With the high- and ultrahigh-strength steels applied in the construction industry, the seismic safety of their structural components are very concerned due to the inferior material ductility of those steels. The current studies on bolted high-strength steel T-stubs mainly focus on their monotonic loading behavior. There is limited research work conducted to study their cyclic loading behavior. In this study, cyclic tests of bolted dual-steel T-stubs were conducted. Their T-elements were produced by Q690 high-strength steel ﬂanges and Q355 normal-strength steel webs, and class 10.9 high-strength bolts with pretension were used to connect the groove-welded T-elements. Failure modes, force–deformation hysteretic and backbone curves, cumulative plastic deformation and energy dissipation capacities were tested and analyzed. The test results indicated that an optimal ratio between the plastic resistances of Mode 1 (neglecting the inﬂuence of bolt action on a ﬁnite contact area) and Mode 3 in Eurocode 3 Part 1-8 could be 0.3 for those bolted T-stubs to maximize hysteretic energy dissipation. Accordingly, predictive formulas with good precision were proposed for the low-cycle fatigue failure criterion and hysteretic energy dissipation capacity of those bolted T-stubs, respectively. Keywords: Bolted T-stub, Dual-steel, High-strength steel, Hysteretic energy, Cyclic, Welded plate Corresponding author Email address: hufx@scut.edu.cn (Fangxin Hu) Preprint submitted to Thin-Walled Structures June 13, 2023 1 Introduction 1 In recent years, there has been an emerging trend to use high-strength steel with a nominal yield 2 strength not less than 460 MPa in the construction industry to gain additional speciﬁc strength, 3 good economic beneﬁts and environmental friendliness compared to conventional low-carbon mild 4 and low-alloy steels [1–6]. In general, welded moment connections are widely used in seismic 5 resistant steel structures [7, 8]. However, it was not easy to ensure the weld of high-strength steel 6 with the same strength as the base metal due to the softening e ect observed in the heat a ected 7 zone (HAZ) [9, 10]. Sometimes, ﬁeld-bolted connections are strongly recommended, and even 8 required, for rapid construction to reduce the construction cycle and simultaneously the associated 9 costs. Therefore, some commonly used ﬁeld-bolted connection types, such as bolted extended 10 and ﬂush end-plate connections, bolted T-stub connections and bolted angle connections, may be 11 utilized to connect high-strength steel members and components [11–15]. Particularly, mild steel 12 is always used in energy dissipative members (e.g. beams and /or braces), while high-strength steel 13 is preferred in the other members that have to remain predominantly elastic, such as columns [16]. 14 Such a case between mild steel beams and high-strength steel columns leads to dual-steel bolted 15 joints. Furthermore, the structural behavior of those bolted joints can be characterized using the 16 component method in Eurocode 3 Part 1-8 [17], and the equivalent T-stub subjected to tension and 17 compression is one of the basic components. Note that earthquake hazard has been one of the most 18 critical factors to threaten the safety of steel structures, and the cyclic behavior of bolted dual-steel 19 or high-strength steel T-stubs are crucial to evaluate its joint and structural behavior. 20 In the last few decades, many researchers have performed experimental and numerical studies 21 on the structural behavior of bolted dual-steel or high-strength steel T-stubs under monotonic 22 loading [11, 18–32]. The previous results revealed the e ects of steel grades, welding-induced 23 softening in the HAZ, post-weld heat treatment, combined loading of tension and shear, and 24 placement of sti eners on the initial sti ness and plastic resistance of bolted T-stubs. Some 25 2 contradictory conclusions were found, and so, through a recent study by the authors [31], it was 26 generally concluded that the softening e ect in the HAZ may be related to the steel production 27 technique as well as the welding process, and if