On the prediction of low-cycle fatigue in steel welded beam-to-column joints

Journal of Constructional Steel Research 117 (2016) 49–63

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Journal of Constructional Steel Research

On the prediction of low-cycle fatigue in steel welded beam-to-column joints Blaž Čermelj, Primož Može, Franc Sinur ⁎ University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, 1000 Ljubljana, Slovenia

a r t i c l e

i n f o

Article history: Received 17 July 2015 Received in revised form 15 September 2015 Accepted 25 September 2015 Available online xxxx Keywords: Low-cycle fatigue Cyclic test Welded stiffened joint Full strength connection Seismic design Crack initiation

a b s t r a c t This paper presents a phenomenological criterion for crack initiation based failure prediction of steel structural components exposed to low-cycle fatigue loading. The criterion was established on the basis of available effective damage concept and associated two-parameter criterion. First, experimental cyclic test results on rib stiffened and cover plate stiffened beam-to-column joints are presented, which were used subsequently to verify the numerical model employed for the development of the proposed crack initiation criterion. The two-parameter criterion in which total accumulated plastic strain and stress triaxiality h were adopted as mechanical parameters that control the LCF cracking was applied to define a new damage curve. Several validation examples are presented to demonstrate the capability and accuracy of the proposed methodology for low-cycle fatigue life prediction. The applicability aspect of the proposed cracking criterion is further presented in terms of systematically defined complementary numerical analysis on welded stiffened beam-to-column joints focused on exploring any potential adverse beam member type and size effects on the cyclic response of the full-strength joint configurations. To this aim a set of eight practically applicable I and H European beam profiles was considered for the joints. All the analysed stiffened joints subjected to cyclic loading simulations possessed sufficient degree of overstrength to allow for the development of the full beam plastic rotation capacity. However, from the subsequent analysis important difference in fatigue behaviour between RS and CP joints was found. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction Stiffened full-strength connection design is one of the possible solutions to improve beam-to-column connection performance under severe seismic loading [1]. Based on numerous research studies it presents substantial improvement in relation to poor response of unstiffened beam-to-column joints from the past damaging earthquakes till 1995, where premature and unexpected brittle fractures of welded beam-to-column connection details appeared in steel structures [2,3]. Stiffened connection solution reduces the possibility for the appearance of brittle failure conditions in welded connection at the column face by shifting inelastic action beyond the stiffened beam section. At the same time constructional details with welding defect at the stiffeners end present possible new critical position for low-cycle fatigue (LCF) crack initiation, which plays a crucial role in terms of safety assessment to prevent beam-to-column joint from premature brittle fracture induced failures. While it is expected that design criteria should assure the full strength connection to allow for the full development of the beam plastic rotation capacity, it may happen, due to material defects or even insufficient geometric details of welded connection, that ⁎ Corresponding author. E-mail addresses: [email protected] (P. Može), [email protected] (F. Sinur).

http://dx.doi.org/10.1016/j.jcsr.2015.09.017 0143-974X/© 2015 Elsevier Ltd. All rights reserved.

premature failure of a joint results from crack occurring around the stiffened connection detail, e.g. due to stress/strain raisers at the end of the stiffener. Fracture and failure modelling allows to maximise the safe operating life of structural components by applying the approaches of fracture or damage mechanics. There exist several models of fracture and damage mechanics, which can be included as a user-defined subroutines in general purpose finite-element (FE) method packages [4]. However, damage effects taken into account in the models by various softening terms make structural response nonlinear and non-smooth. Consequently, numerical methods may have difficulty converging to a solution, depending on the type of problems. As an alternative to damage mechanics, a tool to predict local failure behaviour of structures is also given by damage curves, which present a quantitative relation between equivalent plastic strain and stress triaxiality [5]. The study deals with the prediction of crack initiation based failure in steel components of welded stiffened beam-to-column joints subjected to low-cycle fatigue loading. The subsequent residual life part with crack propagation phase (fatigue crack growth) till the ultimate fracture of a structural component was not subject of the research. In particular, two types of stiffened joints are addressed: rib-stiffened (RS) and coverplate (CP) joints. The description of the performed experimental cyclic tests on sixteen welded RS and CP beam-to-column joints, along with concise report of the test results is given. The description of the FE

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model development with its validation is provided. On the basis of a highly consistent response found between the experiment and the numerical simulation, the development of the proposed damage curve for the prediction of crack initiation based LCF failure is presented, followed by a complementary numerical study on both studied welded stiffened connection configurations. The findings of the parametric analysis are demonstrated and the obtained predictions for LCF resistance of both connection types are discussed, demonstrating verification and practical usage of the proposed LCF evaluation criterion.

