the mechanism of CFRP reinforcement. The research confirmed that the reinforcement using CFRP layers can significantly improve the fatigue life of the girder, especially if the fatigue stress amplitude is not too large. It is suggested to arrange U-shaped hoop with over 3 layers at the end of the longitude layers, and aside the stiffeners at midspan. The longitude CFRP layers should fully cover the side faces of the bottom flange to avoid potential fatigue fraction initiation here. Fisher’s provision will significantly underestimate the fatigue life of CFRP reinforced girders because it cannot consider the stress concentration relief aside the stiffeners. The CFRP layers can perfectly restrain the development of fatigue fracture. Thus, the stress intensity factor of CFRP reinforced girders increases much slower with fracture length in comparison with unreinforced girders, especially after the fracture develops into the flange. The increasing of longitude CFRP layers may just give little decrease of the stress intensity factor, but lower fatigue stress amplitude can significantly decrease the stress intensity factor. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Steel crane girder is one of the most important components in industrial buildings. In recent years, production technology progress and economic development are rapidly ongoing in China, and therefore most industrial buildings were equipped more manufacturing facilities and arranged more production intensity. Thus, the steel crane girders were mostly subjected to much more frequent and larger fatigue load, resulting in fatigue failure earlier to the designed service life [1]. Such phenomenon is very dangerous to the production safety, and it is quite urgent to find an effective approach to reinforce the existing crane girders. The most critical region for fatigue life exists in the welds between the web and the bottom flanges, as well as the welds between the bottom ends of the stiffeners. Such regions are subjected to cyclic mutative tensile stress. Previous research found that the connection between the web and the bottom end of the stiffeners may firstly exhibit fatigue failure [2]. The NCHRP report on the fatigue performance of stiffeners also indicated [3] the distribution of the flexural stress at the weld toe of the bottom end of stiffeners is dominant to the fatigue life, and the fatigue failure initialed at the bottom end of the stiffeners.
⇑ Corresponding author. E-mail address: [email protected] (X.-G. Liu). http://dx.doi.org/10.1016/j.compstruct.2016.07.066 0263-8223/Ó 2016 Elsevier Ltd. All rights reserved.
Traditional steel structure reinforcement can be realized by means of welding or bolting steel plates to the fracture region. However, such means may results in new stress concentration in the reinforcement region, and therefore cause new fatigue problem. CFRP has light weight, high strength, good long-term performance and corrosion resistance, and excellent fatigue performance. In addition, the CFRP strips can be glued to steel structures with complicated details, and is also easy to apply on site, making it widely applicable. Thus, CFRP is an ideal material for reinforcement of existing steel structures [4]. The basic performance of using CFRP overlays to extend fatigue life of steel plates was already experimentally investigated, and such approach was verified to be effective [5–10]. In addition, CFRP also exhibited satisfactory performance in fatigue reinforcement of steel girders [10–16]. Most of the previous research focused on the fatigue reinforcement of the bottom flanges of girders which is subjected to tension, or the complicated welded joins in bridge girders. Little research can be referred to the fatigue reinforcement of the webs with stiffeners for steel crane girders. This study conducted experimental and theoretical research on the fatigue reinforcement of the webs with stiffeners for the steel crane girder. Previous research confirmed that the most critical region exists in the bottom end of the stiffeners welded to the webs [3]. Thus, the comparative study was firstly conducted by experimental investigation of unreinforced girders and reinforced girders with fatigue reinforcement of the webs using CFRP strips.
278
Q.-R. Yue et al. / Composite Structures 154 (2016) 277–285
Afterwards, the fatigue performance of steel crane girders with CFRP reinforcement of the webs will be analytically discussed. In addition, the numerical model of CFRP reinforced girders was also established to give more analysis on the mechanism of CFRP reinforcement from the view of the stress concentration and the stress intensity factor. 2. Experimental research In this work, totally two unreinforced girders and three girders with fatigue reinforcement of the webs using CFRP strips were designed and tested.
Table 2 Material properties of CFRP strips and structural adhesive.
Tensile strength Elastic modulus Elongation ratio Shear strength Thickness Poisson ratio
CFRP strips
Structural adhesive
4306 MPa 245 GPa 1.71% – 0.167 mm 0.3
40.96 MPa 2.50 GPa 3.17% 14.57 MPa / 0.35
According to GB 50017-2003, the relationship between the fatigue life and the stress amplitude for the connection between the flanges and the web can be expressed by Eq. (3):
2.1. Material property
lg N ¼ 14:9350 4 lg Drf
The experimental research used hot-rolled I section girder fabricated by Q345B steel, and the tested mechanical property of the steel is shown in Table 1. The fatigue reinforcement used UT70-30 CFRP strips and JH-01 structural adhesive, and the mechanical property of them is shown in Table 2.
where Drf is the fatigue stress amplitude in the bottom flange, unit in MPa. For girders subjected to four points bending, the nominal fatigue stress amplitude for the bottom end of the stiffener can be calculated using Eq. (4):
2.2. Design of specimens
Dr ¼
The design of experimental specimens needs to consider both the loading capacity of test equipment and the research focus for this study. As the major focus of this research is the fatigue performance of the connection between the web and the bottom end of the stiffeners, the web height should not be too small so that the influence of the bottom flange will not be too large. In addition, the web height should not be too large to exceed the loading capacity of the fatigue testing machine. Thus, the girder was designed to have a length of 5800 mm, and a height of 506 mm. The girder was tested by four points bending, as illustrated in Fig. 1. To exclude unfavorable influences from the welding between flanges and webs, hot rolled section girder was used. In addition, additional steel plate was welded to the upper flange in order to increase the height of the neutral axis and avoid stability problems. The configuration of the girder section is also shown in Fig. 1. The stiffeners were fillet welded to the web. Some of the specimens were locally cut the stiffeners to decrease the fatigue stress amplitude at the bottom end of stiffeners, and the cutting detail is also shown in Fig. 1. According to the Chinese specification GB 50017-2003 [18], for the connection between the web and the stiffeners, the relationship between the fatigue life and the stress amplitude can be expressed by Eq. (1):
lg N ¼ 12:1673 3 lg Dr
ð1Þ
where N is the fatigue cycles, Dr is the fatigue stress amplitude, unit in MPa. Also, the relationship between the fatigue life and the stress amplitude for the connection between the web and the stiffeners is also provided in Fisher’s NCHRP Report [3], and it can be expressed by Eq. (2):
lg N ¼ 10:3142 3:3198 lg rr
ð2Þ
where N is also the fatigue cycles, rr is the stress amplitude, unit in ksi.
Table 1 Material properties of the steel. Yielding stress
Ultimate stress
Elongation ratio
Elastic modulus
Poisson ratio
408 MPa
563 MPa
23%
206 GPa
0.3
DMy DFly ¼ I I
ð3Þ
ð4Þ
where DF is the fatigue force amplitude at the loading point, l is the distance between loading point and supporting point, I is the cross sectional moment of inertia, and y is the distance between the bottom end of the stiffener and the neutral axis. According to Eqs. (1) and (2), the parameters of the unreinforced basic specimen B-1 and B-2 is shown in Table 3. To avoid bottom flange failure, the fatigue life of the bottom flange was also validated to be much larger than that of the connection between the web and the bottom end of stiffeners. As can be seen from Table 3, the predicted fatigue life by GB 50017-2003 is much smaller than that by Fisher’s approach because the result by GB 500172003 has 95% confidence level and is relatively conservative. As can be seen from Eq. (4), the smaller distance between the bottom end of the stiffeners and the neutral axis will give smaller fatigue stress amplitude. Thus, the fatigue stress amplitude of the stiffener bottom end can be decreased by locally cutting the stiffener where the flexural moment is largest. As can be seen from Table 3, where lc is the cut length of the stiffeners, the fatigue life of BCR-1 and BCR-2 can improve about 50% when the stiffeners were cut by a length of 30 mm, as illustrated in Fig. 1. In addition, the specimen BCR-1 and BCR-2 were also reinforced by gluing CFRP layers. During the CFRP reinforcement process, the surface of steel plates was firstly polished to clear the rust. Then, the surface of steel plates and CFRP layers was scrubbed to clear the grease and dust. Finally, the CFRP was glued to the surface of steel plates by structural adhesive. Previous by Nakamura [16] indicated that more CFRP layers can give better reinforcement, but little improvement can be gained after the number of layers exceeded 5. Thus, BCR-1 and BCR-2 were reinforced using 5 CFRP layers. It was recommended that the optimum adhesive thickness in the range of 0.1–0.7 mm [17]. Therefore, the adhesive thickness of the experimental specimen was about 0.2 mm. To guarantee the quality of the reinforcement, the hoop layers were also arranged aside stiffeners and at the end of the longitude CFRP layers, as shown in Fig. 2(a). In order to do comparative research, specimen BR-2 was also reinforced using 5 CFRP layers, but the stiffeners were not cut. BCR-1 had 1 U-shaped hoop layer at the end of the longitude CFRP layers. BCR-2 and BR-2 had 3 U-shaped hoop layers at the end of the longitude CFRP layers, as shown in Fig. 2(b) (the longitude layers are not drawn). The hoop layers aside the stiffeners terminated at the bottom of the web for BCR-1, as shown in Fig. 2(c) (the longitude layers are not drawn). The hoop layers aside the stiffeners were also U-shaped for BCR-2 and BR-2, as shown in
279
Q.-R. Yue et al. / Composite Structures 154 (2016) 277–285
400
14 10
400
250 150
50
50 fillet welding
438
30
506
6 mm 60 60 9 fillet welding
Stiffener cutting 600
600
600
400
400
600
600
600
100
600
Stiffener cutting
30
600
14 30
100
5600
150
Fig. 1. Details of the experimental girders.