this softening can be ignored or alleviated, the 28 current formulae in Eurocode 3 Part 1-8 can be still applied to bolted high-strength steel T-stubs 29 in terms of the initial sti ness, plastic resistance and joint modeling approach. However, limited 30 studies were conducted to evaluate the cyclic behavior. Dubina et al. [19, 20] and Muntean et al. 31 [21] performed cyclic testing on dual-steel bolted T-stubs between grade S235 webs and grade 32 S460 or S690 ﬂanges. They found that compared with the steel grades, the types of failure mode 33 (ﬂange bending, bolt rupture, or combined mode) had much larger inﬂuence on the ductility, and 34 the ductility was largely decreased by cyclic loading when the failure mode was dominated by 35 ﬂange bending. But in the loading history they used the compression force was limited to avoid 36 buckling, which may underestimate the cyclic damage under earthquakes. Kleiner and Kuhlmann 37 [22] conducted experimental studies on two series of bolted dual-steel T-stubs, one group being 38 unsti ened T-stubs and the other being sti ened T-stubs, where web plates were all made of mild 39 steel while S460 or S690 steel end plates were used. The specimens were designed aiming at a 40 Mode 2 failure (bolt failure with ﬂange yielding) in Eurocode 3 Part 1-8, but to exhibit ductile 41 (close to Mode 1, or say, ﬂange yielding) and brittle (close to Mode 3, or say, bolt failure) 42 mechanisms, respectively. However, it was found that the cyclic loading history did not a ect 43 much on the ultimate resistance and ductility of those T-stubs when compared with the results 44 under monotonic loading. This was due to the relatively thick end plates (even in the ductile 45 mode), which made the ultimate performance basically dominated by the identical bolts used in 46 this study. The knowledge on the real cyclic bending deformation capacity of high-strength steel 47 end plates was still limited. Chen et al. [32] reported experimental and numerical studies on 48 cyclic performance of Q460 and Q690 high-strength steel bolted T-stubs. They found by the 49 experimental study that using the same bolts, the increase of the ﬂange thickness aided energy 50 dissipation, and by the numerical study they further conﬁrmed the probable existence of an ﬂange 51 3 thickness to maximize energy dissipation. But their numerical study did not take into account the 52 ultimate failure in the ﬂange or bolts, neither did they present any criteria to evaluate the capacity 53 of energy dissipation. 54 As described previously, there is still no available method to evaluate the energy dissipation 55 capacity of high-strength steel bolted T-stubs. The authors thus report an experimental program 56 consisting of ten bolted dual-steel T-stub specimens fabricated by Q355 steel webs and Q690 high- 57 strength steel ﬂanges in China that were subjected to cyclic loading of both constant and variable 58 amplitudes. The main variable considered in this study was the Q690 ﬂange thickness, while class 59 10.9 high-strength bolts of a nominal diameter of 20 mm (M20) were always used. The test results 60 will be presented in terms of hysteretic and backbone force-deformation curves as well as low- 61 cycle fatigue curves. Accordingly, a curve ﬁt to predict the hysteretic energy dissipation capacity 62 will be proposed. 63 2 Test program 64 2.1 T-stub specimens 65 A series of ten cyclic tests on bolted T-stub specimens made of welded grade Q355 ( fy= 66 355 MPa) normal-strength and grade Q690 high-strength steels was conducted. In each T-stub 67 specimen, two identical T-elements was connected by a pair of preloaded class 10.9 high-strength 68 bolts of a nominal diameter of 20 mm (denoted as M20), as shown in Figure 1. So, only one bolt 69 row was considered. The steel grade and thickness of the ﬂange plates in the T-stubs varied in 70 this study, as shown in Table 1, while the web plates were all made of 14 mm-thick grade Q355 71 steel plates. In this way, those specimens were typical of dual-steel T-stubs that are representative 72 components in bolted beam-to-column connections, such as in extended