2. Reference large-scale experimental tests Cyclic tests on full strength welded stiffened beam-to-column joints were carried out to study their cyclic performance. Two different types of stiffened connections applied to hybrid-steel moment resisting frames were investigated: rib-stiffened (RS) and cover-plate (CP) connections [1]. The design objective of both strengthened beam-to-column connections, based on the capacity seismic design concept, is to transfer inelastic action away from the column face, thus avoiding the problem of poor ductile behaviour and potential fragility of the beamto-column welded region, Fig. 1. In total sixteen tests on large scale single-sided joint specimens were performed [1] to demonstrate that both stiffened connection configurations, with detailing and welding technology applied, perform adequately under cyclic loading. High strength steel (HSS) was used for columns as non-dissipative elastic members, while mild carbon steel (MCS) was used for the beams acting as dissipative members. Beside two different stiffened joint typologies and two different columnbeam material combinations, S460/S690 grade steel column and S355 grade steel beam, another parameter of the study was also quasi-static cyclic loading history: variable and two different constant amplitudes. For convenience, complete nomenclature of the test specimens in relation to the applied cyclic loadings is provided below, followed by a brief overview of the test results [1]. Each of the two stiffened joint configurations (RS and CP) was represented by two different joints, comprising beam IPE270 (RS1, CP1) and IPE240 (RS2, CP2), resulting in four different beam-to-column joint specimens designed for the tests. According to the standard tensile tests, the ratio between the measured yield stress and its nominal value (355 MPa) varied in the range 1.08 to 1.25 and 1.19 to 1.27 for all the beams and the stiffening plates, respectively, with the corresponding ratio between the measured ultimate tensile strength and yield stress for the beams from 1.16 to 1.29. The toughness of all the steel joint components was determined by standard Charpy V-notch test at a temperature of − 20 °C. The values of absorbed energy for steel material grade S355 taken from both flanges and webs of all the beam profiles as well as from all the stiffening plates ranged between 108 and 226 J, which is satisfactory.

For the first eight tests variable – stepwisely increasing – amplitude cyclic loading protocol according to ANSI/AISC 341-10 [6] was adopted: each of the four different joints (RS1, RS2, CP1 and CP2) was tested twice (one repetition), hereinafter designated with suffixes 1 and 2 to the corresponding name of joint specimen, i.e. RS1.1, RS2.1, CP1.1, CP2.1 and RS1.2, RS2.2, CP1.2, CP2.2, respectively. The study is focused on beam-to-column joint response under arbitrary cyclic loading history. To this end, in addition to the variable loading, two different inelastic constant displacement amplitude levels were considered, with total joint rotation θ = 0.019 and 0.033 rad, hereinafter referred to as small and large constant amplitudes, respectively. Both rotation values were chosen to capture two distinct responses of the beam in plastic hinge region: with and without the presence of local buckling for large and small amplitudes, respectively. This allowed damage phenomena due to lowcycle fatigue (LCF) to be properly evaluated. Both constant cyclic loadings were applied on each of the four different joint specimens, hereinafter designated with suffixes 3 and 4 to the joint name for small and large constant amplitudes (e.g. CP1.3, CP1.4), respectively. The experimental results evidenced good behaviour of the joints in terms of shifting inelastic action away from the face of the beam-to-column connection into the beam section without damage of stiffened connection and column, Fig. 1b. At the same time stiffened joints subjected to variable stepwisely increasing loading amplitude revealed stable hysteretic response capable of developing large plastic rotations without premature brittle failure, Fig. 2a. Fair low-cycle fatigue resistance was obtained for all the joints with completed number of cycles in inelastic range for variable stepwisely increasing amplitude between 13 and 17, for constant large amplitude between 29 and 62, and for constant small amplitude between 76 and 155, Figs. 2b and 3. Moment Mh determined at the centreline of the plastic hinge and normalised by the nominal value of the beam plastic moment Mpl,b nom is presented in all the diagrams. Further discussion of low-cycle fatigue response of the tested beam-to-column joint specimens, used to establish LCF failure criterion, is presented in Section 4. 3. Characteristics of the finite-element model 3.1. Geometric properties and finite-element mesh The complete finite-element (FE) model of a beam-to-column joint in Abaqus [7] represents a typical subassembly from a steel frame in which points of contra-flexure of the beams and columns are located near the mid-lengths, Fig. 4. 3D solid-element models were used to study realistic stress and strain distribution in the stiffened beam-tocolumn connections. As an agreement between the computational efficiency on one side and obtained accuracy on the other, the reduced integration elements C3D8R or at the most enhanced C3D8I elements (discretisation of the stiffened region including plastic hinge zone of the beam) were applied. In addition, mesh characterised by the largest

Fig. 1. a) Applied design objective of full-strength stiffened beam-to-column joint, b) typical deformed shape.

