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Resistance of headed studs subjected to fatigue loading
Journal of Constructional Steel Research 63 (2007) 475–484 www.elsevier.com/locate/jcsr
Resistance of headed studs subjected to fatigue loading Part I: Experimental study Gerhard Hanswille ∗ , Markus Porsch, Cenk Ustundag Institute of Steel and Composite Structures, University of Wuppertal, Germany Received 13 March 2006; accepted 30 June 2006
Abstract In steel–concrete composite structures the transfer of longitudinal shear forces at the interface between steel and concrete is mostly realized by headed shear studs. Especially in bridges due to traffic loads these shear connectors are subjected to high-cycle loading and the fatigue resistance governs the design. In this first part of two companion papers a series of experimental work with standard EC4 push-out specimens is presented. The main purpose of these tests was to determine the fatigue life and a possible reduction of the static strength of the headed shear studs subjected to unidirectional cyclic loading. A further aspect was to examine the effects of the loading sequence and damage accumulation on the fatigue life. The results of the experimental investigations show that due to a crack initiation at the stud foot at 10%–15% of the fatigue life, an early reduction of the static strength is caused. Furthermore tests to examine the effects of the loading sequence on the fatigue life revealed that the linear damage accumulation hypothesis according to Palmgren and Miner on which the present design codes are based do not describe the real behaviour. c 2006 Elsevier Ltd. All rights reserved.
Keywords: Fatigue life; Push-out test; Steel; Concrete; Composite; Headed shear studs; Unidirectional; Cyclic loading; Reduced static strength; Damage accumulation
1. Introduction In recent decades as a result of the benefits of combining the advantages of its components, steel–concrete composite beams have seen widespread use in buildings and bridges. The composite action of the components steel and concrete is realized by the shear connectors welded on the steel flange. Because of its economic and fast application headed shear studs are the most commonly used type of shear connectors in steel–concrete composite constructions. Especially in bridges due to traffic actions these studs are subjected to high-cycle fatigue loading. This is also the case in crane runways and composite beams used for industrial buildings exposed to traffic by fork-lift trucks. Because of its costs and difficulties arising in the interpretation of the results of full-scale beam tests, the evaluation of the behaviour of the shear studs generally takes place with standard push-out test specimens. Since the 1960s various researchers have conducted a great number of cyclic ∗ Corresponding address: University of Wuppertal, Institute of Steel and Composite Structures, Pauluskirchstrabe 7, 42285Wuppertal, Germany. E-mail address: [email protected] (G. Hanswille).
c 2006 Elsevier Ltd. All rights reserved. 0143-974X/$ - see front matter doi:10.1016/j.jcsr.2006.06.035
push-out tests to determine the fatigue life of shear connectors. Some of them are given in [1–9]. Maybe one of the remarkable points in these investigations was that repeated loading causes a reduction of the static strength of the shear stud within its lifetime [10]. This is an indication that the design concept in the current codes [11,12] does not describe the real behaviour, because the codes assume that ultimate limit states and fatigue limit states can be verified by independent checks. The design concept, illustrated in Fig. 1(a), of the before mentioned codes is based on the evaluation of internationally performed tests on push-out test specimens to determine the ultimate static strength and fatigue strength [13–16]. The verification of the fatigue resistance takes place comparable to steel structures on the basis of nominal stress concepts and the linear damage accumulation hypothesis according to Palmgren and Miner [17, 18]. Deterioration in strength of stud shear connectors and change in loading condition due to the change in deformation behaviour remain unconsidered which may result in a reduction of the reliability index so that it may fall below the target values in codes as illustrated in Fig. 1(b). So far, except for the test conducted by Oehlers [19], there weren’t enough tests where the reduced static strength
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Notation AD AG Ec N Nf Pmax Pu,0 Pu,N Vx fc 1P δi δ1
fatigue fracture area of the shear stud forced fracture area of the shear stud secant modulus of elasticity of concrete number of load cycles fatigue life peak value of cyclic loading ultimate static strength of the shear stud reduced static strength of the shear stud after N load cycle coefficient of variation cylinder compressive strength of concrete range of the cyclic loading inelastic displacement at ith load cycles plastic slip at the first cycle
after high-cycle preloading was systematically investigated. Thus in the light of the information gained from previous researches a comprehensive program of 71 push-out tests was developed to determine the reduced static strength after high-cycle preloading and to examine the effects of the loading sequence and damage accumulation on the fatigue life. This paper deals with the results of the experimental studies on the behaviour of headed shear studs subjected to unidirectional cyclic loading. Development of semi-empirical analytical methods to determine the reduced static strength and the fatigue life and the development of an improved damage
accumulation hypothesis will be discussed in the companion paper. 2. Push-out tests 2.1. Test program The experimental program consists of a total of 6 series (S1–S6). The first four series S1–S4 deal with constant amplitude tests where the effect of unidirectional cyclic loading on the static strength and the fatigue life of the push-out specimen were investigated with varying loading parameters, peak load Pmax and loading range 1P. In each series initially three static tests were performed to determine the mean value of the ultimate static load P¯u,0 of the push-out specimen. The mean value of the ultimate static load represents the reference parameter for the relative values of loading parameter required for cyclic tests. Using the relative loading parameters, three load controlled cyclic tests were performed to determine the mean fatigue life N¯ f of the push-out specimen. Subsequently six cyclic tests were conducted for approximately 30% and 70% of the mean fatigue life N¯ f . After reaching the corresponding number of cycles each of these six test specimens was statically loaded to failure under displacement control to obtain the reduced static strength after high cycle preloading. The chosen loading parameters and number of performed tests for the first four series are summarized in Table 1. Based on the results of the constant amplitude tests in the series S5 and S6 tests with the two and four blocks loading sequences were performed in which the peak load was
Fig. 1. (a) Safety concept to determine the lifetime of composite structures subjected to high cycle loading according to present codes; (b) actual influence of high cycle loading on lifetime.