Table 3 Parameters of the experimental specimens.
*
Specimen No.
CFRP layer
lc/mm
Fmax/t
Fmin/t
DF/t
Dr/MPa
N/103 Eq. (1)
N/103 Eq. (2)
Drf /MPa
N/103 Eq. (3)
B-1 B-2 BCR-1 BCR-2 BR-2
/ / 5 5 5
/ / 30 30 /
33 26 33 26 26
6.6 5.2 6.6 5.2 5.2
26.4 20.8 26.4 20.8 20.8
177 140 136(157*) 107(124*) 122
261 534 584(377*) 1200(771*) 810
418 912 1008(623*) 2235(1367*) 1446
208 164 / / /
461 1195 / / /
The contribution of CFRP layers was not included.
2
1
5 layers
hoop layer
hoop layer
350
4
180
60
180
1 hoop layer
3
2
1
3
(a). longitude arrangement
1-1
2-2 (BCR-1)
3-3 (BCR-1)
2-2 (BCR-2, BR-2)
60 180
60 180 350
uncovered
hoop layer 60 180
60 180 350
60
180
hoop layer
longitude layer
longitude layer
hoop layer
3-3 (BCR-2, BR-2)
(b). section
(c). section 2-2 for
(d). section 3-3
(e). section 2-2 for
(f). section 3-3 for BCR-2
1-1
BCR-1
for BCR-1
BCR-2 and BR-2
and BR-2
Fig. 2. Configuration of the CFRP reinforcement.
Fig. 2(e) (the longitude layers are not drawn). The side faces of the bottom flange of BCR-1 were not covered by the longitude CFRP layers, as shown in Fig. 2(d) (the hoop layers are not drawn). The side faces of the bottom flange of BCR-2 and BR-2 were fully covered by the longitude CFRP layers, as shown in Fig. 2(f) (the hoop layers are not drawn).Previous research already confirmed that the CFRP can work together with the steel plates. As the elastic modulus of the adhesive is quite small, its contribution to the stiffness of CFRP reinforced steel girder can be neglected. Based on the plane cross section assumption, the CFRP layers can be equivalent to steel layers with a times thickness of the CFRP layers, where a ¼ Ep =Es , Ep is the elastic modulus of CFRP, and Es is the elastic modulus of steel. Thus, the nominal stress amplitude for the bottom end of the stiffener Drp can be calculated using Eq. (5), and
the stress amplitude for CFRP layers at corresponding position can be calculated using Eq. (6):
Dr ¼
DMy DFly ¼ I0 I0
Drp ¼ a
DMy DFly ¼a I0 I0
ð5Þ
ð6Þ
where I0 is the cross sectional moment of inertia considering the contribution of CFRP layers. For specimen BCR-1, BCR-2 and BR-2, the fatigue stress amplitude at the bottom end of the stiffener after reinforced by CFRP layers is presented in Table 3. In addition, the predicted fatigue life by GB 50017-2003 and Fisher’s approach is also presented in Table 3. As can be seen from the data, the existing
Q.-R. Yue et al. / Composite Structures 154 (2016) 277–285
of CFRP layers significantly decreases the fatigue stress amplitude at the bottom end of the stiffener, and therefore significantly improves the fatigue life of the reinforced girders.
2000 midspan
2.3. Loading procedures and results 2
Previous research confirmed that the fatigue life increase with loading frequency, making the results unconservative [19]. However, the experimental cost will be unacceptable if the loading frequency is too small. Cazand [20] suggested that the loading frequency within 500 cycles per minute had little influence on fatigue life. In addition, ASTM also suggested that the loading frequency between 200 and 700 cycles per minute had little influence on fatigue life. Therefore, the loading frequency of this study was 200 cycles per minute. Firstly, the girders were subjected to cyclic fatigue loading until fatigue fracture occurred. The cyclic maximum load Fmax and minimum load Fmin for the specimens are shown in Table 3. Afterwards, the girders were subjected to static loading until totally fracture failure. 2.3.1. B-1 B-1 was first loaded to the maximum load 33 t, and then the fatigue tests started. After about 460,000 fatigue cycles, the initial fatigue fracture exhibited at the connection between web and the bottom end of stiffener in midspan, as shown in Fig. 3(a). The fracture had a length of about 10 mm, and it gradually developed along the stiffener with increasing cycles. After about 565,000 cycles, the fracture went down into the flanges, as shown in Fig. 3(a). Afterwards, the fracture quickly developed in the bottom flange and the web, and the flange totally fractured after about 579,000 cycles, as shown in Fig. 3(a). Thus, the fatigue test terminated and the girder was subjected to static loading to expose the fatigue fracture. The fracture failure mode of the girder is shown in Fig. 3(b), and the detail of fracture for flanges and webs is shown in Fig. 3 (c) and (d), respectively. Strain gauges were also arranged to monitor the strain variations where fatigue fractures may exhibit. The distribution of the strain gauges which give effective measurement data is shown in Fig. 4 (a), and the measured strain data is shown in Fig. 4(b), where MAX presents the strain corresponding to max load and MIN presents the strain corresponding to min load. As can be seen, the strain of the web aside the stiffener in midspan gradually decreases with increasing loading time, and the strain is around zero after fatigue fracture occurs. The strain of the flange has little increase initially, but it increases sharply at the end before totally flange fracture. 2.3.2. B-2 B-2 was first loaded to the maximum load 26 t, and then the fatigue tests started. During the whole loading process, the web
1-MAX 1-MIN
1600
STRAIN / με
280
1200 800 400 0 -400
1
(a). gauge distribution
0
1
(b). failure mode
2 3 4 TIME / 104s
5
6
(b). strain measurement
Fig. 4. Strains of B-1.
aside the stiffeners did not exhibit significant fracture. After about 561,000 cycles, the fatigue fracture unexpectedly occurred in the bottom flange, which was about 50 mm left of the midspan stiffeners, as shown in Fig. 5. Detailed examination of the specimen found that initial defection was observed around the flange fracture. This defection may result in the unexpected flange fracture. In addition, the strain of the flanges and the web were also measured. The strain distribution of BC-2 is shown in Fig. 6(a), and the strain measurement is shown in Fig. 6(b). As can be seen, the strain of the bottom flange and the web has little variation initially, but the strain of the bottom flange sharply decreases to almost zero after fracture occurs. The strain of the web around the flange fracture has a suddenly increase correspondingly, and also sharply decreases after the fracture went into the web. 2.3.3. BCR-1 The basic experimental parameters of BCR-1 are quite similar to that of B-1. The stiffeners of BCR-1 were locally cut to decrease the fatigue stress amplitude of the stiffener bottom end, as shown in Fig. 1. In addition, the bottom flange and the web were also reinforced by CFRP layers to relieve the fatigue problem which occurred in specimen B-1. The reinforcement detail of BCR-1 is already shown in Fig. 2. During the loading process, no significant indication of failure could be observed at first. After about 1,224,000 cycles, fatigue fracture suddenly occurred in the bottom flange, and the fatigue test terminated. Afterwards, the girder was subjected to static loading to expose the fracture. During the static loading, the adhesive continuously failed, and the CFRP layers significantly separated from the steel plates. In addition, the deflection of the girder significantly increased as well. When the static load was 30 t, the bottom flange totally fractured, the CFRP lays totally separated from the steel plates, and the U-shaped CFRP hoop at the side end also fractured. The fracture in bottom flange occurred
460,000 cycle 565,000 cycle 574,000 cycle 579,000 cycle
(a). fracture development
2-MAX 2-MIN
(c). flange fracture
Fig. 3. Phenomenon of B-1.
(d). web fracture
281
Q.-R. Yue et al. / Composite Structures 154 (2016) 277–285
1600
1-MAX 1-MIN
STRAIN / με
1200 800 400 0 -400
0
2
4 6 TIME / 104s
8
Fig. 8. Strain in bottom flange of BCR-1.
Fig. 5. Failure of B-2.
4000
STRAIN / με
midspan
1-MAX 1-MIN 2-MAX 2--MIN
3000 2000 1000
2
0
1
3
(a). gauge distribution
6
9 12 TIME / 104s
15
(b). strain measurement
Fig. 6. Strains of B-2.
about 50 mm from the midspan, and the detail of the fracture is shown in Fig. 7. No defection can be observed in the flange around the fracture, and therefore it can be concluded the fracture initialed in the bottom flange, which is different from B-1 whose fracture initialed in the web next to the bottom end of the stiffeners. As the girder was already reinforced by CFRP layers, the strain was only measured at the side face of the bottom flange in midspan, and the measurement result is shown in Fig. 8. According to the strain data, it can be concluded that the fracture initialed after about 1,100,000 cycles. In addition, the strain of the bottom flange decreases slower in comparison with B-2 which has sharply strain decrease after flange fracture occurs. This phenomenon is due to the contribution of CFRP layers, which restrain the sharp fracture development in the flange.