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Fig. 2. Response of CP1 and CP2 joints: a) hysteresis curves, b) normalised moment at the subsequent joint rotation amplitudes for variable loading.

element in-plane dimension around bf/20 was used in the regions of the beam flange where high stress and strain concentrations were expected. Meshes comprising at least 2 solid elements through the thickness of webs and 4 elements through the thickness of flanges of I and H profiles were used to obtain convergence and reasonable accuracy of results. To reduce the computational cost of FE models, the number of variables in all the beam-to-column joint finite-element models was reduced by using simple beam elements (a 2-node linear beam in space, element B31 from Abaqus element library) to model parts of the beam and the column that remain elastic throughout the entire analysis, Fig. 4. The typical model geometric details and the mesh refinement in the region of the RS and CP connections are presented in Fig. 5. The rib-stiffener and the cover-plate are connected with the beam/column flange by fillet welds only. A gap of 1 mm was modelled between the surface of the beam and the attached surface of the stiffener to imitate realistic conditions. The surface contact between the beam flange and the coverplate was ignored in the study to substantially improve the computational efficiency of the analysis.

3.2. Modelling of beam local imperfections The ultimate bending resistance corresponding to the complete development of the beam local buckling under monotonic loading as well as complete joint hysteretic response under cyclic loading was found highly dependent on the initial beam local imperfection applied in the FE model. The local geometric imperfection on fully laterally supported beam was based on the shape of elastic buckling modes [8], taken as proportion of the amplitude of the first mode of the model, loaded with the transverse concentrated load at the free end of the beam. In case imperfection was introduced on both beam flanges (cyclic loading), also mode with the same, but negative, eigenvalue was

considered. In order to use reasonable values for the resulting imperfection amplitudes, tolerances of out-of-square structural steel I and H sections from the related standard EN 10034 [9] were examined. Additional sensitivity analysis was performed on the developed joint FE model to optimise the mesh as well as to determine proper value of imperfection amplitude in order to produce proper representations of the beam local buckling, while maintaining reasonable computing economies. Based on the FE model calibration against published experimental beam monotonic [10] and beam-to-column joint cyclic [1] response, local beam imperfection amplitude in terms of total out-ofsquare deformation 0.008 bf was chosen to be included in all the subsequent models comprising I and H beam profiles of an arbitrary size. The calibrated value presents 40% of the tolerance on out-of-squareness according to EN 10034 for a cross-section with a flange width more than 110 mm.

3.3. Material model The ultimate flexural behaviour of the beam, i.e. complete development of the beam local buckling, is not influenced only by the beam cross section geometry and other loading conditions affecting stress distribution across the section depth, but largely depends also on the stress–strain characteristics of the beam material [10–15]. To account for the proper steel material behaviour in the beam plastic hinge zone, nonlinear material stress–strain definitions were considered in the simulation of monotonic and cyclic joint response. In fact, much attention was paid to the calibration of nonlinear isotropic/kinematic hardening cyclic constitutive model for cyclic plasticity of metals employed in Abaqus, which is based on the work by Lemaitre and Chaboche [16]. The yielding condition in the FE analysis followed the pressure-independent Mises yield criterion for combined isotropic/kinematic

Fig. 3. Response of CP1 and CP2 joints: a) small const. ampl. θ = 0.019 rad, b) large const. ampl. θ = 0.033 rad.

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Fig. 4. Static model and geometry of single-sided beam-to-column joint FE model.

hardening rule of the cyclic plasticity model, and can be expressed for the uniaxial loading case by Eq. (1).

f σ ij −α ij ¼ σ εp ;

ð1Þ

where σij is the stress tensor, and αij is the back stress tensor. The nonlinear kinematic hardening evolution law, integrated to get the equation for kth backstress evolution, is expressed by Eq. (2). αk ¼

Ck ð1−e−γk γk

εp

Þ þ α k;1  e−γk

εp

;

ð2Þ

where Ck and γk are material constants. The quality of cyclic strain curve description was found adequate in case of using three (max k = 3) evolution parts (α = α1 + α2 + α3), see Fig. 6. For detailed calibration of the kinematic hardening parameters (yield stress σy, C and γ) cyclic stress–strain curve was used, which had been established from the stabilised hysteresis loops with different strain ranges (cyclic strain amplitudes from ±0.25% to ±7%), as obtained from axial cyclic tests of the investigated S355 steel grade material published in literature [17,18]. By the applied kinematic hardening material FE-model, the material damage for LCF cracking can be assumed to be controlled by evolution of long-range internal stress expressed through the back stress [5,19], as presented in more detail in Section 4. The evolution of

the isotropic hardening component, defining the change of the size of the yield surface σ0 as a function of equivalent plastic strain εp, is given by: σ 0 ¼ σj0 þ Q∞ 1−e−bεp




ð3Þ

where σ|0 is the yield stress at zero equivalent plastic strain (defined as the 0.02% proof stress), Q∞ is the maximum change in the size of the yield surface and b is the rate at which the size of the yield surface changes as plastic strain increases. The common values of the applied cyclic plasticity FE model parameters used for all the subsequent FE simulations of the beam-to-column joint LCF response (with constant and variable stepwisely increasing loading amplitude) are presented in Fig. 6. The values of calibrated parameters are based on the values defined by fitting Eqs. (2) and (3) to the considered cyclic material tests data. 3.4. Performance of the FE model Before proceeding with complementary numerical analysis on stiffened beam-to-column joints comprising different beam member sizes, the accuracy of simulated cyclic joint response was checked against the experimental cyclic test results obtained in the framework of this research work as described in Section 2.