end-plate connections 73 using Q690 end plates between Q355 beams and Q690 columns [15]. The dimensions are shown 74 in Figure 1 and Table 1. Note that the web plate was welded to the ﬂange plate using a continuous 75 complete penetration K-type groove weld. This is the case for the connection between the end 76 4 plate and beam ﬂanges in a bolted end-plate joint as required by Chinese Speciﬁcation [33]. Each 77 specimen is given a name for ease of reference, which starts with T indicating T-stubs and a number 78 to represent the ﬂange thickness (in mm), followed by V or C indicating variable-amplitude or 79 constant-amplitude loading, respectively. The number after C is the amplitude magnitude (in mm). 80 Details of the loading amplitudes will be introduced in the following Section 2.3. For example, 81 Specimen T10-V represents a specimen that used 10 mm-thick ﬂange plates and was subjected 82 to variable-amplitude cyclic loading, while Specimen T10-C5 represents a specimen that used 10 83 mm-thick ﬂange plates and was subjected to cyclic loading with a constant amplitude of 5 mm in 84 deformation. 85 tftw = 14 bw = 40035ºK-type CJP butt weld flangeweb webGrade 10.9s M20 bolts tftw = 14 bw = 40035ºK-type CJP butt weld flangeweb webGrade 10.9s M20 bolts Figure 1. T-stub geometry (unit: mm) T-stubs may exhibit di erent failure modes, depending on the ﬂexural resistance of the ﬂange 86 and the tensile resistance of the bolt. According to Eurocode 3 Part 1-8, three collapse mechanisms 87 5 Table 1. Test specimens Specimen labelb (mm)tf (mm)bf (mm)tw (mm)bw (mm)d (mm)e (mm) Amplitude (mm) T8-V 80 8 194 14 400 45 45 0.18Variable T8-C7 7 T8-C11 11 T8-C15 15 T10-V 80 10 194 14 400 45 45 0.31Variable T10-C5 5 T10-C13 13 T12-V 80 12 194 14 400 45 45 0.44Variable T12-C9 9 T12-C13 13 can be identiﬁed, and the corresponding plastic resistances are 88 Fp1=(32n2dwsh)Mpf 8mn(m+n)dwsh(1a) Fp2=2Mpf+2nB m+n(1b) Fp3=2B (1c) where the inﬂuence of the bolt action on a ﬁnite contact area is taken into account in Mode 1 89 collapse; Mpf=be t2 ffy=4 is the plastic ﬂexural resistance of the T-stub ﬂange, where be is the 90 e ective width, which is the minimum value provided by both the circular and non-circular 91 patterns for collapse Mode 1 and that corresponding only to the non-circular pattern for collapse 92 Mode 2, fyis the yield strength of the ﬂange material; dwshis the diameter of the washer; mis the 93 distance between the bolt axis and the conjunction (weld toe) of the ﬂange and web where the 94 formation of a plastic hinge is expected, and m=d0:8hfwhere dis the distance from the bolt 95 axis to the web face and hfis the weld throat height equal to 5 mm, as shown in Figure 1; nis the 96 e ective edge distance, which is the minimum value between e(the distance between the bolt 97 axis and the tip of the ﬂanges, as shown in Figure 1) and 1 :25m;B=0:9fubAeis the axial plastic 98 6 resistance of a single bolt in tension, where fubis the ultimate tensile strength of the bolt material 99 (nominally 1000 MPa for class 10.9 bolts) and Aeis the e ective tensile area of the bolt (245 100 mm2for M20 bolts). The collapse mode is determined by the relative strength between the ﬂange 101 and bolt, and can be characterized by 102 =2Mpf Bm(2) Thus, it was easily veriﬁed that all the three ﬂange thicknesses in Table 1 were characterized 103 by Mode 1 collapse, i.e., only yielding and plastic bending in the ﬂanges. The ratios for the 104 specimens, calculated using the measured material properties in the following subsection, are also 105 shown in Table 1. This was intentionally designed so that the plastic deformation and energy 106 dissipation capacity of the high-strength steel T-stub ﬂange under cyclic bending could be assessed. 107 In case of the ultimate failure controlled by bolt rupture in Mode 2 or Mode 3 rather than ﬂange 108 fracture, the e ect of cyclic loading should be insigniﬁcant, as already evidenced by the previous 109 studies [19, 22]. 