2.3.4. BCR-2 BCR-1 exhibited fatigue fracture in bottom flange. Therefore, in order to improve the fatigue life of the flange, the side face of bottom flange of BCR-2 was also covered by CFRP layers. During the loading process, no significant failure could be observed before 3,050,000 cycles. Afterwards, the deflection gradually increased, indicating that the fracture may develop in the bottom flange. After 3,200,000 cycles, the deflection of the girder increased significantly, and the bottom flange exhibited sign of failure. After about 3,230,000 cycles, the test terminated due to over deflection of the girder, and significant failure could be observed in the bottom flange. When the girder was subjected to static loading after fatigue test, the adhesive continuously failed, and the CFRP layers separated from the steel plates. After the tests, the CFRP layers were cut off, and the fracture detail of the girder is shown in Fig. 9. In addition, the oval-shaped region could be observed around the bottom end of the stiffener in the fracture, indicating that the fatigue fracture initialed here. No such region could be observed in the bottom flange. As the steel plates were fully covered by the CFRP layers, the strains were not effectively measured. 2.3.5. BR-2 Similar as BCR-2, the side face of bottom flange of BR-2 was also covered by CFRP layers. The loading process and the phenomenon of BR-2 were quite similar as that of BCR-2. After about 2,800,000 cycle, the deflection of the girder started increasing. After about 2,830,000 cycles, the test terminated due to over deflection of the girder, and the girder failed due to flange fracture. The failure mode and the fracture detail were also similar as that of BCR-2. 2.4. Summary and discussion of the test results The summary of the fatigue life and the fracture initiation for the specimens is shown in Table 4. As can be seen, the fatigue life
(a). failure mode
(b). flange fracture
Fig. 7. Failure of BCR-1.
Fig. 9. Phenomenon of BCR-2.
282
Q.-R. Yue et al. / Composite Structures 154 (2016) 277–285
of BCR-1 is much higher than that of B-1. The fatigue life of BCR-2 and BR-2 is much higher than B-2 as well. It can be concluded the reinforcement using CFRP layers can significantly improve the fatigue life of the girder. The fatigue life of BCR-2 has more improvement with comparison of BCR-1. This phenomenon may be due to following reasons: (1) the stress amplitude of BCR-2 is smaller than that of BCR-1, and therefore the adhesive has a smaller stress, making it less likely to exhibit adhesive failure. (2) the fatigue fracture of BCR-2 develops slower due to lower fatigue stress amplitude. (3) The hoop layers aside the stiffeners in midspan for BCR-1 terminates at the bottom of the web, and the hoop layers at the end of longitude layers has only 1 layer. Therefore, the hoop layers of BCR-1 cannot provide sufficient restraint for the longitude layers. (4) BCR-1 firstly exhibited fatigue fracture in bottom flange, but BCR-2 firstly exhibited fatigue fracture in the web aside the bottom end of stiffeners because the side face of bottom flanges is also reinforced by CFRP layers, making the fatigue life of bottom flange higher. (5) B-2 firstly exhibited fatigue fracture in bottom flange due to initial defection, making the fatigue life lower than expected. Specimen B-1, BCR-2 and BR-2 exhibited fatigue fracture in the web aside the bottom end of the stiffeners. Fisher’s provision (Eq. (2)) can give relatively good prediction of the fatigue life for the unreinforced specimen B-1. However, Fisher’s provision significantly underestimates the fatigue life for BCR-2 and BR-2 with reinforcement by CFRP layers, indicating that the fatigue life of girders with CFPR reinforcement needs further theoretical research. B-2 exhibited flange fracture due to defection, and therefore its fatigue life is much lower than theoretical results. If we use the theoretical life of B-2 by Fisher’s provision (Eq. (2)) as the real fatigue life, the fatigue life improvement of BCR-2 and BR-2 with comparison by B-2 can be obtained, as shown in Table 5. The reinforcement results are also quite satisfactory. The fatigue life of BCR-2 is just a bit higher than that of BR-2. However, according to the data in Table 4, the theoretical fatigue life of BCR-2 by Eq. (2) is much higher than that of BR-2. This phenomenon may be caused by the stiffener cutting process for BCR-2. The stiffeners of BCR-2 were partly cut using abrasive wheel cutting machine, and the cutting region was polished after cutting. The cutting process may result in initial defection in the cutting region. Therefore, it can be concluded the cutting of stiffeners may be not quite effective to improve the fatigue life of girders because it may cause unexpected defection in the cutting region. 2.5. Suggestions for CFRP reinforcement configuration The reinforcement result of BCR-1 was not satisfactory, and the specimen exhibited unexpected fatigue fracture in bottom flange. This specimen only had 1 U-shaped hoop layer at the end of longitude CFRP layers, and the side faces of the bottom flange were not covered by CFRP layers as well. As the adhesive at the end of longitude CFRP layers is subjected to relatively large shear force, the
Table 4 Summary of the test results. Specimen No.
Dr/ MPa
N/103 by Eq. (1)
N/103 by Eq. (2)
N/103 by test
Fracture initiation
B-1 B-2 BCR-1 BCR-2 BR-2
177 140 136 107 122
261 534 584 1200 810
418 912 1008 2235 1446
579 561 1224 3230 2830
a⁄ b⁄ b⁄ a⁄ a⁄
a – the connection between the web and the bottom end of stiffener. ⁄b – the side face of bottom flange.
⁄
Table 5 Fatigue life improvement of BCR-2 and BR-2. Specimen No.
Dr/MPa
N/103
Fatigue life improvement
B-2 BCR-2 BR-2
140 107 122
912 3230 2830
/ 254% 210%
250 200 150 100 50 0 Fig. 10. Stress concentration aside the stiffeners (specimen B-1).
CFPR layers is likely to separate from the steel plates. The Ushaped hoop can restrain the longitude CFRP layers, making the longitude CFRP layers work together with the steel girder. The Ushaped hoop of BCR-1, which had only 1 layer, exhibited tensile fracture due to the tension from longitude CFRP layers. Yet, the U-shaped hoop of BCR-2 and BR-2, which had 3 layers, only exhibited partially adhesive failure, indicating that the U-shaped hoop with 3 layers at the end of longitude CFRP layers can make the longitude CFPR layers develop their full strength. The hoop layers of BCR-1 at midspan were only glued aside the stiffeners, which terminated at the bottom of the web. The test results confirmed that such configuration was not satisfactory, and the hoop layers were likely to separate. The hoop layers of BCR-2 and BR-2 were also U-shaped, and the test results confirmed such configuration could make the hoop layer work together with longitude layers, and restrained the longitude layers from separating from the steel plates. The side faces of the bottom flange of BCR-1 were not covered by CFRP layers, and the specimens exhibited fatigue fracture initialed from the side face of the bottom flange. Thus, the fatigue life of BCR-1 is much lower than that of BCR-2 and BR-2. Specimen BCR-2 and BR-2 with CFRP layers covering the side faces of the bottom flange both exhibited fatigue fracture initialed from the wed aside the bottom end of the stiffeners, and no fatigue initiation could be observed in the bottom flange. Thus, it can be concluded that the CFRP layers configuration at the side faces of the bottom flange for BCR-2 and BR-2 can provide satisfactory reinforcement. 3. Analytical research In this section, the numerical model of CFRP reinforced steel girder will be established using the finite element software MSC. Marc [21]. The stress concentration aside the stiffeners and the stress intensity factor (SIF) will be discussed to analyze the influence of CFRP reinforcement, and the development of the fatigue fracture before and after CFRP reinforcement will also be comparatively studied. 3.1. Numerical modeling The CFRP reinforced steel girder can be modeled using ‘‘solidshell” model [10]. As the fatigue fracture occurs at the midspan which is subjected to largest flexural moment, the steel plates in
283
Q.-R. Yue et al. / Composite Structures 154 (2016) 277–285 Table 6 The stress concentration factor for the experimental specimens. Specimen No.
B-1
B-2
BCR-1
BCR-2
BR-2
Stress concentration factor
1.41
1.38
1.25
1.24
1.22
within 6 mm from the stiffeners, making the actual stress much larger than the nominal stress. The stress concentration phenomenon will influence the fatigue life. Assuming that we take the stress which is 6 mm away from the stiffeners as the hot spot stress, the stress concentration factor can be defined as the ratio of the hot spot stress to the nominal stress. The stress concentration factor for the experimental specimens is shown in Table 6. Obviously, the stress concentration factor for CFRP reinforced specimens is much smaller that the unreinforced specimens. The existing of CFRP layers not only decreases the nominal stress of steel plates, but also relieves the stress concentration in the web aside the stiffeners. Fisher’s provision (Eq. (2)) significantly underestimates the fatigue life of CFRP reinforced specimens because the relief of stress concentration in the web due to the CFRP layers cannot be considered. Therefore, the fatigue mechanism of CFRP reinforced girder needs further theoretical research. 3.3. Discussions on stress intensity factor After the fatigue fracture initiation occurs, the fracture will gradually develops with increasing fatigue cycles. This period is a major part of the total fatigue life. During this period, the stress intensity factor is the critical parameter for the fatigue life because it is dominant to the fatigue fracture growth rate, as shown in Eq. (7):
lg da=dN ¼ lg C þ m lg K Fig. 11. Element mesh around the fracture tip.
this region are simulated using 20 nodes solid element. To decrease the cost of computation, the steel plates in other regions are simulated using 8 nodes solid element. The two parts of solid elements representing steel girder are glued to make them work together. The adhesive and CFRP layers are simulated using 8 nodes thick shell elements at midspan, and are also simulated using 4 nodes thick shell elements in other regions. The shell elements and the solid elements are all glued to work together. The material property of steel plates, CFRP layers and the adhesive are shown in Tables 1 and 2. 3.2. Discussions on stress concentration Obviously, significant stress concentration will exist aside the welding between the web and the stiffeners, and the typical stress concentration of BC-1 aside the stiffeners is shown in Fig. 10. According to the figure, the stress concentration is significant
stage-4 10mm stage-3 40mm stage-2 30mm stage-1 30mm stage-3 14mm stage-4 10mm
B-1 & B-2
stage-5 30mm stage-4 10mm
stage-5 30mm stage-4 10mm
stage-3 80mm
stage-3 80mm
stage-2 40mm
stage-2 70mm
stage-1 60mm
stage-1 30mm stage-3 14mm stage-4 10mm stage-5 30mm
stage-3 14mm stage-4 10mm stage-5 30mm
BCR-1 & BCR-2
(a). B-1 and B-2
ð7Þ
where a is the fatigue fracture length, N is the fatigue cycle, C and m is the material constants, and K is the stress intensity factor (SIF). J integral method [22,23] is a basic approach to calculate the stress intensity factor, and it can be realized in the finite element software MSC. Marc. The optimization of mesh can improve the accuracy of J integral. MSC. Marc [21] suggests radial mesh grid around the fracture tip, and higher order elements are also suggested to be used around the fracture. Barsoum [24] suggested the 20 nodes solid elements used around the fracture tip, and the suggested element mesh is shown in Fig. 11. The calculation of the stress intensity factor by numerical simulation needs to define the fracture development first. According to the experimental research, the fracture development for the specimens is assumed as shown in Fig. 12. Thus, by modeling different fatigue fractures in the specimen, the stress intensity factors corresponding to different fracture lengths for all the experimental specimens are calculated by numerical analysis, as shown in Fig. 13(a&b). The stress intensity factor K of unreinforced experimental specimen B-1 and B-2 keeps increasing with the fracture
(b). BCR-1 and BCR-2
BR-2
(b). BR-2
Fig. 12. Fracture development for the experimental specimens.