Fig. 5. Geometric details with the applied mesh of the RS and CP beam-to-column joint FE models.

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Fig. 6. Parameters of the nonlinear combined isotropic/kinematic hardening model used in Abaqus.

Simulated response of all the sixteen full-strength beam-to-column joints subjected to variable and constant amplitude cyclic loadings showed close agreement with the experimental results for both global and local joint response. The developed FE model, accounting for nonlinear material and geometric issues, was able to capture all the key features of local inelastic beam flexural response with satisfactory accuracy, Figs 7 and 8; e.g. the extent of plastic strain field in the plastic hinge zone and in the vicinity of the stiffened connection, beam local buckling shape, beam out of plane displacements as well as local strain response on the joint specimens measured with strain gauges. More precise quantitative estimation of the accuracy of the simulated response relative to experimental results can be obtained by comparison of hysteresis loop areas, which present direct estimation of the amount of structural dissipated energy, Fig. 8b. Values of the total accumulated hysteretic energy obtained from all cycles till estimated crack occurrence, see Section 4, were accounted with the following ratios obtained: for the four constant small rotation amplitude tests (θ = 0.019 rad) between 4.9 and 12.4%; for the four constant large rotation amplitude tests (θ = 0.033 rad) between 0.8 and 3.8%; and for the rest eight variable amplitude cyclic loading tests between 1.9 and 11.6%. In the engineering sense, a good match between numerical and experimental results was obtained for the applied cyclic loadings. While the applied numerical model consistently accounts for the beam local buckling in the plastic hinge zone, it does not allow for the material degradation due to the LCF effects. To overcome this limitation, phenomenological approach using stress/strain response indices was used to simulate the LCF behaviour of beam-to-column joints up to the cracking initiation phase.

dominant mechanism for ductile cracking is nucleation of micro-voids after large-scale plastic straining. In this case two-parameter critical condition for ductile crack initiation may be established from smallscale test specimens under single tension. Its applicability in case of local material response characterised by increasing cyclic loading stress/strain demand was confirmed also during this particular research study. However, the adopted approach was not able to give either accurate or reasonable solution for all observed critical locations, especially in case of specimens subjected to constant cyclic loading. To overcome the above limitation, unified approach for the evaluation of LCF induced cracking was proposed in this work, which allows for the identification of crack initiation due to the accumulated LCF damage effects under cyclic loading with arbitrary loading amplitude history. The approach was established on the basis of results from all the 16 constant and variable cyclic loading experimental tests on stiffened beam-to-column joints as presented in Section 2. The proposed concept was applied for the improved and consistent assessment of local ductility and LCF resistance of simulated joint response in complementary parametric numerical analysis presented later on in Section 5. Since no damage evolution law under LCF is accounted for in the applied cyclic material model in Abaqus, further softening behaviour of steel components after the predicted occurrence of cracking was not simulated. In fact, the identification of locations with the most severe plastic strain concentrations till the predicted onset of cracking gives important information on ductility and the start of failure mechanism in particular component of a joint under the applied cyclic loading. 4.1. Prediction of LCF cracking onset using effective damage concept

4. Evaluation of crack initiation based LCF failure in steel elements For the simulation of the LCF response of all the eight test specimens subjected to stepwisely increasing loading amplitude damage concept as proposed by Ohata and Toyoda [5] was applied. This advanced twoparameter criterion associated with effective damage concept is applicable to ductile cracking estimation of structural steel members if the

After establishing reliable FE-model for monotonic and cyclic loading, the next objective of the study was to compare each beam-to-column joint local response with the simulated stress/strain field from the FE-model. The prediction of ductile cracking initiation for all eight joints tested under increasing cyclic loading amplitude was performed based on the effective damage curve for the S355 J2 structural steel

Fig. 7. Experimental and simulated response for specimen CP1.2: a) deformed shape, see also Fig. 1, b) comparison of hysteretic response.