110 2.2 Material properties 111 The steel materials used in this study are identical to a previous study by the authors [31]. The 112 mechanical properties of the Q690 steel used in the T-stub ﬂanges are shown in Table 2, where 113 Eis the elastic modulus, fyis the yield strength, fuis the ultimate strength, stis the strain at 114 the end of the yield plateau, uis the ultimate strain, and is the elongation after fracture. The 115 corresponding stress–strain curves are shown in Figure 2. Note that the 8 mm– and 10 mm–thick 116 Q690 steel plates did not exhibit any distinct yield plateau in their stress–strain curves. In these 117 cases, the yield strength is the proof stress corresponding to a residual plastic strain of 0.2%. 118 Tension test on the class 10.9 high-strength bolt was also conducted to obtain its elastic 119 modulus E, ultimate strength fuand ultimate strain u, as shown in Table 2. The measured 120 diameter of the washers ( dw) used with those class 10.9 M20 high-strength bolts was about 38.4 121 mm. Manual gas shielding arc welding using a consumable electrode of grade E50, which ﬁts to 122 7 Table 2. Material properties Steel Gr. Plate thickness (mm)E (GPa)fy (MPa)fu (MPa)stu(%) Q6908 208.3 723 822 — 0.100 20 10 189.4 794 902 — 0.106 21 12 205.8 775 816 0.018 0.060 16 10.9s M20 206.0 — 1135 — 0.110 — 00.050.10.150.20.250.3 Strain01002003004005006007008009001000Stress (MPa) Q690-PL8 Q690-PL10 Q690-PL12 Figure 2. Q690 steel stress-strain curves Q355 normal-strength steel, was adopted for the groove welds between the T-stub webs and 123 ﬂanges. Since the T-stub webs only transfer the axial load to the ﬂanges, the material properties 124 of the T-stub webs were not measured. 125 2.3 Test setup and procedures 126 Before the formal test, the class 10.9 high-strength bolts in the T-stub specimens were tightened 127 by a torque wrench to achieve a design preload of 155 kN according to Chinese Speciﬁcation [33]. 128 The specimens were then placed into a servo-hydraulic universal test machine and aligned, so that 129 the grips were centered with respect to the T-stub webs, as shown in Fig. 3. Cyclic loading tests 130 were performed with displacement control until failure, while the opening gap between the ﬂanges 131 was monitored by a displacement transducer at the centerline of the webs. In constant-amplitude 132 tests the measured opening gap was loaded to the target amplitude in tension, and was reversed 133 8 to zero in compression. In variable-amplitude tests, at the ﬁrst stage the measured opening gap 134 was loaded to 5 mm in tension and then reversed to zero; the tension amplitude was incremented 135 by 2 mm in every subsequent stage but the compression amplitude was always kept as zero. Note 136 that three cycles were implemented at each stage. These cyclic loading histories well replicate the 137 situation for T-stubs when the prototype bolted beam-to-column joint is subjected to symmetric 138 cyclic reversals of constant or variable amplitudes. 139 T-stub specimengrip Displacement transducer grip Figure 3. Test setup 3 Test results 140 3.1 Failure modes 141 All the T-stub specimens were designed to undergo Model 1 failure. Thus, they all 142 experienced cracking in the HAZ of the ﬂange near the weld between the ﬂange and web plates, 143 and such cracking ﬁnally induced total fracture of the ﬂange, as shown in Figure 4 for typical 144 tests. The cracking process, along with loud noises, however, was di cult to trace accurately. 145 Therefore, only ﬁnal complete fracture of the ﬂange is summarized here. For Specimen T8-V , the 146 ﬂange completely fractured when the opening gap reached 13 mm at the second cycle of 15 mm 147 amplitude, and a major crack was observed in the other ﬂange. For Specimens T8-C7, T8-C11, 148 9 (a) T8-V (b) T8-C11 (c) T8-C15 (d) T10-V (e) T12-V (f) T12-C9 (g) T12-C13 Figure 4. Typical failure modes and T8-C15, complete fracture in the ﬂange was noticed when the opening gap reached 6 mm, 6 149 mm, and 7 mm, at the 25th, 10th, and 7th cycle, respectively. Similarly, for Specimen T10-V , the 150 ﬂange completely fractured when the opening gap reached 9 mm at the second cycle of 13 mm 151 amplitude. For Specimens T10-C5 and T10-C13, complete fracture in the ﬂange was noticed 152 when the opening gap reached the corresponding tension amplitude at the 61st and 8th cycle, 153 respectively. Lastly, for Specimen T12-V , the ﬂange completely fractured when the opening gap 154 reached 11 mm at the second cycle of 13 mm amplitude, while for Specimens T12-C9 and 155 T12-C13, complete fracture in the ﬂange was noticed when the opening gap reached 6 mm and 156 13 mm at the 20th and 5th cycle, respectively. 