Q.-R. Yue et al. / Composite Structures 154 (2016) 277–285
4000
B-1 BCR-1
3200
K / MPA.m0.5
K / MPA.m0.5
4000
2400 1600 800 0
1500
B-2 BCR-2 BR-2
3200 2400 1600 800
0
50
100 150 200 250 300 a / mm
(a). B-1 vs. BCR-1
0
BCR-1 BCR-1*(3 LAYER) BCR-2
1200
K / MPA.m0.5
284
900 600 300
0
50
100 150 200 250 300 a / mm
(b). B-2 vs. BCR-2, BR-2
0
0
50
100 150 200 250 300 a / mm
(b). BCR-1(*) vs. BCR-2
Fig. 13. Stress intensity factor corresponding to different fracture lengths.
length a. When the fracture develops in the web (a < 60 mm), K increases relatively slower with a. Yet, when the fracture goes into the flange (a > 60 mm), K increases faster with a, indicating the fracture develops faster. Compared with the unreinforced specimen, the stress intensity factor of the reinforced specimen BCR-1, BCR-2 and BR-2 increases much slower, indicating the reinforcement result is satisfactory. The influence of CFRP reinforcement becomes more significant when the fracture is longer. When the fracture goes into the flange (100 mm < a < 194 mm), the stress intensity factor also has a fast increase, which also indicating the fracture develops faster. However, the stress intensity factor of CFRP reinforced specimen has no continuous significant increase after the fracture develops in the flange in comparison with the unreinforced specimen, indicating that the CFRP layers can perfectly restrain the development of fatigue fracture. The relationship between the stress intensity factor and fracture length for BCR-2 and BR-2 had little difference. Yet, the stress intensity factor of BR-2 increases a bit faster with fracture length than BCR-2 at the beginning of fracture. This is because the stress at the bottom end of the stiffener for BR-2 is a bit larger as its stiffener is not cut. The comparison between BCR-1 and BCR-1⁄ which has 3 longitude CFRP reinforcement layers is shown in Fig. 13(c). As can be seen, the stress intensity factor of BCR-1⁄ with 3 longitude CFRP layers is a bit larger, but not quite significant. That’s to say, the continuous increasing of CFRP reinforcement layers may just give little improvement. The stress intensity factor of BCR-2 with lower fatigue stress amplitude is much smaller than that of BCR-1, indicating that the stress amplitude has significant influence on the fracture growth speed. 4. Conclusions This paper studied the fatigue performance of CFRP reinforced steel crane girders. Firstly, the experimental research was conducted to explore the fatigue behavior of the CFRP reinforced girders. On this basis, the influence of different reinforcement parameters was discussed, and the configuration details for CFRP reinforcement were proposed. Finally, the numerical model of CFRP reinforced girder was established using MSC. Marc. On this basis, the influence of CFRP on the stress concentration behavior before fatigue fracture and stress intensity factor after fatigue fracture was discussed to analyze the mechanism of CFRP reinforcement. The conclusions are as follows: (1) The reinforcement using CFRP layers can significantly improve the fatigue life of the girder. The lower fatigue stress amplitude, the more significant reinforcement result.
(2) Fisher’s provision can give relatively good prediction for the fatigue life of the unreinforced steel girder, but will also significantly underestimate the fatigue life for the fatigue life of reinforced girders using CFRP layers. (3) The approach of partially cutting stiffeners is not effective to improve the fatigue life of girders because it may cause unexpected defection in the cutting region. (4) The U-shaped hoop can restrain the longitude CFRP layers, making the longitude CFRP layers work together with the steel girder. It is suggested that the U-shaped hoop arranged both aside the stiffeners at midspan and at the end of the longitude layers, and the U-shaped hoop at the end of longitude layers has more than 3 layers. (5) The longitude CFRP layers should have good configuration detail to fully cover the side faces of the bottom flange to avoid the fatigue fracture initiation here. (6) Numerical analysis indicates that the CFRP layers can relieve the stress concentration aside the stiffeners, and therefore the fatigue mechanism of CFRP reinforced girder needs further theoretical research. (7) The CFRP layers can perfectly restrain the development of the fatigue fracture. The stress intensity factor of CFRP reinforced girders increases much slower with fracture length in comparison with unreinforced girders, especially after the fracture develops into the flange. The continuous increasing of CFRP layers may just give little decrease of the stress intensity factor, but the lower fatigue stress amplitude can significantly decrease the stress intensity factor.
Acknowledgement The authors gratefully appreciate the financial support provided by the National Natural Science Foundation of China (51578559). References [1] Zhao Z, Haldar A, Breen FLJ. Fatigue-reliability evaluation of steel bridges. J Struct Eng-ASCE 1994;120(5):1604–23. [2] Metallurgical Industry Ministry Building Research Institute. Fatigue data report of steel structures; 1978 [in Chinese]. [3] Fisher JW, Albrecht RA. Fatigue strength of steel beams with welded stiffeners and attachments, National cooperative highway research program report 147. Leigh University; 1974. [4] Zhao XL, Zhang L. State-of-the-art review on FRP strengthened steel structures. Eng Struct 2007;29(8):1808–23. [5] Colombi P, Bassetti A, Nussbaumer A. Analysis of cracked steel members reinforce by pre-tress composite patch. Fatigue Fract Eng Mater Struct 2003;26:59–66. [6] Jones SC, Civjan SA. Application of fiber reinforced polymer overlays to extend steel fatigue life. J Compos Constr 2003;7(4):331–8. [7] Feng P, Hu LL, Zhao XL, et al. Study on thermal effects on fatigue behavior of cracked steel plates strengthened by CFRP sheets. Thin-Walled Struct 2014;82:311–20.
Q.-R. Yue et al. / Composite Structures 154 (2016) 277–285 [8] Hu LL, Zhao XL, Feng P. Fatigue behaviour of cracked high strength steel plates strengthened by CFRP. J Compos Constr 2016. http://dx.doi.org/10.1061/(ASCE) CC.1943-5614.0000698. [9] Colombi P, Fava G, Sonzogni L. Fatigue crack growth in CFRP-strengthened steel plates. Compos Part B 2015;72:87–96. [10] Zheng Y, Ye LP, Yue QR. Study on fatigue behavior of cracked tensile steel plates reinforced with CFRP plates. Eng Mech 2007;24(6):91–7 [in Chinese]. [11] Miller T, Chajes M, Mertz D, Hastings J. Strengthening of a steel bridge girder using CFRP plates. J Bridge Eng 2001;6(6):514–22. [12] Tavakkolizadeh M, Saadatmanesh H. Fatigue strength of steel girders strengthened with CFRP patch. J Struct Eng-ASCE 2003;129(2):186–96. [13] Nozaka K. Repair of fatigue steel bridge girders with carbon fiber strips [Doctoral dissertation]. University of Minnesota; 2002. [14] Deng J, Lee MMK. Fatigue performance of metallic beam strengthened with a bonded CFRP plate. Compos Struct 2007;78:222–31. [15] Teng JG, Yu T, Fernando D. Strengthening of steel structures with fiberreinforced polymer composites. J Constr Steel Res 2012;78:131–43.
285
[16] Nakamura H. Experimental study on repair of fatigue cracks at welded web gusset joint. Thin-Walled Struct 2009;47:1059–68. [17] Sela N, Ishai O, Banks-Sillst L. The effect of adhesive thickness on interlaminar fracture toughness of interleaved CFRP specimens. Composites 1989;20 (3):257–63. [18] GB50017-2003. Code for design of steel structures (in Chinese). [19] Zhao QL, Wang JQ, Jin GQ. Analysis on the ‘‘reverse-arch prestressed technique” and the improved bearing capacity for steel structures strengthened by carbon-fiber. Steel Constr 2002;17(59):51–4 [in Chinese]. [20] Cazand R. Fatigue of metals, 1953. [21] MSC Software Corporation. Marc 2010 user’s guide. [22] Rice JR. A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 1968;35:379–86. [23] Moura B, Shih CF. A treatment of crack tip contour integrals. Int J Fract 1987;35:295–310. [24] Barsoum RS. On the use of isoparametric finite elements in linear fracture mechanics. Int J Numer Meth Eng 1976;10:25–37.