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Fig. 2. Tests with multiple blocks of loading (a) two blocks; (b) four blocks. Table 1 Summary of the single level tests Series
S1 S2 S3 S4 S5E
1P/ P¯u,0 0.20 0.25 0.25 0.20 0.25
Pmax / P¯u,0 0.44 0.71 0.44 0.71 0.30
Number of tests P¯u,0 N¯ f N ∼ 0.3 N¯ f
N ∼ 0.7 N¯ f
3 3 3 3 3
3 3 3 3 1
3 3 3 3 1
3 3 3 3 1
Table 2 Summary of the tests with multiple blocks of loading Series
Number of tests
S5-2 S5-3 S5-4 S5-6
3 1 4 4
S6-3 S6-4
3 3
1P/ P¯u,0
Pmax / P¯u,0 Block 1 Block 2
Block 3
Block 4
0.25
0.71 0.44 0.44 0.30
0.44 0.71 0.30 0.44
– – – –
– – – –
0.20
0.44 0.74
0.54 0.64
0.64 0.54
0.74 0.44
increased or decreased subsequently while the loading range was held constant (see Fig. 2 and Table 2). Like the constant amplitude tests the series S5 and S6 were initiated with short-time static tests to determine the ultimate static load. During the tests with multiple blocks of loading it appeared necessary to perform further constant amplitude tests with a not investigated low peak load (Pmax / P¯u,0 = 0.3). Thus, 3 complementary constant amplitude cyclic tests (referred as series S5E) were performed in these series. The chosen loading parameters and number of performed tests for tests with multiple blocks of loading are summarized in Table 2. 2.2. Test specimens The specimen used in the push-out tests consists of a 650 mm long HEB260 profile and two 650 mm long, 600 mm wide and 150 mm thick concrete slabs. The slabs are connected to the steel beam by means of four headed shear studs of 22 mm diameter welded on each side of the beam. The weld collars complied with the requirements of EN ISO 13918 [20].
The mean height of the weld collars was 8.4 mm and the mean diameter 28.9 mm. The height of the welded stud was 125 mm. For casting the steel beams were cut into two halves and the concrete slabs were cast horizontally. The steel flanges were greased prior to casting to remove friction between the concrete and steel. The two halves were subsequently welded together. This test specimen complies with the standard pushout specimen according to Eurocode 4 with an exception of lateral restraints of the concrete slabs at the specimen bottom. The lateral restraints avoid especially in the lower row of shear studs the introduction of additional tensile forces resulting from the moment of eccentricity and enable a better simulation of the real behaviour in composite beams. Details of the push-out specimens are given in Fig. 3. 2.3. Test setup and loading procedure Cyclic and monotonic loading was applied by a 2500 kN servo hydraulic actuator. The load was introduced into the steel beam by means of a head plate welded on the cross section of the beam. The actuator was controlled by an Instron 8800 controller which allowed load and displacement control, and had sinusoidal control waveforms which were utilized for the cyclic testing. Displacement control was used for the monotonic tests, and load control was used for all cyclic testing. The test setup used in the experiments is shown in Fig. 4. The monotonic tests were conducted at a displacement rate of 0.004 mm/s. The time taken to reach the ultimate load was typically of the order of 50 min. After reaching the ultimate load the displacement rate was increased up to 0.008 mm/s. Cyclic tests were conducted with a load frequency of 3 Hz. In order to collect data about the stiffness and plastic deformation, cyclic tests were held after a specific number of cycles and the specimens were released and reloaded monotonically. During the tests the time, load from the actuator load cell, ram displacement from the built-in transducer in the actuator, longitudinal displacement between the concrete slab and steel beam and uplift of the slabs were measured. The ram displacement included movement due to the compliance of the test rig, and therefore it was not used in any subsequent data analysis. The longitudinal displacements were measured by two
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Fig. 3. Details of the push-out test specimen. Table 4 Average test results per stud
Fig. 4. Test setup and the hydraulic actuator. Table 3 Mean values of material properties of concrete
f c (N/mm2 ) E cm (N/mm2 )
Series S1
S2
S3
S4
S5
S6
44–52 36 400
42–45 36 400
53–56 39 000
43 33 900
43 33 500
46 33 700
LVDT’s on each steel flange to which the studs were welded (see Fig. 4). 2.4. Material properties At various intervals during the curing process at 28 days as well as at the beginning, in the middle and at the end of each series cylinder compression tests were carried out to determine the compressive cylinder strength and elastic stiffness of the concrete. Standard cylinders of 150 mm in diameter and 300 mm in length were used. Table 3 presents the range of the mean concrete strength and the mean modulus of elasticity associated with the test start for each series according to EN 206-1 [21]. In all series structural steel beams, headed shear studs and reinforcing bars used in the tests were from the same batch.
P¯u, N¯
Series (–)
P¯u,0 (kN)
N¯ f (–)
P¯u, N¯ 1 (kN)
(–)
S1 S2 S3 S4 S5E
205 184 201 181 189
6.2 × 106 1.2 × 106 5.1 × 106 3.5 × 106 6.4 × 106
154 174 133 181 111
0.75 0.95 0.66 1 0.59
1
P¯u,0
N¯ 1 N¯ f
P¯u, N¯
N¯ 2 N¯ f
(–)
P¯u, N¯ 2 (kN)
(–)
(–)
0.32 0.32 0.24 0.29 0.19
129 154 123 156 114
0.63 0.84 0.61 0.86 0.60
0.90 0.70 0.69 0.72 0.73
2
P¯u,0
The structural steel beams of HEB 260 section with the material quality S235 J2G3 were used in each test. From the tensile tests the mean yield strength and ultimate stress were determined as 337 N/mm2 and 448 N/mm2 , respectively. The modulus of elasticity of the beam was 209 341 N/mm2 . Stud shear connectors, which were welded automatically onto the steel beam flange, had a material quality of S235 J2G3+C450. Based on the tensile tests, the yield strength and the ultimate tensile strength of the connectors were determined as 440 N/mm2 and 528 N/mm2 , respectively. The modulus of elasticity of the studs was 216 351 N/mm2 . As reinforcing steel, standard deformed bars with diameters of 10 mm and 12 mm were used in the concrete slabs. Four tensile tests were performed on each bar sample. The average yield strength and ultimate strength was obtained as 549 N/mm2 and 606 N/mm2 for the bars of 10 mm, and 501 N/mm2 and 561 N/mm2 for the bars of 12 mm, respectively. The modulus of elasticity of the bars with diameters of 10 mm and 12 mm were determined as 197 779 N/mm2 and 204 540 N/mm2 , respectively. 3. Results of the constant amplitude tests Table 4 shows the results of the static strength, the fatigue life N¯ f and the reduced static strength after high cycle preloading for series S1–S5E. The limit state of fatigue is given, when the reduced strength has reached the value of the peak load. Because of different static strength within each test series the absolute values of Pmax and 1P differ slightly. All data given in Table 4 represent generally the mean values of
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Fig. 5. Comparison of Pe –Pt of the static tests (Pu,0 ) in series S1–S6 with the Pe –Pt data of the model of Eurocode 4.