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Fig. 8. Experimental and simulated response for specimen CP1.2: a) distribution of Mc at rotation amplitudes, b) distribution of accumulated energy.

adopted from Bleck et al. and Feldmann et al. [4,20]. The evaluation of critical loading cycle was performed in conjunction with the material effective damage concept proposed by Ohata and Toyoda [5], which correlates the material damage for micro void nucleation to macro-scale mechanical parameters, as described below. For this purpose, the stress and strain fields in the specimens, as obtained by the FE analysis, were used to identify the mechanical conditions under which the crack initiation mechanism would operate. For each of the eight specimens (RS1.1, RS1.2, RS2.1, RS2.2, CP1.1, CP1.2, CP2.1 and CP2.2) the FE simulation was done for a complete number of inelastic cycles performed in the particular test. Cumulative history of effective plastic strain ðεpl Þeff for the critical location in the plastic hinge zone on the beam, i.e. the estimated crack initiation point, was related to the corresponding stress triaxiality h = σ m =σ (σm is mean stress and σ is von Mises equivalent stress). For each simulated case the location with the most critical (unfavourable) history of effective plastic strain accumulation with stress triaxiality was chosen. Actually, these locations corresponded to the ductile crack initiation areas observed in the tests, as presented afterwards in this section. The estimated parameters were adopted from integration point of finite-element from the critical region close to the top or bottom beam flange surface. Fig. 9 gives an example of the estimation of effective plastic strain ðεpl Þeff obtained from the analysed evolution of effective back stress α, and cumulative history of ðεpl Þeff as a function of stress triaxiality h in case of RS2.1 specimen. Fig. 10 presents the predicted location of the local failure for the same specimen RS2.1 in terms of PEEQ plotted over the deformed shape, at the instance of the ductile cracking criterion met, and compared with the experimental result. As can be observed, the simulation shows close agreement with the experimentally obtained location of failure in the unstiffened beam region somewhat remote from the tip of the rib-stiffener. Also in case of the remaining three RS specimens – RS1.1, RS2.1 and RS2.2 – the

simulation result was found consistent with the experimental response, with ductile cracking region located away from the end of the rib-stiffener in the most buckled region of the beam flange. Similarly, high level of consistency between experimental and simulated response was noticed in all four CP specimens — CP1.1, CP1.2, CP2.1 and CP2.2. Although some local concentrations are present close to the end of the cover plate at the beam flange edges - also observed from the tests, see Fig. 1b — the highest concentration of plastic strain field successfully shifted from the end of the cover-plate into the buckled plastic hinge region of the unstiffened beam section, Fig. 11. The critical cycles with the onset of ductile cracking in the most buckled region on the beam flange in the plastic hinge zone as observed from the experiments and those predicted by FE-simulations, applying the effective damage concept as proposed by Ohata and Toyoda [5], is presented in Table 1. The last uncompleted cycle from the experiment with the ultimate failure of specimen, characterised by the fracture of the beam flange followed by the loss of load resistance, is reported as well. As observed from Table 1, predictions for ductile cracking initiation based on the two-parameter critical condition are non-conservative for all the eight specimens subjected to variable cyclic loading. Compared to the cycle number with the first ductile cracking observed from experiments, the applied approach results in 1 to 2 cycles more in case of RS specimens, and 2 to 3 cycles more for CP specimens. However, in this case it is not the applied approach, but the type of the problem simulated that is responsible for the reported mismatch. As a result of locally softened response, due to the large plastic straining and consequently damage concentrations (ductile cracks) in the steel at inflexion points, flange buckle amplitudes during the tests grew faster compared to the simulated response. Although the shape of the locally deformed beam shows close agreement with the one from the experiment, no such prominent progress of the beam local buckling was obtained from the simulations, since no LCF damage is accounted for in the

Fig. 9. Evaluation of ductile crack initiation based on the advanced 2-parameter criterion: a) evolution of equivalent backstress and estimation of effective damage strain, b) cumulative history of ðεpl Þeff vs:σ m =σ .

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Fig. 10. Location of crack initiation for specimen RS2.1: a) experiment — deformation after the test, b) simulation — state with predicted onset of ductile cracking.

applied cyclic plasticity model, see Figs 1, 7 and 8. This is the reason for the non-conservative results from the simulation. Larger mismatch is observed in case of CP specimens, where the cover-plate provides restraint to the beam flange over its complete width, causing more pronounced beam local buckling effects behind the stiffened region.

4.2. Prediction of crack initiation based LCF failure — proposed damage curve As already explained, the main motivation for the development of new crack initiation criteria for steel components subjected to LCF loading is the limitation of already applied effective damage concept proposed by Ohata and Toyoda [5]. In case of beam-to-column joints subjected to variable stepwisely increasing cyclic loading amplitude, the effective damage approach provided reasonable results for the buckled plastic hinge region, where the localised continually increasing plastic strain demand is present, Table 1. However, for other potentially critical locations with not so prominent increase of plastic straining (e.g. the end of the stiffened connection) it failed to provide appropriate result. Even more, in case of all the four specimens subjected to constant small amplitude and the four specimens with constant large amplitude cycling, critical cycle with LCF cracking onset could not be determined by applying the effective damage approach. To this aim the development of a new crack initiation based LCF failure criterion for structural steel components subjected to low-cycle fatigue loading with arbitrary loading conditions is presented in this section. The two-parameter criterion in which equivalent (total accumulated) plastic strain εpl and stress triaxiality h were adopted as mechanical parameters that control the LCF cracking was applied to define new corresponding damage curve. However, it is not the intention of this work to develop a comprehensive criterion for material