Contents lists available at ScienceDirect
Composite Structures journal homepage: www.elsevier.com/locate/compstruct
Research on fatigue performance of CFRP reinforced steel crane girder Qing-Rui Yue, Yun Zheng, Xuan Chen, Xiao-Gang Liu ⇑ National Engineering Research Center for Steel Construction, Central Research Institute of Building and Construction CO. Ltd. MCC, Beijing 100088, China
a r t i c l e
i n f o
Article history: Received 7 April 2016 Revised 5 July 2016 Accepted 25 July 2016 Available online 26 July 2016 Keywords: CFRP reinforcement Steel crane girder Fatigue performance Stress intensity factor
a b s t r a c t The fatigue performance of CFRP reinforced steel crane girders was comparatively studied by experimental research. In addition, the stress concentration behavior and the stress intensity factor were also discussed to analyze the mechanism of CFRP reinforcement. The research confirmed that the reinforcement using CFRP layers can significantly improve the fatigue life of the girder, especially if the fatigue stress amplitude is not too large. It is suggested to arrange U-shaped hoop with over 3 layers at the end of the longitude layers, and aside the stiffeners at midspan. The longitude CFRP layers should fully cover the side faces of the bottom flange to avoid potential fatigue fraction initiation here. Fisher’s provision will significantly underestimate the fatigue life of CFRP reinforced girders because it cannot consider the stress concentration relief aside the stiffeners. The CFRP layers can perfectly restrain the development of fatigue fracture. Thus, the stress intensity factor of CFRP reinforced girders increases much slower with fracture length in comparison with unreinforced girders, especially after the fracture develops into the flange. The increasing of longitude CFRP layers may just give little decrease of the stress intensity factor, but lower fatigue stress amplitude can significantly decrease the stress intensity factor. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Steel crane girder is one of the most important components in industrial buildings. In recent years, production technology progress and economic development are rapidly ongoing in China, and therefore most industrial buildings were equipped more manufacturing facilities and arranged more production intensity. Thus, the steel crane girders were mostly subjected to much more frequent and larger fatigue load, resulting in fatigue failure earlier to the designed service life [1]. Such phenomenon is very dangerous to the production safety, and it is quite urgent to find an effective approach to reinforce the existing crane girders. The most critical region for fatigue life exists in the welds between the web and the bottom flanges, as well as the welds between the bottom ends of the stiffeners. Such regions are subjected to cyclic mutative tensile stress. Previous research found that the connection between the web and the bottom end of the stiffeners may firstly exhibit fatigue failure [2]. The NCHRP report on the fatigue performance of stiffeners also indicated [3] the distribution of the flexural stress at the weld toe of the bottom end of stiffeners is dominant to the fatigue life, and the fatigue failure initialed at the bottom end of the stiffeners.
⇑ Corresponding author. E-mail address: [email protected] (X.-G. Liu). http://dx.doi.org/10.1016/j.compstruct.2016.07.066 0263-8223/Ó 2016 Elsevier Ltd. All rights reserved.
Traditional steel structure reinforcement can be realized by means of welding or bolting steel plates to the fracture region. However, such means may results in new stress concentration in the reinforcement region, and therefore cause new fatigue problem. CFRP has light weight, high strength, good long-term performance and corrosion resistance, and excellent fatigue performance. In addition, the CFRP strips can be glued to steel structures with complicated details, and is also easy to apply on site, making it widely applicable. Thus, CFRP is an ideal material for reinforcement of existing steel structures [4]. The basic performance of using CFRP overlays to extend fatigue life of steel plates was already experimentally investigated, and such approach was verified to be effective [5–10]. In addition, CFRP also exhibited satisfactory performance in fatigue reinforcement of steel girders [10–16]. Most of the previous research focused on the fatigue reinforcement of the bottom flanges of girders which is subjected to tension, or the complicated welded joins in bridge girders. Little research can be referred to the fatigue reinforcement of the webs with stiffeners for steel crane girders. This study conducted experimental and theoretical research on the fatigue reinforcement of the webs with stiffeners for the steel crane girder. Previous research confirmed that the most critical region exists in the bottom end of the stiffeners welded to the webs [3]. Thus, the comparative study was firstly conducted by experimental investigation of unreinforced girders and reinforced girders with fatigue reinforcement of the webs using CFRP strips.
278
Q.-R. Yue et al. / Composite Structures 154 (2016) 277–285
Afterwards, the fatigue performance of steel crane girders with CFRP reinforcement of the webs will be analytically discussed. In addition, the numerical model of CFRP reinforced girders was also established to give more analysis on the mechanism of CFRP reinforcement from the view of the stress concentration and the stress intensity factor. 2. Experimental research In this work, totally two unreinforced girders and three girders with fatigue reinforcement of the webs using CFRP strips were designed and tested.
Table 2 Material properties of CFRP strips and structural adhesive.
Tensile strength Elastic modulus Elongation ratio Shear strength Thickness Poisson ratio
CFRP strips
Structural adhesive
4306 MPa 245 GPa 1.71% – 0.167 mm 0.3
40.96 MPa 2.50 GPa 3.17% 14.57 MPa / 0.35
According to GB 50017-2003, the relationship between the fatigue life and the stress amplitude for the connection between the flanges and the web can be expressed by Eq. (3):
2.1. Material property
lg N ¼ 14:9350 4 lg Drf
The experimental research used hot-rolled I section girder fabricated by Q345B steel, and the tested mechanical property of the steel is shown in Table 1. The fatigue reinforcement used UT70-30 CFRP strips and JH-01 structural adhesive, and the mechanical property of them is shown in Table 2.
where Drf is the fatigue stress amplitude in the bottom flange, unit in MPa. For girders subjected to four points bending, the nominal fatigue stress amplitude for the bottom end of the stiffener can be calculated using Eq. (4):
2.2. Design of specimens
Dr ¼
The design of experimental specimens needs to consider both the loading capacity of test equipment and the research focus for this study. As the major focus of this research is the fatigue performance of the connection between the web and the bottom end of the stiffeners, the web height should not be too small so that the influence of the bottom flange will not be too large. In addition, the web height should not be too large to exceed the loading capacity of the fatigue testing machine. Thus, the girder was designed to have a length of 5800 mm, and a height of 506 mm. The girder was tested by four points bending, as illustrated in Fig. 1. To exclude unfavorable influences from the welding between flanges and webs, hot rolled section girder was used. In addition, additional steel plate was welded to the upper flange in order to increase the height of the neutral axis and avoid stability problems. The configuration of the girder section is also shown in Fig. 1. The stiffeners were fillet welded to the web. Some of the specimens were locally cut the stiffeners to decrease the fatigue stress amplitude at the bottom end of stiffeners, and the cutting detail is also shown in Fig. 1. According to the Chinese specification GB 50017-2003 [18], for the connection between the web and the stiffeners, the relationship between the fatigue life and the stress amplitude can be expressed by Eq. (1):
lg N ¼ 12:1673 3 lg Dr
ð1Þ
where N is the fatigue cycles, Dr is the fatigue stress amplitude, unit in MPa. Also, the relationship between the fatigue life and the stress amplitude for the connection between the web and the stiffeners is also provided in Fisher’s NCHRP Report [3], and it can be expressed by Eq. (2):
lg N ¼ 10:3142 3:3198 lg rr
ð2Þ
where N is also the fatigue cycles, rr is the stress amplitude, unit in ksi.
Table 1 Material properties of the steel. Yielding stress
Ultimate stress
Elongation ratio
Elastic modulus
Poisson ratio
408 MPa
563 MPa
23%
206 GPa
0.3
DMy DFly ¼ I I
ð3Þ
ð4Þ
where DF is the fatigue force amplitude at the loading point, l is the distance between loading point and supporting point, I is the cross sectional moment of inertia, and y is the distance between the bottom end of the stiffener and the neutral axis. According to Eqs. (1) and (2), the parameters of the unreinforced basic specimen B-1 and B-2 is shown in Table 3. To avoid bottom flange failure, the fatigue life of the bottom flange was also validated to be much larger than that of the connection between the web and the bottom end of stiffeners. As can be seen from Table 3, the predicted fatigue life by GB 50017-2003 is much smaller than that by Fisher’s approach because the result by GB 500172003 has 95% confidence level and is relatively conservative. As can be seen from Eq. (4), the smaller distance between the bottom end of the stiffeners and the neutral axis will give smaller fatigue stress amplitude. Thus, the fatigue stress amplitude of the stiffener bottom end can be decreased by locally cutting the stiffener where the flexural moment is largest. As can be seen from Table 3, where lc is the cut length of the stiffeners, the fatigue life of BCR-1 and BCR-2 can improve about 50% when the stiffeners were cut by a length of 30 mm, as illustrated in Fig. 1. In addition, the specimen BCR-1 and BCR-2 were also reinforced by gluing CFRP layers. During the CFRP reinforcement process, the surface of steel plates was firstly polished to clear the rust. Then, the surface of steel plates and CFRP layers was scrubbed to clear the grease and dust. Finally, the CFRP was glued to the surface of steel plates by structural adhesive. Previous by Nakamura [16] indicated that more CFRP layers can give better reinforcement, but little improvement can be gained after the number of layers exceeded 5. Thus, BCR-1 and BCR-2 were reinforced using 5 CFRP layers. It was recommended that the optimum adhesive thickness in the range of 0.1–0.7 mm [17]. Therefore, the adhesive thickness of the experimental specimen was about 0.2 mm. To guarantee the quality of the reinforcement, the hoop layers were also arranged aside stiffeners and at the end of the longitude CFRP layers, as shown in Fig. 2(a). In order to do comparative research, specimen BR-2 was also reinforced using 5 CFRP layers, but the stiffeners were not cut. BCR-1 had 1 U-shaped hoop layer at the end of the longitude CFRP layers. BCR-2 and BR-2 had 3 U-shaped hoop layers at the end of the longitude CFRP layers, as shown in Fig. 2(b) (the longitude layers are not drawn). The hoop layers aside the stiffeners terminated at the bottom of the web for BCR-1, as shown in Fig. 2(c) (the longitude layers are not drawn). The hoop layers aside the stiffeners were also U-shaped for BCR-2 and BR-2, as shown in
279
Q.-R. Yue et al. / Composite Structures 154 (2016) 277–285
400
14 10
400
250 150
50
50 fillet welding
438
30
506
6 mm 60 60 9 fillet welding
Stiffener cutting 600
600
600
400
400
600
600
600
100
600
Stiffener cutting
30
600
14 30
100
5600
150
Fig. 1. Details of the experimental girders.