three similar tests. The strength data are based on short time behaviour, so when relaxation must be taken into account, it is necessary to reduce the values by 10%. In contrast to series S2 and S4 the low peak loads in series S1, S3 and S5E led to very high fatigue lives N¯ f . Fig. 5 shows the comparison of static tests results (Pe ) for series S1–S6 with the corresponding data of theoretical shear resistance (Pt ) according to the empirical model of Eurocode 4 [15]. The resistance is given by the minimum of two equations, which describe the shear resistance in the case of “shear failure of the stud” and “failure of the concrete”, respectively. This model is based on the assumption, that in case of low concrete strength the shear resistance is determined only by the failure of concrete in the lower part of the shank. In the case of high concrete strength it is assumed, that the shear resistance is determined by the shear resistance of the stud shank. The results of the static tests are in good agreement with the prediction of the theoretical model, on which the design rules in Eurocode 4 are based. In Fig. 6 the results of the fatigue tests of series S1–S5E are compared with the corresponding test results, from which the fatigue strength curve in Eurocode 4 was derived. The test results are in good agreement with the given prediction according to Eurocode 4. 3.1. Plastic slip—load cycles In case of cyclic loading the load–deformation behaviour is characterized by an increasing plastic slip and a decreasing elastic stiffness K el . In Fig. 7 the inelastic slip δi related to the plastic slip in the first cycle δ1 is plotted against the number of cycles over the fatigue life N¯ i / N¯ f for series S1–S4. The beginning and the end of the lifetime are associated with a steep
Fig. 6. Comparison of fatigue test results with the prediction in Eurocode 4.
increase in the plastic slip with the number of cycles while in the remaining part of the lifetime a nearly linear increase of the plastic slip occurs with the number of cycles. The mean value of the initial plastic slip δ 1 in the first cycle is in series with high peak loads approximately 8 times greater than in series with low peak loads. 3.2. Static strength versus lifetime The influence of the cyclic loading becomes evident, when the static strengths are plotted versus number of load cycles. This is shown in Fig. 8, where the results are related to the mean static strength and the mean fatigue life of each series respectively. Especially in series S1, S3 and S5E with low peak loads the rapid decrease of the static strength within the first 20% of the fatigue life is noteworthy. On the other hand N¯ f is much greater than for the series with high peak loads. The reduction of the static strength over the lifetime is considered in four stages. In stage I there is no significant
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Fig. 7. Plastic slip over the fatigue life in series S1–S4.
Fig. 8. Decrease of static strength versus lifetime due to high cycle loading.
damage in concrete and steel and therefore no reduction. In stage II and stage IV there is an instable reduction of the static strength. Stage III shows a linear variation of the static strength
with the number of cycles. In Fig. 8 the coefficient of variation Vx of the static strengths gained from three similar tests is marked out exemplarily for the series S4. The scatter of the
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Fig. 9. Preparation stages for examination purposes.
results increases with the degradation of the strength of the shear studs. Comparison of the series with the same load range and different peak load makes clear that the static strength and the fatigue life are affected not only from the load range but also from the peak load of the cyclic loading. Furthermore it is also obvious that for the same amount of change the effect of the load range on the static strength is much greater than on the peak load. 3.3. Failure modes To investigate the reasons for the reduction of the static strength, the concrete slabs were separated from the steel beam and the fractured surfaces at the foot of each headed stud were examined. Fig. 9 gives in detail the stages of preparation of the test specimens after each push-out test for examination purposes. Also in some cases metallurgical investigations were carried out. The examined fracture surfaces consist of the typical dull fatigue fracture and bright forced fracture zones, where in the fatigue tests the former one is formed by cracks propagating to a critical length and the second one due to forced shear fracture. Furthermore the tests reveal two failure modes, which closely correlate with the peak load Pmax . For high peak loads such as in series S2 and S4 only mode A (see Fig. 10) occurs. For lower peak loads such as in series S1, S3, S5E in most cases mode B occurs, even though it must be mentioned, that in some cases both mode A and mode B were detected at the same time at one stud foot. This means, that there were formed two cracks and both could initiate forced fracture. Investigation of the microstructure reveals that both points, P1 and P2, show high
geometrical and metallurgical notch effects due to the welding technique. Furthermore the short time static tests carried out after high cycle preloading show in case of mode B more ductile behaviour than mode A, which is in good agreement with both crack forms. The fractured surfaces at the stud feet in case of failure mode A show typical arrest lines, so that it was possible to detail the crack development for this mode. Unfortunately for mode B there couldn’t be observed any stop marks except for one test specimen although the testing procedure was always the same. The evaluation of the test results as yet showed that for mode A (series S2 and S4) and mode B (series S1, S3 and S5E) there is a linear relationship between the reduced static strength and the size of the fatigue cracking zone. This relationship is illustrated in Fig. 11 schematically, where A D is the area of the fatigue cracking zone and A G the area of the forced shear fracture. In case of mode A the whole fracture area (A D + A G ) corresponds to the stud area. In case of mode B the whole fracture area is much larger than the stud area. The coefficient of correlation of the linear relationship is 0.99 for mode A and 0.85 for mode B. If the analysis is based on all tests of mode A and B, a coefficient of 0.88 results (Fig. 11). From the given linear correlations can be deduced that the crack propagation in the shear stud has approximately 60% attribution in the reduction of the static strength. 4. Results of tests with multiple blocks of loading The results of the two and four blocks loading sequences (see Fig. 2) are given in Tables 5 and 6 respectively. The mean value of the reference ultimate static strength P¯u,0 of the shear studs
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Fig. 10. Failure modes A and B.
Fig. 11. Relationship between reduced static strength and fatigue fracture area.
is 186 kN for the tests with two blocks of loading in series S5 and 196 kN for the tests with four blocks of loading in series S6. It is to be noticed that in tests with multiple blocks of loading the failure of the shear studs can occur on the one hand during the cyclic loading by the decrease of static strength to the peak load and on the other during switching to the next block with a higher peak load by exceeding the reduced static strength. A typical example for the last case occurred in the test S5-3a during switching to the second block with a peak load of 133 kN by exceeding the reduced static strength of 124 kN per stud.