157 10 3.2 Hysteretic and backbone curves 158 Axial force–deformation hysteretic curves of all the tested T-stub specimens are shown in 159 Figure 5, where the deformation is the measured opening gap between the ﬂanges at the web 160 centerline. The moments of complete ﬂange fracture are also marked in the ﬁgure, along with the 161 number of cycle when the fracture occurred. It is clear that as the ﬂange thickness increases from 162 8 mm to 12 mm, pinching e ect in the hysteretic curves becomes more apparent. This is because 163 the thicker the ﬂange, the larger the bolt deformation (elongation and ﬂexure), which introduces a 164 signiﬁcant slippage stage in the curves under unloading from tension and reloading into 165 compression. Cyclic degradation of both sti ness and strength are also apparent in the curves, 166 due to crack initiation and its associated propagation in the ﬂanges. In addition, shown in Figure 167 6 are backbone curves from the hysteretic curves under variable-amplitude loading only, that 168 were constructed by connecting the ﬁrst loading branch with subsequent tension amplitudes. It is 169 clear that the thicker the ﬂange, the higher the ultimate (maximum) strength. And this maximum 170 strength was reached at the deformation of 9 mm for the three specimens (T8-V , T10-V and 171 T12-V). 172 3.3 Strength, ductility and energy dissipation 173 According to the method recommended by ECCS [34], the yield point was detected in the 174 backbone curve based on the intersection of an initial straight line whose slope is the initial 175 sti ness, and a subsequent tangent line to the curve whose slope is one-tenth of the initial 176 sti ness. Due to the highly nonlinear initial branch of the backbone curve, the initial sti ness ( K) 177 was obtained by a linear ﬁt to the ﬁrst unloading branch after the achievement of 5 mm 178 deformation in each variable-amplitude hysteretic curve. The axial force and deformation at the 179 yield point were then deﬁned as the yield strength ( Fy) and deformation ( y), respectively, as 180 shown in Table 3. The ultimate strength ( Fu) was easily obtained as the maximum force in the 181 backbone curves. The ultimate deformation ( u) was counted only if a least one complete cycle of 182 11 -20246810121416 Deformation (mm)-200-1000100200Axial force (kN) Flange fracture (17)T8-V(a) T8-V -2 02468 Deformation (mm)-200-1000100200Axial force (kN)Flange fracture (25)T8-C7 (b) T8-C7 -2024681012 Deformation (mm)-200-1000100200Axial force (kN)Flange fracture (10)T8-C11 (c) T8-C11 -20246810121416 Deformation (mm)-200-1000100200Axial force (kN)Flange fracture (7)T8-C15 (d) T8-C15 -202468101214 Deformation (mm)-200-1000100200300Axial force (kN) Flange fracture (14)T10-V (e) T10-V -2 0 2 4 6 Deformation (mm)-200-1000100200300Axial force (kN)Flange fracture (61)T10-C5 (f) T10-C5 12 -202468101214 Deformation (mm)-200-1000100200300Axial force (kN) Flange fracture (8)T10-C13(g) T10-C13 -202468101214 Deformation (mm)-200-1000100200300400Axial force (kN)Flange fracture (14)T12-V (h) T12-V -20246810 Deformation (mm)-200-1000100200300400Axial force (kN)Flange fracture (20)T12-C9 (i) T12-C9 -202468101214 Deformation (mm)-200-1000100200300400Axial force (kN) Flange fracture (5)T12-C13 (j) T12-C13 Figure 5. Axial force–deformation hysteretic curves 13 -20246810121416 Deformation (mm)050100150200250300350400450Axial force (kN)T12-V T10-V T8-VFigure 6. Axial force–deformation backbone curves the target deformation amplitude was completed before total ﬂange fracture or bolt rupture 183 occurred. For example, Specimen T8-V failed by complete ﬂange fracture at the second cycle of 184 15 mm amplitude in tension, then its ultimate deformation was taken as 15 mm. The calculated 