Table 3 Parameters of the experimental specimens.
*
Specimen No.
CFRP layer
lc/mm
Fmax/t
Fmin/t
DF/t
Dr/MPa
N/103 Eq. (1)
N/103 Eq. (2)
Drf /MPa
N/103 Eq. (3)
B-1 B-2 BCR-1 BCR-2 BR-2
/ / 5 5 5
/ / 30 30 /
33 26 33 26 26
6.6 5.2 6.6 5.2 5.2
26.4 20.8 26.4 20.8 20.8
177 140 136(157*) 107(124*) 122
261 534 584(377*) 1200(771*) 810
418 912 1008(623*) 2235(1367*) 1446
208 164 / / /
461 1195 / / /
The contribution of CFRP layers was not included.
2
1
5 layers
hoop layer
hoop layer
350
4
180
60
180
1 hoop layer
3
2
1
3
(a). longitude arrangement
1-1
2-2 (BCR-1)
3-3 (BCR-1)
2-2 (BCR-2, BR-2)
60 180
60 180 350
uncovered
hoop layer 60 180
60 180 350
60
180
hoop layer
longitude layer
longitude layer
hoop layer
3-3 (BCR-2, BR-2)
(b). section
(c). section 2-2 for
(d). section 3-3
(e). section 2-2 for
(f). section 3-3 for BCR-2
1-1
BCR-1
for BCR-1
BCR-2 and BR-2
and BR-2
Fig. 2. Configuration of the CFRP reinforcement.
Fig. 2(e) (the longitude layers are not drawn). The side faces of the bottom flange of BCR-1 were not covered by the longitude CFRP layers, as shown in Fig. 2(d) (the hoop layers are not drawn). The side faces of the bottom flange of BCR-2 and BR-2 were fully covered by the longitude CFRP layers, as shown in Fig. 2(f) (the hoop layers are not drawn).Previous research already confirmed that the CFRP can work together with the steel plates. As the elastic modulus of the adhesive is quite small, its contribution to the stiffness of CFRP reinforced steel girder can be neglected. Based on the plane cross section assumption, the CFRP layers can be equivalent to steel layers with a times thickness of the CFRP layers, where a ¼ Ep =Es , Ep is the elastic modulus of CFRP, and Es is the elastic modulus of steel. Thus, the nominal stress amplitude for the bottom end of the stiffener Drp can be calculated using Eq. (5), and
the stress amplitude for CFRP layers at corresponding position can be calculated using Eq. (6):
Dr ¼
DMy DFly ¼ I0 I0
Drp ¼ a
DMy DFly ¼a I0 I0
ð5Þ
ð6Þ
where I0 is the cross sectional moment of inertia considering the contribution of CFRP layers. For specimen BCR-1, BCR-2 and BR-2, the fatigue stress amplitude at the bottom end of the stiffener after reinforced by CFRP layers is presented in Table 3. In addition, the predicted fatigue life by GB 50017-2003 and Fisher’s approach is also presented in Table 3. As can be seen from the data, the existing
Q.-R. Yue et al. / Composite Structures 154 (2016) 277–285
of CFRP layers significantly decreases the fatigue stress amplitude at the bottom end of the stiffener, and therefore significantly improves the fatigue life of the reinforced girders.
2000 midspan
2.3. Loading procedures and results 2
Previous research confirmed that the fatigue life increase with loading frequency, making the results unconservative [19]. However, the experimental cost will be unacceptable if the loading frequency is too small. Cazand [20] suggested that the loading frequency within 500 cycles per minute had little influence on fatigue life. In addition, ASTM also suggested that the loading frequency between 200 and 700 cycles per minute had little influence on fatigue life. Therefore, the loading frequency of this study was 200 cycles per minute. Firstly, the girders were subjected to cyclic fatigue loading until fatigue fracture occurred. The cyclic maximum load Fmax and minimum load Fmin for the specimens are shown in Table 3. Afterwards, the girders were subjected to static loading until totally fracture failure. 2.3.1. B-1 B-1 was first loaded to the maximum load 33 t, and then the fatigue tests started. After about 460,000 fatigue cycles, the initial fatigue fracture exhibited at the connection between web and the bottom end of stiffener in midspan, as shown in Fig. 3(a). The fracture had a length of about 10 mm, and it gradually developed along the stiffener with increasing cycles. After about 565,000 cycles, the fracture went down into the flanges, as shown in Fig. 3(a). Afterwards, the fracture quickly developed in the bottom flange and the web, and the flange totally fractured after about 579,000 cycles, as shown in Fig. 3(a). Thus, the fatigue test terminated and the girder was subjected to static loading to expose the fatigue fracture. The fracture failure mode of the girder is shown in Fig. 3(b), and the detail of fracture for flanges and webs is shown in Fig. 3 (c) and (d), respectively. Strain gauges were also arranged to monitor the strain variations where fatigue fractures may exhibit. The distribution of the strain gauges which give effective measurement data is shown in Fig. 4 (a), and the measured strain data is shown in Fig. 4(b), where MAX presents the strain corresponding to max load and MIN presents the strain corresponding to min load. As can be seen, the strain of the web aside the stiffener in midspan gradually decreases with increasing loading time, and the strain is around zero after fatigue fracture occurs. The strain of the flange has little increase initially, but it increases sharply at the end before totally flange fracture. 2.3.2. B-2 B-2 was first loaded to the maximum load 26 t, and then the fatigue tests started. During the whole loading process, the web
1-MAX 1-MIN
1600
STRAIN / με
280
1200 800 400 0 -400
1
(a). gauge distribution
0
1
(b). failure mode
2 3 4 TIME / 104s
5
6
(b). strain measurement
Fig. 4. Strains of B-1.
aside the stiffeners did not exhibit significant fracture. After about 561,000 cycles, the fatigue fracture unexpectedly occurred in the bottom flange, which was about 50 mm left of the midspan stiffeners, as shown in Fig. 5. Detailed examination of the specimen found that initial defection was observed around the flange fracture. This defection may result in the unexpected flange fracture. In addition, the strain of the flanges and the web were also measured. The strain distribution of BC-2 is shown in Fig. 6(a), and the strain measurement is shown in Fig. 6(b). As can be seen, the strain of the bottom flange and the web has little variation initially, but the strain of the bottom flange sharply decreases to almost zero after fracture occurs. The strain of the web around the flange fracture has a suddenly increase correspondingly, and also sharply decreases after the fracture went into the web. 2.3.3. BCR-1 The basic experimental parameters of BCR-1 are quite similar to that of B-1. The stiffeners of BCR-1 were locally cut to decrease the fatigue stress amplitude of the stiffener bottom end, as shown in Fig. 1. In addition, the bottom flange and the web were also reinforced by CFRP layers to relieve the fatigue problem which occurred in specimen B-1. The reinforcement detail of BCR-1 is already shown in Fig. 2. During the loading process, no significant indication of failure could be observed at first. After about 1,224,000 cycles, fatigue fracture suddenly occurred in the bottom flange, and the fatigue test terminated. Afterwards, the girder was subjected to static loading to expose the fracture. During the static loading, the adhesive continuously failed, and the CFRP layers significantly separated from the steel plates. In addition, the deflection of the girder significantly increased as well. When the static load was 30 t, the bottom flange totally fractured, the CFRP lays totally separated from the steel plates, and the U-shaped CFRP hoop at the side end also fractured. The fracture in bottom flange occurred
460,000 cycle 565,000 cycle 574,000 cycle 579,000 cycle
(a). fracture development
2-MAX 2-MIN
(c). flange fracture
Fig. 3. Phenomenon of B-1.
(d). web fracture
281
Q.-R. Yue et al. / Composite Structures 154 (2016) 277–285
1600
1-MAX 1-MIN
STRAIN / με
1200 800 400 0 -400
0
2
4 6 TIME / 104s
8
Fig. 8. Strain in bottom flange of BCR-1.
Fig. 5. Failure of B-2.
4000
STRAIN / με
midspan
1-MAX 1-MIN 2-MAX 2--MIN
3000 2000 1000
2
0
1
3
(a). gauge distribution
6
9 12 TIME / 104s
15
(b). strain measurement
Fig. 6. Strains of B-2.
about 50 mm from the midspan, and the detail of the fracture is shown in Fig. 7. No defection can be observed in the flange around the fracture, and therefore it can be concluded the fracture initialed in the bottom flange, which is different from B-1 whose fracture initialed in the web next to the bottom end of the stiffeners. As the girder was already reinforced by CFRP layers, the strain was only measured at the side face of the bottom flange in midspan, and the measurement result is shown in Fig. 8. According to the strain data, it can be concluded that the fracture initialed after about 1,100,000 cycles. In addition, the strain of the bottom flange decreases slower in comparison with B-2 which has sharply strain decrease after flange fracture occurs. This phenomenon is due to the contribution of CFRP layers, which restrain the sharp fracture development in the flange.