Evaluation of the tests with multiple blocks of loading on the basis of the linear damage accumulation hypothesis of Palmgren and Miner, on which the present design codes rely, is shown in Fig. 12. The fatigue life Nfi corresponding to each block of cyclic loading is gained from the results of the constant amplitude tests of series S1–S4 and S5E. The missing values of number of cycles to fatigue for the blocks 2 and 3 in the test with four blocks of loading are determined by means of a linear interpolation from the results of series S1 and S4. Thus, for the peak loads of 101 kN and 120 kN per stud the fatigue life N f
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G. Hanswille et al. / Journal of Constructional Steel Research 63 (2007) 475–484 Table 5 Loading parameters and results of the tests with two blocks of loading (series S5) Test (–)
Block 1 Pmax,1 (kN)
S5-2a S5-2c S5-3a S5-4a S5-4b S5-4c S5-4d S5-6a S5-6b S5-6c S5-6d
133 133 83 83 83 83 83 56 56 56 56
N1 + N2 (×106 )
Block 2 1P (kN)
N1 (×106 )
Pmax,2 (kN)
47
0.204 0.198 1.099 0.473 0.517 0.544 0.542 0.537 1.223 1.295 1.277
83 83 133 56 56 56 56 83 83 83 83
1P (kN)
N2 (×106 )
47
0.792 1.440 – 1.365 0.772 0.735 3.396 5.821 0.761 1.744 3.206
0.996 1.638 1.099 1.838 1.289 1.2791 3.938 6.358 1.984 3.039 4.483
Table 6 Loading parameters and results of the tests with four blocks of loading (series S6) Test (–)
S6-3a S6-3b S6-3c S6-4a S6-4b S6-4c
1P (kN)
38 38 38 38 38 38
Block 1
Block 2
Block 3
P4
6 i=1 Ni (×10 )
Block 4
Pmax,1 (kN)
N1 (×106 )
Pmax,2 (kN)
N2 (×106 )
Pmax,3 (kN)
N3 (×106 )
Pmax,4 (kN)
N4 (×106 )
83 83 83 139 139 139
0.756 0.765 0.754 0.550 0.550 0.540
101 101 101 120 120 120
0.768 0.804 0.759 0.763 0.758 0.753
120 120 120 101 101 101
0.770 0.785 0.750 0.754 0.750 0.753
139 139 139 83 83 83
0.868 0.324 0.449 0.583 0.756 1.208
3.162 2.678 2.712 2.650 2.815 3.254
5. Summary and conclusions A total of 71 push-out tests was performed to determine the reduced static strength after high-cycle preloading and to examine the effects of the loading sequence on the fatigue life. The test results, especially the observation of arrest lines, indicate an early crack initiation in approximately 10%–20% of the fatigue life which causes the reduction of the static strength. Constant amplitude tests have shown that the magnitude of the peak load Pmax of the cyclic loading has a significant effect on the crack form occurring at the stud foot. Evaluation of the tests with multiple block loading sequences on the basis of the linear damage accumulation according to Palmgren–Miner yields unsafe results. Development of analytical methods to determine the reduced static strength and the fatigue life and the development of a modified damage accumulation hypothesis will be discussed in the companion paper. Acknowledgement Fig. 12. Comparison between the test results with the results of the lifetime prediction according to Palmgren–Miner.
is determined as 5.3 × 106 and 4.4 × 106 number of cycles, respectively. It is obvious that except for one test in Fig. 12 all results of the lifetime prediction according to Palmgren and Miner lie on the unsafe side. The main reason for this is the omission of the effects due to crack propagation in the shank of the stud and the increasing local crushing of concrete surrounding the stud weld.
The experimental program described in this paper is financed by the German Research Foundation (DFG) within the scope of Collaborative Research Centre 398. References [1] Slutter RG, Fisher JW. Fatigue strength of shear connectors. Highway research record no. 147. New York; 1966. [2] Mainstone RJ, Menzies JB. Shear connectors in steel–concrete composite beams for bridges, Part 1 and 2. Concrete 1967;1(9–10).
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[3] Hallam MW. The behaviour of stud shear connectors under repeated Loading. Research report R281. School of Civil Engineering, University of Sydney; 1976. [4] Roderick JW, Ansourian P. Repeated loading of composite beams, The civil engineering transactions of the Institution of Engineers. Austria; 1976. [5] Akao S, Kurita A, Hiragi H. Fatigue strength of stud shear connectors with concrete deposited from different placing directions. IABSE Fatigue, Lausanne; 1982. [6] Oehlers DJ. A new approach to the design of stud shear connectors in composite bridge beams. Research report R82. University of Adelaide; 1989. [7] Th¨urlimann B. Fatigue and static strength of stud shear connectors. Journal of ACI 1966;30(12). [8] Roik K, Holtkamp HJ. Untersuchungen zur Dauer- und Betriebfestigkeit von Verbundtr¨agern mit Kopfbolzend¨ubeln. Stahlbau 58. 1989. [9] Roik K, Hanswille G. Zur Dauerfestigkeit von Kopfbolzend¨ubeln bei Verbundtr¨agern. Bauingenieur 62. 1987. [10] Oehlers DJ, Foley L. The fatigue strength of stud shear connections in composite beams. Proceedings of the Institute of Civil Engineering 1985; 79(2):349–64. [11] EN 1994-1-1. Eurocode 4: Design of composite steel and concrete structures. Part 1-1: General rules and rules for buildings. Brussels: CEN; 2004. [12] EN 1994-2. Eurocode 4: Design of composite steel and concrete structures. Part 2: General rules and rules for bridges. Brussels: CEN; 2004. [13] Roik K, Hanswille G. Beitrag zur Bestimmung der Tragf¨ahigkeit von Kopfbolzend¨ubeln. Stahlbau 10. 1983. [14] Roik K, Hanswille G. Bemessungswerte f¨ur Kopfbolzend¨ubel nach Eurocode 4. Festschrift Polonyi. 1990.
[15] Roik K, Hanswille G. Background report on Eurocode 4 — stud connectors, Minister f¨ur Raumordnung, Bauwesen und St¨adtebau, Forschungsprojekt: RS II, 674102-8630. Bonn; 1989. [16] Roik K, Hanswille G. Background Report on Eurocode 4 — limit state of fatigue for headed studs, Minister f¨ur Raumordnung. Bauwesen und St¨adtebau. Forschungsprojekt: RS II, 674102-88.17. Bonn; 1990. [17] Palmgren A. Die Lebensdauer von Kugellagern. Zeitschrift des Vereins Deutscher Ingenieure 1924;68:339–41. [18] Miner MA. Cumulative damage in fatigue. Journal of Applied Mechanics 1945;12:159–64. [19] Oehlers DJ. Deterioration in strength of stud connectors in composite bridge beams. Journal of Structural Engineering 1990;116(12):3417–31. [20] EN ISO 13918. Welding — studs and ceramic ferrules for arc stud welding. 1998. [21] EN 206 – 1. Concrete — Part 1: Specification, performance, production and conformity. 2000. Gerhard Hanswille, Prof. Dr.-Ing. Since 1992 Professor for Steel and Composite Structures at the University of Wuppertal, Germany. Chairman of the German Standard Committee for Composite Structures and member of the Project Team for Eurocode 4 Part 1-1 and Part 2. Senior partner of HRA consulting engineers in Bochum, Germany and involved in composite and steel bridge and building design. Markus Porsch, Dipl.-Ing. Since 2000 assistant at the Institute for Steel and Composite Structures at the University of Wuppertal, Germany. International Welding Engineer (IWE). Cenk Ustundag, M.Sc. Since 2002 doctoral candidate at the Institute for Steel and Composite Structures at the University of Wuppertal, Germany. Holder of the German Academic Exchange Service (DAAD) Research Grant for Doctoral Candidates since 2003.