185 plastic resistance ( Fp) based on Eurocode 3 Part 1-8, which was obtained by Eq. (1a) as Mode 1 186 dominated collapse, is shown in Table 3. As shown clearly, the ratios between the test yield and 187 calculated plastic strength ( Fy=Fp) range from 0.77 to 0.92, demonstrating conservatism in the 188 theoretical method. This evidences that the formulae in Eurocode 3 Part 1-8 can be still applied to 189 Q690 high-strength steel, which is in accordance with the ﬁndings in the previous studies 190 [31, 32]. Besides, the overstrength ( Fu=Fy) revealed by the tests ranges from 1.19 to 1.26, and it 191 generally increases with the decrease of the ﬂange thickness. Table 3. Sti ness, strength and ductility Specimen labelK (kN/mm)Fy (kN)Fu (kN)Fu=Fy Fp (kN)Fp=Fyy (mm)u (mm) T8-V 69.8 142.8 180.5 1.26 110.1 0.77 2.05 15 7.3 T10-V 116.3 205.9 256.0 1.24 188.9 0.92 1.77 13 7.3 T12-V 149.2 312.9 371.6 1.19 265.6 0.85 2.10 13 6.2 192 The ductility factor, , deﬁned as u=y, was also calculated and is shown in Table 3. Its 193 values range from 6 to 7, indicating good ductility. In order to further examine the deformation 194 14 capacity under cyclic loading, the maximum plastic deformation amplitude, p, cumulative plastic 195 deformation, p, and energy dissipation, A, of all the specimens were determined based on the 196 method in ATC-24 [35], as shown in Figure 7. Those values were counted until the last successful 197 excursion (or half-cycle) before complete ﬂange fracture or bolt rupture occurred, as summarized 198 in Table 4. The normalized cumulative plastic deformation by the plastic deformation amplitude, 199 p=p, is also included in this table. It should be mentioned that for the easiness of comparison, 200 the plastic deformation amplitudes for three variable-amplitude tests were directly taken as those in 201 the constant-amplitude tests of the same ultimate total deformation. It is clear that those cumulative 202 quantities are highly variable in the constant-amplitude tests, and generally, the cumulative plastic 203 deformation ( porp=p) and energy dissipation ( A) both decrease with the increase of 204 loading amplitude. Besides, the plastic deformation quantities ( ,p,p, and p=p) revealed 205 by the variable-amplitude tests all show a decreasing trend with the increase in ﬂange thickness. 206 This is reasonable since the specimens failed all by collapse Mode 1, and more plastic rotation, 207 associated with the axial plastic deformation of the whole T-stub, could be tolerated by thinner 208 ﬂanges. But the total energy dissipated under the same variable-amplitude cyclic history actually 209 shows a maximum (16.8 kJ) if the ﬂange thickness is an intermediate value (10 mm), slightly 210 higher than that (16.2 kJ) if the ﬂange thickness is 8 mm but obviously more than that (13.4 kJ) 211 if the ﬂange thickness is 12 mm. This suggests an optimal balance in proportioning the ﬂange 212 and bolt to maximize energy dissipation capacity. In this study, such an optimal balance may be 213 achieved in Specimen T10-V by setting as 0.3 (see Table 1). Such a result is in accordance 214 with the conclusion in a previous study by the authors on the maximum ductility under monotonic 215 loading [31]. But further study on more specimens is still needed for evidence. 216 15 DeformationAxial force " /piAi" /pi+1Ai+1 /pKFigure 7. Deﬁnition of plastic deformation amplitude, cumulative plastic deformation and energy dissipation 4 Discussions 217 4.1 Low-cycle fatigue curves 218 Low-cycle fatigue of steel structural components, including the bolted T-stubs examined in this 219 study, can be captured by a Co n-Manson type relationship as [36, 37] 220 p=aNb f (3) wherepis the plastic deformation amplitude (see Table 4), Nfis the number of complete cycles 221 before failure, aandbare coe cients related to structural details. Three constant-amplitude tests 222 on the specimens with a ﬂange thickness of 8 mm (T8-C7, T8-C11 and T8-C15) were conducted, 223 and so a ﬁt could be carried out directly on this ﬂange thickness specimens, which led to values 224 of 40.0 and 0:69 for aandb, respectively. Due to