2.3.4. BCR-2 BCR-1 exhibited fatigue fracture in bottom flange. Therefore, in order to improve the fatigue life of the flange, the side face of bottom flange of BCR-2 was also covered by CFRP layers. During the loading process, no significant failure could be observed before 3,050,000 cycles. Afterwards, the deflection gradually increased, indicating that the fracture may develop in the bottom flange. After 3,200,000 cycles, the deflection of the girder increased significantly, and the bottom flange exhibited sign of failure. After about 3,230,000 cycles, the test terminated due to over deflection of the girder, and significant failure could be observed in the bottom flange. When the girder was subjected to static loading after fatigue test, the adhesive continuously failed, and the CFRP layers separated from the steel plates. After the tests, the CFRP layers were cut off, and the fracture detail of the girder is shown in Fig. 9. In addition, the oval-shaped region could be observed around the bottom end of the stiffener in the fracture, indicating that the fatigue fracture initialed here. No such region could be observed in the bottom flange. As the steel plates were fully covered by the CFRP layers, the strains were not effectively measured. 2.3.5. BR-2 Similar as BCR-2, the side face of bottom flange of BR-2 was also covered by CFRP layers. The loading process and the phenomenon of BR-2 were quite similar as that of BCR-2. After about 2,800,000 cycle, the deflection of the girder started increasing. After about 2,830,000 cycles, the test terminated due to over deflection of the girder, and the girder failed due to flange fracture. The failure mode and the fracture detail were also similar as that of BCR-2. 2.4. Summary and discussion of the test results The summary of the fatigue life and the fracture initiation for the specimens is shown in Table 4. As can be seen, the fatigue life
(a). failure mode
(b). flange fracture
Fig. 7. Failure of BCR-1.
Fig. 9. Phenomenon of BCR-2.
282
Q.-R. Yue et al. / Composite Structures 154 (2016) 277–285
of BCR-1 is much higher than that of B-1. The fatigue life of BCR-2 and BR-2 is much higher than B-2 as well. It can be concluded the reinforcement using CFRP layers can significantly improve the fatigue life of the girder. The fatigue life of BCR-2 has more improvement with comparison of BCR-1. This phenomenon may be due to following reasons: (1) the stress amplitude of BCR-2 is smaller than that of BCR-1, and therefore the adhesive has a smaller stress, making it less likely to exhibit adhesive failure. (2) the fatigue fracture of BCR-2 develops slower due to lower fatigue stress amplitude. (3) The hoop layers aside the stiffeners in midspan for BCR-1 terminates at the bottom of the web, and the hoop layers at the end of longitude layers has only 1 layer. Therefore, the hoop layers of BCR-1 cannot provide sufficient restraint for the longitude layers. (4) BCR-1 firstly exhibited fatigue fracture in bottom flange, but BCR-2 firstly exhibited fatigue fracture in the web aside the bottom end of stiffeners because the side face of bottom flanges is also reinforced by CFRP layers, making the fatigue life of bottom flange higher. (5) B-2 firstly exhibited fatigue fracture in bottom flange due to initial defection, making the fatigue life lower than expected. Specimen B-1, BCR-2 and BR-2 exhibited fatigue fracture in the web aside the bottom end of the stiffeners. Fisher’s provision (Eq. (2)) can give relatively good prediction of the fatigue life for the unreinforced specimen B-1. However, Fisher’s provision significantly underestimates the fatigue life for BCR-2 and BR-2 with reinforcement by CFRP layers, indicating that the fatigue life of girders with CFPR reinforcement needs further theoretical research. B-2 exhibited flange fracture due to defection, and therefore its fatigue life is much lower than theoretical results. If we use the theoretical life of B-2 by Fisher’s provision (Eq. (2)) as the real fatigue life, the fatigue life improvement of BCR-2 and BR-2 with comparison by B-2 can be obtained, as shown in Table 5. The reinforcement results are also quite satisfactory. The fatigue life of BCR-2 is just a bit higher than that of BR-2. However, according to the data in Table 4, the theoretical fatigue life of BCR-2 by Eq. (2) is much higher than that of BR-2. This phenomenon may be caused by the stiffener cutting process for BCR-2. The stiffeners of BCR-2 were partly cut using abrasive wheel cutting machine, and the cutting region was polished after cutting. The cutting process may result in initial defection in the cutting region. Therefore, it can be concluded the cutting of stiffeners may be not quite effective to improve the fatigue life of girders because it may cause unexpected defection in the cutting region. 2.5. Suggestions for CFRP reinforcement configuration The reinforcement result of BCR-1 was not satisfactory, and the specimen exhibited unexpected fatigue fracture in bottom flange. This specimen only had 1 U-shaped hoop layer at the end of longitude CFRP layers, and the side faces of the bottom flange were not covered by CFRP layers as well. As the adhesive at the end of longitude CFRP layers is subjected to relatively large shear force, the
Table 4 Summary of the test results. Specimen No.
Dr/ MPa
N/103 by Eq. (1)
N/103 by Eq. (2)
N/103 by test
Fracture initiation
B-1 B-2 BCR-1 BCR-2 BR-2
177 140 136 107 122
261 534 584 1200 810
418 912 1008 2235 1446
579 561 1224 3230 2830
a⁄ b⁄ b⁄ a⁄ a⁄
a – the connection between the web and the bottom end of stiffener. ⁄b – the side face of bottom flange.
⁄
Table 5 Fatigue life improvement of BCR-2 and BR-2. Specimen No.
Dr/MPa
N/103
Fatigue life improvement
B-2 BCR-2 BR-2
140 107 122
912 3230 2830
/ 254% 210%
250 200 150 100 50 0 Fig. 10. Stress concentration aside the stiffeners (specimen B-1).
CFPR layers is likely to separate from the steel plates. The Ushaped hoop can restrain the longitude CFRP layers, making the longitude CFRP layers work together with the steel girder. The Ushaped hoop of BCR-1, which had only 1 layer, exhibited tensile fracture due to the tension from longitude CFRP layers. Yet, the U-shaped hoop of BCR-2 and BR-2, which had 3 layers, only exhibited partially adhesive failure, indicating that the U-shaped hoop with 3 layers at the end of longitude CFRP layers can make the longitude CFPR layers develop their full strength. The hoop layers of BCR-1 at midspan were only glued aside the stiffeners, which terminated at the bottom of the web. The test results confirmed that such configuration was not satisfactory, and the hoop layers were likely to separate. The hoop layers of BCR-2 and BR-2 were also U-shaped, and the test results confirmed such configuration could make the hoop layer work together with longitude layers, and restrained the longitude layers from separating from the steel plates. The side faces of the bottom flange of BCR-1 were not covered by CFRP layers, and the specimens exhibited fatigue fracture initialed from the side face of the bottom flange. Thus, the fatigue life of BCR-1 is much lower than that of BCR-2 and BR-2. Specimen BCR-2 and BR-2 with CFRP layers covering the side faces of the bottom flange both exhibited fatigue fracture initialed from the wed aside the bottom end of the stiffeners, and no fatigue initiation could be observed in the bottom flange. Thus, it can be concluded that the CFRP layers configuration at the side faces of the bottom flange for BCR-2 and BR-2 can provide satisfactory reinforcement. 3. Analytical research In this section, the numerical model of CFRP reinforced steel girder will be established using the finite element software MSC. Marc [21]. The stress concentration aside the stiffeners and the stress intensity factor (SIF) will be discussed to analyze the influence of CFRP reinforcement, and the development of the fatigue fracture before and after CFRP reinforcement will also be comparatively studied. 3.1. Numerical modeling The CFRP reinforced steel girder can be modeled using ‘‘solidshell” model [10]. As the fatigue fracture occurs at the midspan which is subjected to largest flexural moment, the steel plates in
283
Q.-R. Yue et al. / Composite Structures 154 (2016) 277–285 Table 6 The stress concentration factor for the experimental specimens. Specimen No.
B-1
B-2
BCR-1
BCR-2
BR-2
Stress concentration factor
1.41
1.38
1.25
1.24
1.22
within 6 mm from the stiffeners, making the actual stress much larger than the nominal stress. The stress concentration phenomenon will influence the fatigue life. Assuming that we take the stress which is 6 mm away from the stiffeners as the hot spot stress, the stress concentration factor can be defined as the ratio of the hot spot stress to the nominal stress. The stress concentration factor for the experimental specimens is shown in Table 6. Obviously, the stress concentration factor for CFRP reinforced specimens is much smaller that the unreinforced specimens. The existing of CFRP layers not only decreases the nominal stress of steel plates, but also relieves the stress concentration in the web aside the stiffeners. Fisher’s provision (Eq. (2)) significantly underestimates the fatigue life of CFRP reinforced specimens because the relief of stress concentration in the web due to the CFRP layers cannot be considered. Therefore, the fatigue mechanism of CFRP reinforced girder needs further theoretical research. 3.3. Discussions on stress intensity factor After the fatigue fracture initiation occurs, the fracture will gradually develops with increasing fatigue cycles. This period is a major part of the total fatigue life. During this period, the stress intensity factor is the critical parameter for the fatigue life because it is dominant to the fatigue fracture growth rate, as shown in Eq. (7):
lg da=dN ¼ lg C þ m lg K Fig. 11. Element mesh around the fracture tip.