Resistance of headed studs subjected to fatigue loading Part I: Experimental study Gerhard Hanswille ∗ , Markus Porsch, Cenk Ustundag Institute of Steel and Composite Structures, University of Wuppertal, Germany Received 13 March 2006; accepted 30 June 2006
Abstract In steel–concrete composite structures the transfer of longitudinal shear forces at the interface between steel and concrete is mostly realized by headed shear studs. Especially in bridges due to traffic loads these shear connectors are subjected to high-cycle loading and the fatigue resistance governs the design. In this first part of two companion papers a series of experimental work with standard EC4 push-out specimens is presented. The main purpose of these tests was to determine the fatigue life and a possible reduction of the static strength of the headed shear studs subjected to unidirectional cyclic loading. A further aspect was to examine the effects of the loading sequence and damage accumulation on the fatigue life. The results of the experimental investigations show that due to a crack initiation at the stud foot at 10%–15% of the fatigue life, an early reduction of the static strength is caused. Furthermore tests to examine the effects of the loading sequence on the fatigue life revealed that the linear damage accumulation hypothesis according to Palmgren and Miner on which the present design codes are based do not describe the real behaviour. c 2006 Elsevier Ltd. All rights reserved.
Keywords: Fatigue life; Push-out test; Steel; Concrete; Composite; Headed shear studs; Unidirectional; Cyclic loading; Reduced static strength; Damage accumulation
1. Introduction In recent decades as a result of the benefits of combining the advantages of its components, steel–concrete composite beams have seen widespread use in buildings and bridges. The composite action of the components steel and concrete is realized by the shear connectors welded on the steel flange. Because of its economic and fast application headed shear studs are the most commonly used type of shear connectors in steel–concrete composite constructions. Especially in bridges due to traffic actions these studs are subjected to high-cycle fatigue loading. This is also the case in crane runways and composite beams used for industrial buildings exposed to traffic by fork-lift trucks. Because of its costs and difficulties arising in the interpretation of the results of full-scale beam tests, the evaluation of the behaviour of the shear studs generally takes place with standard push-out test specimens. Since the 1960s various researchers have conducted a great number of cyclic ∗ Corresponding address: University of Wuppertal, Institute of Steel and Composite Structures, Pauluskirchstrabe 7, 42285Wuppertal, Germany. E-mail address: [email protected] (G. Hanswille).
c 2006 Elsevier Ltd. All rights reserved. 0143-974X/$ - see front matter doi:10.1016/j.jcsr.2006.06.035
push-out tests to determine the fatigue life of shear connectors. Some of them are given in [1–9]. Maybe one of the remarkable points in these investigations was that repeated loading causes a reduction of the static strength of the shear stud within its lifetime [10]. This is an indication that the design concept in the current codes [11,12] does not describe the real behaviour, because the codes assume that ultimate limit states and fatigue limit states can be verified by independent checks. The design concept, illustrated in Fig. 1(a), of the before mentioned codes is based on the evaluation of internationally performed tests on push-out test specimens to determine the ultimate static strength and fatigue strength [13–16]. The verification of the fatigue resistance takes place comparable to steel structures on the basis of nominal stress concepts and the linear damage accumulation hypothesis according to Palmgren and Miner [17, 18]. Deterioration in strength of stud shear connectors and change in loading condition due to the change in deformation behaviour remain unconsidered which may result in a reduction of the reliability index so that it may fall below the target values in codes as illustrated in Fig. 1(b). So far, except for the test conducted by Oehlers [19], there weren’t enough tests where the reduced static strength
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Notation AD AG Ec N Nf Pmax Pu,0 Pu,N Vx fc 1P δi δ1
fatigue fracture area of the shear stud forced fracture area of the shear stud secant modulus of elasticity of concrete number of load cycles fatigue life peak value of cyclic loading ultimate static strength of the shear stud reduced static strength of the shear stud after N load cycle coefficient of variation cylinder compressive strength of concrete range of the cyclic loading inelastic displacement at ith load cycles plastic slip at the first cycle
after high-cycle preloading was systematically investigated. Thus in the light of the information gained from previous researches a comprehensive program of 71 push-out tests was developed to determine the reduced static strength after high-cycle preloading and to examine the effects of the loading sequence and damage accumulation on the fatigue life. This paper deals with the results of the experimental studies on the behaviour of headed shear studs subjected to unidirectional cyclic loading. Development of semi-empirical analytical methods to determine the reduced static strength and the fatigue life and the development of an improved damage
accumulation hypothesis will be discussed in the companion paper. 2. Push-out tests 2.1. Test program The experimental program consists of a total of 6 series (S1–S6). The first four series S1–S4 deal with constant amplitude tests where the effect of unidirectional cyclic loading on the static strength and the fatigue life of the push-out specimen were investigated with varying loading parameters, peak load Pmax and loading range 1P. In each series initially three static tests were performed to determine the mean value of the ultimate static load P¯u,0 of the push-out specimen. The mean value of the ultimate static load represents the reference parameter for the relative values of loading parameter required for cyclic tests. Using the relative loading parameters, three load controlled cyclic tests were performed to determine the mean fatigue life N¯ f of the push-out specimen. Subsequently six cyclic tests were conducted for approximately 30% and 70% of the mean fatigue life N¯ f . After reaching the corresponding number of cycles each of these six test specimens was statically loaded to failure under displacement control to obtain the reduced static strength after high cycle preloading. The chosen loading parameters and number of performed tests for the first four series are summarized in Table 1. Based on the results of the constant amplitude tests in the series S5 and S6 tests with the two and four blocks loading sequences were performed in which the peak load was
Fig. 1. (a) Safety concept to determine the lifetime of composite structures subjected to high cycle loading according to present codes; (b) actual influence of high cycle loading on lifetime.