the limited number of constant-amplitude 225 tests for the other two ﬂange thickness specimens conducted in this study, all the specimens with 226 three ﬂange thicknesses were incorporated to ﬁt the coe cients aandb, and the result is shown 227 in Figure 8. The overall ﬁtted values of aandbare 26.8 and 0:52, respectively. Such overall 228 ﬁtted result should not be reasonable enough since the ﬂange thickness does have an impact on the 229 16 Table 4. Cumulative plastic deformation and energy dissipation Specimen labelp(mm) p(mm) p=p A(kJ) T8-V 12.32 169.9 13.8 16.2 T8-C7 4.63 163.9 35.4 13.7 T8-C11 8.30 119.1 14.4 11.4 T8-C15 12.32 126.7 10.3 13.6 T10-V 10.97 127.9 11.7 16.8 T10-C5 3.07 243.1 79.2 20.3 T10-C13 10.97 126.1 11.5 14.6 T12-V 10.50 74.9 7.1 13.4 T12-C9 6.53 107.6 16.5 16.5 T12-C13 10.50 54.1 5.2 8.3 plastic deformation capacity, and theoretically, the ﬁt of Eq. (3) should be done for each group of 230 specimens of individual ﬂange thickness. But the overall ﬁtted values of aandbin such a limited 231 number of all the constant-amplitude tests still provide a clear picture on the fatigue performance 232 of bolted T-stubs with high-strength steel ﬂanges, if compared to that of normal-strength steel 233 counterparts. 234 100101102 Nf1020/p(mm)overall fit a=26.8 b=-0.52 fit on T8 series only a=40.0 b=-0.69T8 T10 T12 Figure 8. Low-cycle fatigue curves Faella et al. [37, 38] have reported comprehensive cyclic test results on normal-strength steel 235 (grade Fe430) T-stubs, using class 10.9 high-strength bolts with a pretension force equal to 0.80 236 17 times the bolt yield resistance. They found that the ﬁtted coe cient aranged from 86.1 to 136.3, 237 and branged from 0:54 to 0:71, depending on the geometrical properties (HEA160 or 238 HEA200 hot-rolled proﬁles) and also on the criterion used to deﬁne failure (50% degradation of, 239 the maximum strength attained during each semicycle, the sti ness of the unloading branch of 240 each semicycle, or the energy dissipated during each semicycle). Note that in this study the 241 complete fracture of the ﬂange or bolt was used to deﬁne the moment of failure. Therefore, the 242 criterion used by Faella et al. [37] is absolutely conservative compared to the one used by the 243 authors here. But it is interesting to notice that the ﬁtted coe cient bhere ( 0:52 for overall ﬁt, 244 or0:69 for T8 series only) are still very close to that range ( 0:54 to 0:71) obtained for bolted 245 normal-strength steel hot-rolled T-stubs. It seems that the steel grade does not a ect much on the 246 coecient b, neither does the structural detail including the geometrical properties and type of 247 proﬁle. On the contrary, the coe cient aobtained here (26.8 for overall ﬁt, or 40 for T8 series 248 only) is substantially lower than the above corresponding range (86.1 to 136.3). It does make 249 sense, as the coe cient acan be interpreted as the plastic deformation that can be achieved 250 before failure under monotonic loading and is absolutely lower for high-strength steel as a result 251 of its poorer material ductility than normal-strength steel. The welded-plate detail used in this 252 study, if compared with the hot-rolled proﬁle used in that previous study, contributed further to 253 this large di erence. 254 4.2 Hysteretic energy dissipation capacity 255 Table 4 shows that the total cumulative energy dissipation varies signiﬁcantly among di erent 256 cyclic loading amplitudes. Such a fact has already been recognized previously. In order to predict 257 the hysteretic energy dissipation capacity, Faella et al. [37], Piluso and Rizzano [39] derived a 258 method in their study on bolted normal-strength steel T-stubs. In their method, the hysteretic 259 energy dissipation and plastic deformation amplitude are normalized before subsequent 260 calibration. If the failure is controlled by ﬂange fracture as in Model 1, the plastic deformation 261 amplitude, p, under a constant-amplitude cyclic loading, could be normalized by the ultimate 262 18 plastic deformation that can be achieved under monotonic loading, p;th. Faella et al. [38] and 263 Piluso et