failure mechanism based on observations of micro void formation, nucleation and their subsequent growth to final coalescence; i.e. crack initiation criterion was not defined as a specific instance in a cyclic loading at which a ductile crack of specific extent would be measured. The tough experimental clarification of a mechanism for cracking under LCF loading conditions is beyond the scope of this study. The onset of failure in the material was simply related to the observations of experimentally obtained strain history data, measured by uniaxial strain gauges oriented along the beam and placed in close vicinity of potentially critical locations on the specimen, where fracture growth on the beam flange took place during the experiments, Fig. 12 a). The measured strain-fatigue life data from the particular strain gauge were analysed and divided into a part till the onset of crack and the subsequent residual life part with crack propagation till the final fracture of a structural component. The cycle with the estimated crack initiation, referred to as a critical cycle, was defined as the last cycle conforming to the slope of the peak strain amplitudes characteristic for the stabilised strain response, see Fig. 12 b). The information on the critical cycle number with the onset of particular observed failure instance for the selected six specimens subjected to the constant amplitude cycling is gathered in Table 2. The reader may also refer to the illustrative graphic representation presented in Figs. 13 and 14 for the selected two joint specimens. It is to be noted that the effects of eventually changed base steel material properties in HAZ of welds and other possible welding effects (residual stresses) at the end of the stiffened connections had not been quantified before the joint testing. They may be considered as initial conditions in the proposed criterion, taken into account via the experimental strain-life data. The complete procedure for the definition of the derived damage curve as a criterion for the LCF crack initiation, based on the experimental joint test results, is presented in below.

Fig. 11. Location of crack initiation for specimen CP1.2: a) experiment (deformation after the test), b) simulation (state with prediction of ductile cracking onset).

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Table 1 Critical loading cycle for specimens tested with increasing cyclic loading amplitude: experiment vs. simulation prediction (effective damage concept by Ohata and Toyoda [5]). RS specimen RS1.1 RS1.2 RS2.1 RS2.2

Simulation Experiment Npredicted crack

Ncrack Nfailure

12 11 15 15

10 10 13 13

14 15 18 18

CP specimen

Simulation Experiment Npredicted crack

Ncrack Nfailure

CP1.1 CP1.2 CP2.1 CP2.2

14 13 16 15

11 11 13 13

16 16 18 17

For each of the 16 specimens the mechanical conditions under which the crack initiation mechanism would operate were defined for the stress and the strain field obtained by the FE-analyses. To determine particular critical point (εpl, h) on the damage curve, information on the critical loading cycle with the instance of crack initiation is needed. For this purpose, the test results were analysed separately for two distinct groups of specimens, depending on the type of LCF joint response. The first group consisted of the four beam-to-column joints subjected to small constant amplitude cyclic loading, RS1.3, RS2.3, CP1.3 and CP2.3, and the two joints subjected to large constant amplitude cycling, RS1.4 and RS2.4. In case of all the above six specimens the final failure occurred due to the fracture of the beam flange just behind the stiffened region near the fillet weld, Fig. 12a. In all the six tests taken into account the beam local buckling, if any, had limited extent. Information on the critical loading cycle defined from the experimentally obtained strainlife data in the vicinity of the crack propagation site, Fig. 12, for this group of specimens is presented in Table 2. In case of all the rest 10 specimens (eight joints subjected to cyclic loading with stepwisely increasing amplitude and two joints(CP1.4, CP2.4) subjected to cyclic loading with large constant amplitude) the LCF failure occurred due to the progress of the beam local buckling in the middle of the plastic hinge zone. Due to the extremely high plastic straining in this buckled region, all strain gauges soon became overloaded and it was practically impossible to measure the actual local strain values. Consequently, information on the critical loading cycle from experiment could not be obtained for this group of specimens. Therefore, results from Table 1 already defined by using effective damage concept according to Ohata and Toyoda [5], in conjunction with damage curve for S355 J2 steel from literature [4,20], were adopted. It is important to emphasise that the accuracy of mechanical conditions determined in the latter case remains unaffected by the non-conservative results presented in Table 1, as it still remains exclusively dependent upon parameters defined by the authors of the proposed effective damage procedure. It should be noted that high level of consistency in terms of both the failure mechanism and the critical location in the unstiffened beam region was found between the experimental and the simulated response for all the specimens, see Section 4.3. The estimated stress and strain parameters from the FE-analyses were adopted from

Table 2 Determined onset of failure instance for selected specimens subjected to constant amplitude cycling. Specimen Actual measured rotation amplitude