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Fig. 2. Tests with multiple blocks of loading (a) two blocks; (b) four blocks. Table 1 Summary of the single level tests Series
S1 S2 S3 S4 S5E
1P/ P¯u,0 0.20 0.25 0.25 0.20 0.25
Pmax / P¯u,0 0.44 0.71 0.44 0.71 0.30
Number of tests P¯u,0 N¯ f N ∼ 0.3 N¯ f
N ∼ 0.7 N¯ f
3 3 3 3 3
3 3 3 3 1
3 3 3 3 1
3 3 3 3 1
Table 2 Summary of the tests with multiple blocks of loading Series
Number of tests
S5-2 S5-3 S5-4 S5-6
3 1 4 4
S6-3 S6-4
3 3
1P/ P¯u,0
Pmax / P¯u,0 Block 1 Block 2
Block 3
Block 4
0.25
0.71 0.44 0.44 0.30
0.44 0.71 0.30 0.44
– – – –
– – – –
0.20
0.44 0.74
0.54 0.64
0.64 0.54
0.74 0.44
increased or decreased subsequently while the loading range was held constant (see Fig. 2 and Table 2). Like the constant amplitude tests the series S5 and S6 were initiated with short-time static tests to determine the ultimate static load. During the tests with multiple blocks of loading it appeared necessary to perform further constant amplitude tests with a not investigated low peak load (Pmax / P¯u,0 = 0.3). Thus, 3 complementary constant amplitude cyclic tests (referred as series S5E) were performed in these series. The chosen loading parameters and number of performed tests for tests with multiple blocks of loading are summarized in Table 2. 2.2. Test specimens The specimen used in the push-out tests consists of a 650 mm long HEB260 profile and two 650 mm long, 600 mm wide and 150 mm thick concrete slabs. The slabs are connected to the steel beam by means of four headed shear studs of 22 mm diameter welded on each side of the beam. The weld collars complied with the requirements of EN ISO 13918 [20].
The mean height of the weld collars was 8.4 mm and the mean diameter 28.9 mm. The height of the welded stud was 125 mm. For casting the steel beams were cut into two halves and the concrete slabs were cast horizontally. The steel flanges were greased prior to casting to remove friction between the concrete and steel. The two halves were subsequently welded together. This test specimen complies with the standard pushout specimen according to Eurocode 4 with an exception of lateral restraints of the concrete slabs at the specimen bottom. The lateral restraints avoid especially in the lower row of shear studs the introduction of additional tensile forces resulting from the moment of eccentricity and enable a better simulation of the real behaviour in composite beams. Details of the push-out specimens are given in Fig. 3. 2.3. Test setup and loading procedure Cyclic and monotonic loading was applied by a 2500 kN servo hydraulic actuator. The load was introduced into the steel beam by means of a head plate welded on the cross section of the beam. The actuator was controlled by an Instron 8800 controller which allowed load and displacement control, and had sinusoidal control waveforms which were utilized for the cyclic testing. Displacement control was used for the monotonic tests, and load control was used for all cyclic testing. The test setup used in the experiments is shown in Fig. 4. The monotonic tests were conducted at a displacement rate of 0.004 mm/s. The time taken to reach the ultimate load was typically of the order of 50 min. After reaching the ultimate load the displacement rate was increased up to 0.008 mm/s. Cyclic tests were conducted with a load frequency of 3 Hz. In order to collect data about the stiffness and plastic deformation, cyclic tests were held after a specific number of cycles and the specimens were released and reloaded monotonically. During the tests the time, load from the actuator load cell, ram displacement from the built-in transducer in the actuator, longitudinal displacement between the concrete slab and steel beam and uplift of the slabs were measured. The ram displacement included movement due to the compliance of the test rig, and therefore it was not used in any subsequent data analysis. The longitudinal displacements were measured by two
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Fig. 3. Details of the push-out test specimen. Table 4 Average test results per stud
Fig. 4. Test setup and the hydraulic actuator. Table 3 Mean values of material properties of concrete
f c (N/mm2 ) E cm (N/mm2 )
Series S1
S2
S3
S4
S5
S6
44–52 36 400
42–45 36 400
53–56 39 000
43 33 900
43 33 500
46 33 700
LVDT’s on each steel flange to which the studs were welded (see Fig. 4). 2.4. Material properties At various intervals during the curing process at 28 days as well as at the beginning, in the middle and at the end of each series cylinder compression tests were carried out to determine the compressive cylinder strength and elastic stiffness of the concrete. Standard cylinders of 150 mm in diameter and 300 mm in length were used. Table 3 presents the range of the mean concrete strength and the mean modulus of elasticity associated with the test start for each series according to EN 206-1 [21]. In all series structural steel beams, headed shear studs and reinforcing bars used in the tests were from the same batch.
P¯u, N¯
Series (–)
P¯u,0 (kN)
N¯ f (–)
P¯u, N¯ 1 (kN)
(–)
S1 S2 S3 S4 S5E
205 184 201 181 189
6.2 × 106 1.2 × 106 5.1 × 106 3.5 × 106 6.4 × 106
154 174 133 181 111
0.75 0.95 0.66 1 0.59
1
P¯u,0
N¯ 1 N¯ f
P¯u, N¯
N¯ 2 N¯ f
(–)
P¯u, N¯ 2 (kN)
(–)
(–)
0.32 0.32 0.24 0.29 0.19
129 154 123 156 114
0.63 0.84 0.61 0.86 0.60
0.90 0.70 0.69 0.72 0.73
2
P¯u,0
The structural steel beams of HEB 260 section with the material quality S235 J2G3 were used in each test. From the tensile tests the mean yield strength and ultimate stress were determined as 337 N/mm2 and 448 N/mm2 , respectively. The modulus of elasticity of the beam was 209 341 N/mm2 . Stud shear connectors, which were welded automatically onto the steel beam flange, had a material quality of S235 J2G3+C450. Based on the tensile tests, the yield strength and the ultimate tensile strength of the connectors were determined as 440 N/mm2 and 528 N/mm2 , respectively. The modulus of elasticity of the studs was 216 351 N/mm2 . As reinforcing steel, standard deformed bars with diameters of 10 mm and 12 mm were used in the concrete slabs. Four tensile tests were performed on each bar sample. The average yield strength and ultimate strength was obtained as 549 N/mm2 and 606 N/mm2 for the bars of 10 mm, and 501 N/mm2 and 561 N/mm2 for the bars of 12 mm, respectively. The modulus of elasticity of the bars with diameters of 10 mm and 12 mm were determined as 197 779 N/mm2 and 204 540 N/mm2 , respectively. 3. Results of the constant amplitude tests Table 4 shows the results of the static strength, the fatigue life N¯ f and the reduced static strength after high cycle preloading for series S1–S5E. The limit state of fatigue is given, when the reduced strength has reached the value of the peak load. Because of different static strength within each test series the absolute values of Pmax and 1P differ slightly. All data given in Table 4 represent generally the mean values of
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Fig. 5. Comparison of Pe –Pt of the static tests (Pu,0 ) in series S1–S6 with the Pe –Pt data of the model of Eurocode 4.