al. [40, 41] proposed by theoretical derivation that 264 p;th=m2 tfC (4) where mandtfhave been illustrated in Section 2.1, Cis a coe cient determined based on the 265 stress–strain curve of the ﬂange material. Then the normalized plastic deformation amplitude is 266 ¯=p p;th=ptf 2Cm2(5) Meanwhile, the cumulative hysteretic energy dissipation, Ecc, under the constant-amplitude cyclic 267 loading, could be normalized by the energy dissipation achieved under monotonic loading until 268 failure, E0. That means, the normalized cumulative energy dissipation is 269 ¯E=Ecc E0(6) In this way, an exponential relationship between ¯Eand¯can be empirically determined as 270 ¯E= 1¯ 2(7) Substituting Eqs. (5) and (6) into Eq. (7) results in 271 Ecc E0= 1 tfp 2Cm2! 2 =¯ 1 tfp 2m2! 2 (8) where ¯ 1(or 1) and 2are positive empirical coe cients that should be ﬁtted by test results. 272 Based on the test results of constant-amplitude loading in this study, the ﬁt of Eq. (8) is shown 273 in Figure 9. The ﬁtted values of ¯ 1and 2are 0.036 and 1.403, respectively. The coe cient of 274 correlation is 0.89, indicating a good agreement. The ﬁtted Eq. (8) can be used in predicting the 275 19 cumulative hysteretic energy dissipation capacity of the dual-steel T-stubs. 276 0 0.01 0.02 0.03 0.04 tf/p/m2051015202530Ecc/E0 Ecc/E0=0.036(tf/p/2m2)-1.403T8 T10 T12 Figure 9. Normalized cumulative hysteretic energy dissipation–plastic deformation amplitude relationship The above results can be further compared to those obtained for normal-strength steel (grade 277 Fe430) T-stubs by Piluso and Rizzano [39]. In their study, for hot-rolled T-stubs, 1=2:081 278 (or¯ 1=0:6260:806 based on C=0:3710:457) and 2=1:212; for welded-plate T- 279 stubs, 1=0:485 (or ¯ 1=0:1570:167 based on C=0:3640:384) and 2=1:117. It is 280 clear that, the coe cient 2ﬁtted in this study (1.403) is slightly larger than the above results for 281 normal-strength steel T-stubs, indicating a slightly increased rate of deterioration in cumulative 282 energy dissipation capacity with the plastic deformation amplitude. In addition, the coe cient ¯ 1283 ﬁtted in this study (0.036) is signiﬁcantly lower than those for normal-strength steel T-stubs (even 284 lower than a range of 0 :1570:167 for comparison on the basis of welded-plate T-stubs). This 285 provides the evidence of lower energy dissipation capacity of dual-steel (or high-strength steel) 286 T-stubs compared to normal-strength steel counterparts. 287 5 Conclusions 288 Cyclic testing of dual-steel welded-plate (Q355 web-Q690 ﬂange) bolted T-stubs was 289 conducted to evaluate their strength, ductility and energy dissipation. The T-stub specimens with 290 20 three ﬂange thicknesses were designed to undergo Mode 1 collapse (i.e., only ﬂange yielding). A 291 special emphasis was placed on the calibration of low-cycle fatigue curves and cumulative 292 hysteretic energy dissipation capacity. Conclusions are as follows. 293 1) The plastic resistance formulae in Eurocode 3 Part 1-8 can be applied to the dual-steel (or high- 294 strength steel) T-stubs, and is conservative to the yield resistance calibrated from the tests. The 295 overstrength factor of the ultimate resistance is about 1.2. 296 2) The ductility of the dual-steel T-stubs ranges from 6 to 7. Both the ductility and the cumulative 297 plastic deformation capacity increase with a decrease in the ﬂange thickness. 298 3) The cumulative energy dissipation capacity is the maximum in case of an intermediate ﬂange 299 thickness, which corresponds to the ratio (see Eq. (2)) of around 0.3. 300 4) Low-cycle fatigue failure of the dual-steel T-stubs could be roughly predicted by 301 p=26:8N0:52 f(see Eq. (3)). More accurate equations on independent ﬂange thickness 302 deserve to be calibrated by further study. 303 5) Cumulative hysteretic energy dissipation capacity of the dual-steel T-stubs could be predicted 304 byEcc=E0=0:036 tfp=2m21:403(see Eq. (8)). 305 Acknowledgments 306 The authors would like to acknowledge the ﬁnancial supports for this work by the National 307 Natural Science Foundation of China (Grant Nos. 51638009, 51978279 and 52108145). 308