Total no. of cycles

θb/θpl,b RS1.3 RS2.3 CP1.3 CP2.3 RS1.4 RS2.4

1.73 1.30 1.64 1.29 3.21 2.56

76 138 126 155 29 32

Failure instance Onset of strength degradation

Estimated crack initiation

40 90 100 120 24 23

35 60 77 102 15 17

locations corresponding to the crack initiation areas observed on particular test specimen. The resulting points presenting the mechanical condition for the LCF crack initiation mechanism, obtained by following the described approach for both groups of specimens (taking into account 14 beam-tocolumn joint specimens in total), are presented in Fig. 15. Depicted curves for the first group of six specimens, RS1.3, RS2.3, CP1.3, CP2.3, RS1.4 and RS2.4, belong to the cyclic loading until the estimated onset of cracking defined from the experimental strain data, and include points with the maximum value of the stress triaxiality reached per cycle. For the remaining two specimens, CP1.4 and CP2.4, the corresponding critical points, to be included in the diagram in Fig. 15, were not defined, since the effective damage concept proposed by Ohata and Toyoda [5] failed to provide the critical cycle with crack initiation within the range of all the performed cycles in the tests. The two tests are used later as part of verification of the proposed LCF damage curve, as described hereinafter. As shown in Fig. 15, all of the obtained 14 critical points present reasonable and consistent result. The obtained critical local equivalent plastic strain required to initiate ductile cracking depends largely on the stress triaxiality. When the stress triaxiality is increased, critical equivalent plastic strain decreases. Following the observations of other authors from literature [4,5,20], the model of exponential decrease was used to define the mathematical relation between the two mechanical parameters selected to describe the LCF crack initiation criterion. All 14 data points obtained on the basis of the experimental tests and the FE analyses were best fit to an exponential function of the form a ⋅ Exp(−b ⋅ h), where h is the stress triaxiality. Parameters a and b were numerically defined to obtain the following equation: εpl ¼ 4:74  Expð−0:89  hÞ:

ð4Þ

At this stage it is necessary to note that the established LCF damage curve primarily applies to the range of parameter h for which the

Fig. 12. Specimen CP2.3: a) strain gauges placed in the vicinity of the beam flange final fracture, b) experimentally obtained strain-life diagram with the determination of estimated onset of crack growth.

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Fig. 13. Response of specimen RS1.3: a) distribution of maximum moment per cycle, b) distribution of complete joint stiffness per cycle.

experimental results are available, red solid line in Fig. 15. Accordingly, dashed red line is used outside the examined range of h. 4.3. Applicability of the proposed criterion As already mentioned, the validity and consistency of the proposed LCF failure criterion was first verified against CP1.4 and CP2.4 test results. Figs 16 and 17 show close agreement with experimental results in terms of the deformed shape and the location of the critical region on the buckled beam flange in terms of the accumulated plastic deformation. In case of both specimens, two critical regions on the beam flanges were taken into account for the estimation of the critical cycle: at the buckled flange in the centre of the plastic hinge region, and at the beam flange edge just behind the fillet weld at the end of the coverplate, see Figs 16b and 17b. In case of CP1.4, according to the proposed criterion, the onset of cracking due to the beam local buckling is present in the 19th cycle, whereas cracking at the flange edge at the end of the stiffened connection appears already in the 17th cycle. Although somewhat larger plastic strain concentrations appear at the end of the cover plate, the observed critical plastic region in the buckled zone is significantly larger, which is consistent with the experimental result, where final fracture occurred in the buckled beam flange region with the first ductile cracks observed in the 22nd cycle. Similarly, in case of CP2.4 specimen, the predicted onset of cracking in the most buckled region and at the flange edge just behind the fillet weld of the cover-plate, are both present in the 33rd cycle. Again, despite somewhat intensive plastic strain concentrations at the end of the stiffened region, critical plastic region in the buckled zone is significantly larger, Fig. 17. This is the same region where the final fracture in the test occurred, after the first ductile cracking in this region of the beam flange was observed in the 24th cycle. Simulated response in combination with the proposed cracking criterion proved to be fully consistent with observations from the experiment.

In addition, consistency of the proposed LCF crack initiation criterion was checked against the experimental response of all the eight joint specimens subjected to stepwisely increasing cyclic loading amplitude. In this case, the analysis is not about the most critical region in the buckled zone of the beam, which was already used for the derivation of the proposed cracking criterion. Rather than this, local region just behind the end of the stiffened region (fillet weld HAZ), where damage concentrations with minor cracking were also observed in the experiments, though not resulting in the final fracture, was taken under investigation. Evolution of the critical combined stress–strain damage index (εpl vs. h) in terms of points with the maximum value of stress triaxiality reached per cycle, for the eight joint specimens, as reported in Table 1, is depicted in Fig. 18. The damage evolution till the predicted cycle with the onset of cracking already defined for the buckled beam flange region of particular specimen is denoted with thicker curve (filled markers). The subsequent part of each curve (empty markers) belongs to the residual life of specimen, where cracks in the buckled flange of the plastic hinge region already propagated to the ultimate fracture. The actual demand on the residual part of the curves may in reality be considered somewhat reduced due to larger strength degradation present in the plastic hinge zone of the beam as a result of progressive material damage, which is not accounted for in the numerical model. As observed from the diagram, in case of all the eight beam-to-column joints, mechanical condition in the observed local region at the end of the stiffened beam section is very close to or even reaches (in case of RS joints) the proposed crack initiation criterion. Also, in this case all the FE results in combination with the proposed cracking criterion show close agreement with the experimental results. For this group of joints damage concentrations with moderate cracking were observed during the tests on the beam flanges at the end of the stiffened region in fillet weld HAZ: minor cracks at flange edges in case of CP specimens, whereas more prominent notch induced cracks at the end of the ribstiffener in case of all RS joints, Fig. 19.