three similar tests. The strength data are based on short time behaviour, so when relaxation must be taken into account, it is necessary to reduce the values by 10%. In contrast to series S2 and S4 the low peak loads in series S1, S3 and S5E led to very high fatigue lives N¯ f . Fig. 5 shows the comparison of static tests results (Pe ) for series S1–S6 with the corresponding data of theoretical shear resistance (Pt ) according to the empirical model of Eurocode 4 [15]. The resistance is given by the minimum of two equations, which describe the shear resistance in the case of “shear failure of the stud” and “failure of the concrete”, respectively. This model is based on the assumption, that in case of low concrete strength the shear resistance is determined only by the failure of concrete in the lower part of the shank. In the case of high concrete strength it is assumed, that the shear resistance is determined by the shear resistance of the stud shank. The results of the static tests are in good agreement with the prediction of the theoretical model, on which the design rules in Eurocode 4 are based. In Fig. 6 the results of the fatigue tests of series S1–S5E are compared with the corresponding test results, from which the fatigue strength curve in Eurocode 4 was derived. The test results are in good agreement with the given prediction according to Eurocode 4. 3.1. Plastic slip—load cycles In case of cyclic loading the load–deformation behaviour is characterized by an increasing plastic slip and a decreasing elastic stiffness K el . In Fig. 7 the inelastic slip δi related to the plastic slip in the first cycle δ1 is plotted against the number of cycles over the fatigue life N¯ i / N¯ f for series S1–S4. The beginning and the end of the lifetime are associated with a steep
Fig. 6. Comparison of fatigue test results with the prediction in Eurocode 4.
increase in the plastic slip with the number of cycles while in the remaining part of the lifetime a nearly linear increase of the plastic slip occurs with the number of cycles. The mean value of the initial plastic slip δ 1 in the first cycle is in series with high peak loads approximately 8 times greater than in series with low peak loads. 3.2. Static strength versus lifetime The influence of the cyclic loading becomes evident, when the static strengths are plotted versus number of load cycles. This is shown in Fig. 8, where the results are related to the mean static strength and the mean fatigue life of each series respectively. Especially in series S1, S3 and S5E with low peak loads the rapid decrease of the static strength within the first 20% of the fatigue life is noteworthy. On the other hand N¯ f is much greater than for the series with high peak loads. The reduction of the static strength over the lifetime is considered in four stages. In stage I there is no significant
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Fig. 7. Plastic slip over the fatigue life in series S1–S4.
Fig. 8. Decrease of static strength versus lifetime due to high cycle loading.
damage in concrete and steel and therefore no reduction. In stage II and stage IV there is an instable reduction of the static strength. Stage III shows a linear variation of the static strength
with the number of cycles. In Fig. 8 the coefficient of variation Vx of the static strengths gained from three similar tests is marked out exemplarily for the series S4. The scatter of the
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Fig. 9. Preparation stages for examination purposes.
results increases with the degradation of the strength of the shear studs. Comparison of the series with the same load range and different peak load makes clear that the static strength and the fatigue life are affected not only from the load range but also from the peak load of the cyclic loading. Furthermore it is also obvious that for the same amount of change the effect of the load range on the static strength is much greater than on the peak load. 3.3. Failure modes To investigate the reasons for the reduction of the static strength, the concrete slabs were separated from the steel beam and the fractured surfaces at the foot of each headed stud were examined. Fig. 9 gives in detail the stages of preparation of the test specimens after each push-out test for examination purposes. Also in some cases metallurgical investigations were carried out. The examined fracture surfaces consist of the typical dull fatigue fracture and bright forced fracture zones, where in the fatigue tests the former one is formed by cracks propagating to a critical length and the second one due to forced shear fracture. Furthermore the tests reveal two failure modes, which closely correlate with the peak load Pmax . For high peak loads such as in series S2 and S4 only mode A (see Fig. 10) occurs. For lower peak loads such as in series S1, S3, S5E in most cases mode B occurs, even though it must be mentioned, that in some cases both mode A and mode B were detected at the same time at one stud foot. This means, that there were formed two cracks and both could initiate forced fracture. Investigation of the microstructure reveals that both points, P1 and P2, show high
geometrical and metallurgical notch effects due to the welding technique. Furthermore the short time static tests carried out after high cycle preloading show in case of mode B more ductile behaviour than mode A, which is in good agreement with both crack forms. The fractured surfaces at the stud feet in case of failure mode A show typical arrest lines, so that it was possible to detail the crack development for this mode. Unfortunately for mode B there couldn’t be observed any stop marks except for one test specimen although the testing procedure was always the same. The evaluation of the test results as yet showed that for mode A (series S2 and S4) and mode B (series S1, S3 and S5E) there is a linear relationship between the reduced static strength and the size of the fatigue cracking zone. This relationship is illustrated in Fig. 11 schematically, where A D is the area of the fatigue cracking zone and A G the area of the forced shear fracture. In case of mode A the whole fracture area (A D + A G ) corresponds to the stud area. In case of mode B the whole fracture area is much larger than the stud area. The coefficient of correlation of the linear relationship is 0.99 for mode A and 0.85 for mode B. If the analysis is based on all tests of mode A and B, a coefficient of 0.88 results (Fig. 11). From the given linear correlations can be deduced that the crack propagation in the shear stud has approximately 60% attribution in the reduction of the static strength. 4. Results of tests with multiple blocks of loading The results of the two and four blocks loading sequences (see Fig. 2) are given in Tables 5 and 6 respectively. The mean value of the reference ultimate static strength P¯u,0 of the shear studs
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Fig. 10. Failure modes A and B.
Fig. 11. Relationship between reduced static strength and fatigue fracture area.
is 186 kN for the tests with two blocks of loading in series S5 and 196 kN for the tests with four blocks of loading in series S6. It is to be noticed that in tests with multiple blocks of loading the failure of the shear studs can occur on the one hand during the cyclic loading by the decrease of static strength to the peak load and on the other during switching to the next block with a higher peak load by exceeding the reduced static strength. A typical example for the last case occurred in the test S5-3a during switching to the second block with a peak load of 133 kN by exceeding the reduced static strength of 124 kN per stud.