this region are simulated using 20 nodes solid element. To decrease the cost of computation, the steel plates in other regions are simulated using 8 nodes solid element. The two parts of solid elements representing steel girder are glued to make them work together. The adhesive and CFRP layers are simulated using 8 nodes thick shell elements at midspan, and are also simulated using 4 nodes thick shell elements in other regions. The shell elements and the solid elements are all glued to work together. The material property of steel plates, CFRP layers and the adhesive are shown in Tables 1 and 2. 3.2. Discussions on stress concentration Obviously, significant stress concentration will exist aside the welding between the web and the stiffeners, and the typical stress concentration of BC-1 aside the stiffeners is shown in Fig. 10. According to the figure, the stress concentration is significant
stage-4 10mm stage-3 40mm stage-2 30mm stage-1 30mm stage-3 14mm stage-4 10mm
B-1 & B-2
stage-5 30mm stage-4 10mm
stage-5 30mm stage-4 10mm
stage-3 80mm
stage-3 80mm
stage-2 40mm
stage-2 70mm
stage-1 60mm
stage-1 30mm stage-3 14mm stage-4 10mm stage-5 30mm
stage-3 14mm stage-4 10mm stage-5 30mm
BCR-1 & BCR-2
(a). B-1 and B-2
ð7Þ
where a is the fatigue fracture length, N is the fatigue cycle, C and m is the material constants, and K is the stress intensity factor (SIF). J integral method [22,23] is a basic approach to calculate the stress intensity factor, and it can be realized in the finite element software MSC. Marc. The optimization of mesh can improve the accuracy of J integral. MSC. Marc [21] suggests radial mesh grid around the fracture tip, and higher order elements are also suggested to be used around the fracture. Barsoum [24] suggested the 20 nodes solid elements used around the fracture tip, and the suggested element mesh is shown in Fig. 11. The calculation of the stress intensity factor by numerical simulation needs to define the fracture development first. According to the experimental research, the fracture development for the specimens is assumed as shown in Fig. 12. Thus, by modeling different fatigue fractures in the specimen, the stress intensity factors corresponding to different fracture lengths for all the experimental specimens are calculated by numerical analysis, as shown in Fig. 13(a&b). The stress intensity factor K of unreinforced experimental specimen B-1 and B-2 keeps increasing with the fracture
(b). BCR-1 and BCR-2
BR-2
(b). BR-2
Fig. 12. Fracture development for the experimental specimens.
Q.-R. Yue et al. / Composite Structures 154 (2016) 277–285
4000
B-1 BCR-1
3200
K / MPA.m0.5
K / MPA.m0.5
4000
2400 1600 800 0
1500
B-2 BCR-2 BR-2
3200 2400 1600 800
0
50
100 150 200 250 300 a / mm
(a). B-1 vs. BCR-1
0
BCR-1 BCR-1*(3 LAYER) BCR-2
1200
K / MPA.m0.5
284
900 600 300
0
50
100 150 200 250 300 a / mm
(b). B-2 vs. BCR-2, BR-2
0
0
50
100 150 200 250 300 a / mm
(b). BCR-1(*) vs. BCR-2
Fig. 13. Stress intensity factor corresponding to different fracture lengths.
length a. When the fracture develops in the web (a < 60 mm), K increases relatively slower with a. Yet, when the fracture goes into the flange (a > 60 mm), K increases faster with a, indicating the fracture develops faster. Compared with the unreinforced specimen, the stress intensity factor of the reinforced specimen BCR-1, BCR-2 and BR-2 increases much slower, indicating the reinforcement result is satisfactory. The influence of CFRP reinforcement becomes more significant when the fracture is longer. When the fracture goes into the flange (100 mm < a < 194 mm), the stress intensity factor also has a fast increase, which also indicating the fracture develops faster. However, the stress intensity factor of CFRP reinforced specimen has no continuous significant increase after the fracture develops in the flange in comparison with the unreinforced specimen, indicating that the CFRP layers can perfectly restrain the development of fatigue fracture. The relationship between the stress intensity factor and fracture length for BCR-2 and BR-2 had little difference. Yet, the stress intensity factor of BR-2 increases a bit faster with fracture length than BCR-2 at the beginning of fracture. This is because the stress at the bottom end of the stiffener for BR-2 is a bit larger as its stiffener is not cut. The comparison between BCR-1 and BCR-1⁄ which has 3 longitude CFRP reinforcement layers is shown in Fig. 13(c). As can be seen, the stress intensity factor of BCR-1⁄ with 3 longitude CFRP layers is a bit larger, but not quite significant. That’s to say, the continuous increasing of CFRP reinforcement layers may just give little improvement. The stress intensity factor of BCR-2 with lower fatigue stress amplitude is much smaller than that of BCR-1, indicating that the stress amplitude has significant influence on the fracture growth speed. 4. Conclusions This paper studied the fatigue performance of CFRP reinforced steel crane girders. Firstly, the experimental research was conducted to explore the fatigue behavior of the CFRP reinforced girders. On this basis, the influence of different reinforcement parameters was discussed, and the configuration details for CFRP reinforcement were proposed. Finally, the numerical model of CFRP reinforced girder was established using MSC. Marc. On this basis, the influence of CFRP on the stress concentration behavior before fatigue fracture and stress intensity factor after fatigue fracture was discussed to analyze the mechanism of CFRP reinforcement. The conclusions are as follows: (1) The reinforcement using CFRP layers can significantly improve the fatigue life of the girder. The lower fatigue stress amplitude, the more significant reinforcement result.
(2) Fisher’s provision can give relatively good prediction for the fatigue life of the unreinforced steel girder, but will also significantly underestimate the fatigue life for the fatigue life of reinforced girders using CFRP layers. (3) The approach of partially cutting stiffeners is not effective to improve the fatigue life of girders because it may cause unexpected defection in the cutting region. (4) The U-shaped hoop can restrain the longitude CFRP layers, making the longitude CFRP layers work together with the steel girder. It is suggested that the U-shaped hoop arranged both aside the stiffeners at midspan and at the end of the longitude layers, and the U-shaped hoop at the end of longitude layers has more than 3 layers. (5) The longitude CFRP layers should have good configuration detail to fully cover the side faces of the bottom flange to avoid the fatigue fracture initiation here. (6) Numerical analysis indicates that the CFRP layers can relieve the stress concentration aside the stiffeners, and therefore the fatigue mechanism of CFRP reinforced girder needs further theoretical research. (7) The CFRP layers can perfectly restrain the development of the fatigue fracture. The stress intensity factor of CFRP reinforced girders increases much slower with fracture length in comparison with unreinforced girders, especially after the fracture develops into the flange. The continuous increasing of CFRP layers may just give little decrease of the stress intensity factor, but the lower fatigue stress amplitude can significantly decrease the stress intensity factor.
Acknowledgement The authors gratefully appreciate the financial support provided by the National Natural Science Foundation of China (51578559). References [1] Zhao Z, Haldar A, Breen FLJ. Fatigue-reliability evaluation of steel bridges. J Struct Eng-ASCE 1994;120(5):1604–23. [2] Metallurgical Industry Ministry Building Research Institute. Fatigue data report of steel structures; 1978 [in Chinese]. [3] Fisher JW, Albrecht RA. Fatigue strength of steel beams with welded stiffeners and attachments, National cooperative highway research program report 147. Leigh University; 1974. [4] Zhao XL, Zhang L. State-of-the-art review on FRP strengthened steel structures. Eng Struct 2007;29(8):1808–23. [5] Colombi P, Bassetti A, Nussbaumer A. Analysis of cracked steel members reinforce by pre-tress composite patch. Fatigue Fract Eng Mater Struct 2003;26:59–66. [6] Jones SC, Civjan SA. Application of fiber reinforced polymer overlays to extend steel fatigue life. J Compos Constr 2003;7(4):331–8. [7] Feng P, Hu LL, Zhao XL, et al. Study on thermal effects on fatigue behavior of cracked steel plates strengthened by CFRP sheets. Thin-Walled Struct 2014;82:311–20.
Q.-R. Yue et al. / Composite Structures 154 (2016) 277–285 [8] Hu LL, Zhao XL, Feng P. Fatigue behaviour of cracked high strength steel plates strengthened by CFRP. J Compos Constr 2016. http://dx.doi.org/10.1061/(ASCE) CC.1943-5614.0000698. [9] Colombi P, Fava G, Sonzogni L. Fatigue crack growth in CFRP-strengthened steel plates. Compos Part B 2015;72:87–96. [10] Zheng Y, Ye LP, Yue QR. Study on fatigue behavior of cracked tensile steel plates reinforced with CFRP plates. Eng Mech 2007;24(6):91–7 [in Chinese]. [11] Miller T, Chajes M, Mertz D, Hastings J. Strengthening of a steel bridge girder using CFRP plates. J Bridge Eng 2001;6(6):514–22. [12] Tavakkolizadeh M, Saadatmanesh H. Fatigue strength of steel girders strengthened with CFRP patch. J Struct Eng-ASCE 2003;129(2):186–96. [13] Nozaka K. Repair of fatigue steel bridge girders with carbon fiber strips [Doctoral dissertation]. University of Minnesota; 2002. [14] Deng J, Lee MMK. Fatigue performance of metallic beam strengthened with a bonded CFRP plate. Compos Struct 2007;78:222–31. [15] Teng JG, Yu T, Fernando D. Strengthening of steel structures with fiberreinforced polymer composites. J Constr Steel Res 2012;78:131–43.
285
[16] Nakamura H. Experimental study on repair of fatigue cracks at welded web gusset joint. Thin-Walled Struct 2009;47:1059–68. [17] Sela N, Ishai O, Banks-Sillst L. The effect of adhesive thickness on interlaminar fracture toughness of interleaved CFRP specimens. Composites 1989;20 (3):257–63. [18] GB50017-2003. Code for design of steel structures (in Chinese). [19] Zhao QL, Wang JQ, Jin GQ. Analysis on the ‘‘reverse-arch prestressed technique” and the improved bearing capacity for steel structures strengthened by carbon-fiber. Steel Constr 2002;17(59):51–4 [in Chinese]. [20] Cazand R. Fatigue of metals, 1953. [21] MSC Software Corporation. Marc 2010 user’s guide. [22] Rice JR. A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 1968;35:379–86. [23] Moura B, Shih CF. A treatment of crack tip contour integrals. Int J Fract 1987;35:295–310. [24] Barsoum RS. On the use of isoparametric finite elements in linear fracture mechanics. Int J Numer Meth Eng 1976;10:25–37.