Evaluation of the tests with multiple blocks of loading on the basis of the linear damage accumulation hypothesis of Palmgren and Miner, on which the present design codes rely, is shown in Fig. 12. The fatigue life Nfi corresponding to each block of cyclic loading is gained from the results of the constant amplitude tests of series S1–S4 and S5E. The missing values of number of cycles to fatigue for the blocks 2 and 3 in the test with four blocks of loading are determined by means of a linear interpolation from the results of series S1 and S4. Thus, for the peak loads of 101 kN and 120 kN per stud the fatigue life N f
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G. Hanswille et al. / Journal of Constructional Steel Research 63 (2007) 475–484 Table 5 Loading parameters and results of the tests with two blocks of loading (series S5) Test (–)
Block 1 Pmax,1 (kN)
S5-2a S5-2c S5-3a S5-4a S5-4b S5-4c S5-4d S5-6a S5-6b S5-6c S5-6d
133 133 83 83 83 83 83 56 56 56 56
N1 + N2 (×106 )
Block 2 1P (kN)
N1 (×106 )
Pmax,2 (kN)
47
0.204 0.198 1.099 0.473 0.517 0.544 0.542 0.537 1.223 1.295 1.277
83 83 133 56 56 56 56 83 83 83 83
1P (kN)
N2 (×106 )
47
0.792 1.440 – 1.365 0.772 0.735 3.396 5.821 0.761 1.744 3.206
0.996 1.638 1.099 1.838 1.289 1.2791 3.938 6.358 1.984 3.039 4.483
Table 6 Loading parameters and results of the tests with four blocks of loading (series S6) Test (–)
S6-3a S6-3b S6-3c S6-4a S6-4b S6-4c
1P (kN)
38 38 38 38 38 38
Block 1
Block 2
Block 3
P4
6 i=1 Ni (×10 )
Block 4
Pmax,1 (kN)
N1 (×106 )
Pmax,2 (kN)
N2 (×106 )
Pmax,3 (kN)
N3 (×106 )
Pmax,4 (kN)
N4 (×106 )
83 83 83 139 139 139
0.756 0.765 0.754 0.550 0.550 0.540
101 101 101 120 120 120
0.768 0.804 0.759 0.763 0.758 0.753
120 120 120 101 101 101
0.770 0.785 0.750 0.754 0.750 0.753
139 139 139 83 83 83
0.868 0.324 0.449 0.583 0.756 1.208
3.162 2.678 2.712 2.650 2.815 3.254
5. Summary and conclusions A total of 71 push-out tests was performed to determine the reduced static strength after high-cycle preloading and to examine the effects of the loading sequence on the fatigue life. The test results, especially the observation of arrest lines, indicate an early crack initiation in approximately 10%–20% of the fatigue life which causes the reduction of the static strength. Constant amplitude tests have shown that the magnitude of the peak load Pmax of the cyclic loading has a significant effect on the crack form occurring at the stud foot. Evaluation of the tests with multiple block loading sequences on the basis of the linear damage accumulation according to Palmgren–Miner yields unsafe results. Development of analytical methods to determine the reduced static strength and the fatigue life and the development of a modified damage accumulation hypothesis will be discussed in the companion paper. Acknowledgement Fig. 12. Comparison between the test results with the results of the lifetime prediction according to Palmgren–Miner.
is determined as 5.3 × 106 and 4.4 × 106 number of cycles, respectively. It is obvious that except for one test in Fig. 12 all results of the lifetime prediction according to Palmgren and Miner lie on the unsafe side. The main reason for this is the omission of the effects due to crack propagation in the shank of the stud and the increasing local crushing of concrete surrounding the stud weld.
The experimental program described in this paper is financed by the German Research Foundation (DFG) within the scope of Collaborative Research Centre 398. References [1] Slutter RG, Fisher JW. Fatigue strength of shear connectors. Highway research record no. 147. New York; 1966. [2] Mainstone RJ, Menzies JB. Shear connectors in steel–concrete composite beams for bridges, Part 1 and 2. Concrete 1967;1(9–10).
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[3] Hallam MW. The behaviour of stud shear connectors under repeated Loading. Research report R281. School of Civil Engineering, University of Sydney; 1976. [4] Roderick JW, Ansourian P. Repeated loading of composite beams, The civil engineering transactions of the Institution of Engineers. Austria; 1976. [5] Akao S, Kurita A, Hiragi H. Fatigue strength of stud shear connectors with concrete deposited from different placing directions. IABSE Fatigue, Lausanne; 1982. [6] Oehlers DJ. A new approach to the design of stud shear connectors in composite bridge beams. Research report R82. University of Adelaide; 1989. [7] Th¨urlimann B. Fatigue and static strength of stud shear connectors. Journal of ACI 1966;30(12). [8] Roik K, Holtkamp HJ. Untersuchungen zur Dauer- und Betriebfestigkeit von Verbundtr¨agern mit Kopfbolzend¨ubeln. Stahlbau 58. 1989. [9] Roik K, Hanswille G. Zur Dauerfestigkeit von Kopfbolzend¨ubeln bei Verbundtr¨agern. Bauingenieur 62. 1987. [10] Oehlers DJ, Foley L. The fatigue strength of stud shear connections in composite beams. Proceedings of the Institute of Civil Engineering 1985; 79(2):349–64. [11] EN 1994-1-1. Eurocode 4: Design of composite steel and concrete structures. Part 1-1: General rules and rules for buildings. Brussels: CEN; 2004. [12] EN 1994-2. Eurocode 4: Design of composite steel and concrete structures. Part 2: General rules and rules for bridges. Brussels: CEN; 2004. [13] Roik K, Hanswille G. Beitrag zur Bestimmung der Tragf¨ahigkeit von Kopfbolzend¨ubeln. Stahlbau 10. 1983. [14] Roik K, Hanswille G. Bemessungswerte f¨ur Kopfbolzend¨ubel nach Eurocode 4. Festschrift Polonyi. 1990.
[15] Roik K, Hanswille G. Background report on Eurocode 4 — stud connectors, Minister f¨ur Raumordnung, Bauwesen und St¨adtebau, Forschungsprojekt: RS II, 674102-8630. Bonn; 1989. [16] Roik K, Hanswille G. Background Report on Eurocode 4 — limit state of fatigue for headed studs, Minister f¨ur Raumordnung. Bauwesen und St¨adtebau. Forschungsprojekt: RS II, 674102-88.17. Bonn; 1990. [17] Palmgren A. Die Lebensdauer von Kugellagern. Zeitschrift des Vereins Deutscher Ingenieure 1924;68:339–41. [18] Miner MA. Cumulative damage in fatigue. Journal of Applied Mechanics 1945;12:159–64. [19] Oehlers DJ. Deterioration in strength of stud connectors in composite bridge beams. Journal of Structural Engineering 1990;116(12):3417–31. [20] EN ISO 13918. Welding — studs and ceramic ferrules for arc stud welding. 1998. [21] EN 206 – 1. Concrete — Part 1: Specification, performance, production and conformity. 2000. Gerhard Hanswille, Prof. Dr.-Ing. Since 1992 Professor for Steel and Composite Structures at the University of Wuppertal, Germany. Chairman of the German Standard Committee for Composite Structures and member of the Project Team for Eurocode 4 Part 1-1 and Part 2. Senior partner of HRA consulting engineers in Bochum, Germany and involved in composite and steel bridge and building design. Markus Porsch, Dipl.-Ing. Since 2000 assistant at the Institute for Steel and Composite Structures at the University of Wuppertal, Germany. International Welding Engineer (IWE). Cenk Ustundag, M.Sc. Since 2002 doctoral candidate at the Institute for Steel and Composite Structures at the University of Wuppertal, Germany. Holder of the German Academic Exchange Service (DAAD) Research Grant for Doctoral Candidates since 2003.