Fig. 14. Response of specimen CP2.3: a) distribution of maximum moment per cycle, b) distribution of complete joint stiffness per cycle.

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Fig. 15. Proposed damage curve for LCF crack initiation. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

Fig. 18. Evolution of combined stress–strain damage index from the end of the stiffened region of the beam against the proposed LCF crack initiation criterion for complete loading history applied in tests.

5. Complementary numerical FE study on cyclic joint response

they become deeper and heavier. For this purpose, the developed FE model was applied to analyse additional joints comprising a set of different I and H European beam profiles.

Applicability of the proposed two-parameter criterion for LCF response estimation is further presented on complementary set of welded stiffened full-strength joints. In particular, the numerical study aims at exploring any potentially adverse beam member size effects on the cyclic response of RS and CP full-strength joints. It is a well known fact within the engineering community that extrapolation of joint behaviour prediction to connections of a substantially different size should be undertaken with care [21–23]. As shown by the experimental test results performed in the framework of this research work [1], the ability of beams to develop inelastic rotation may be somewhat diminished as

5.1. Complementary set of stiffened joints The basic parameter controlling the range and the application of the complementary numerical analysis was a beam member cross-section type and size. According to the basic seismic design concept of fullstrength welded stiffened beam-to-column moment-resisting connections, it is the ultimate behaviour of the steel beam that deeply influences the overall performance of the joint. In order to complement the

Fig. 16. Location of crack initiation for specimen CP1.4: a) experiment (24th cycle) and b) simulation (at the instance of LCF cracking criterion met in 19th cycle).

Fig. 17. Location of crack initiation for specimen CP2.4: a) experiment (45th cycle) and b) simulation (at the instance of LCF cracking criterion met in the 33rd cycle).

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Fig. 19. Damage concentrations in the beam flange at the end of the stiffened region after the test: a) RS1.1, b) CP2.2.

set of beams that was already experimentally tested (IPE240, IPE270), additional eight different hot rolled I and H beam profiles were selected to design sixteen beam-to-column RS and CP full-strength joints for the simulation of their response under cyclic loading, Fig. 20 and Table 3. All the sixteen stiffened beam-to-column joints were designed according to the detailing and design guidelines already used to construct the test specimens [1]. Strong column/weak beam requirement according to EN 1998-1 [24] was used. Single sided beam-to-column joints only were analysed, since the response of stiffened connection with the ultimate performance of the steel beam was put under investigation. All the eight beam cross-sections selected for the study meet the limits of the required cross-sectional Class 1 for dissipative members in bending according to EN 1998-1 [24] and EN 1993-1-1 [25]. At the same time, the set of profiles covers different local flange (in compression) and web (in bending) cross-sectional slenderness ratios. Research activities [10,11,13–15] early underlined that the ultimate behaviour of steel beams, i.e. rotation capacity and degree of developed overstrength, is governed by considerable number of parameters. Beside inherent steel material properties in the plastic hinge zone in the beam, the ductility and the degree of beam-to-column connection overstrength, needed to assure the full strength requirement, is directly related to the behavioural class of the beam section. Decreasing the width-to-thickness ratio of the beam cross-sectional plates, the plastic deformation of the beam increases, but at the same time increased beam resistance may lead to the exploitation of the connection overstrength. Systematic characterisation of the parameters influencing flexural ultimate beam response is provided in the text below in order to provide consistent comparison between the responses of all the joints. The determination of cantilever beam length for particular beam-tocolumn joint was governed by the shear force-to-beam plastic shear

resistance ratio being close to 0.5 in the supposed centreline of the plastic hinge on the beam (1/4 hb from the end of the stiffener for both RS and CP joints) [1,26]. The same material properties were used for all the joints, with the same material definition for particular group of joint components, i.e. for the beam, as dissipative member, and for the stiffening plates together with the column acting as non-dissipative components. Hybrid steel approach was applied with mild carbon steel grade S355 for the beam and the stiffening plates, whereas high strength steel grade S690 was used for the column. According to the applied design procedure for both stiffened connections, unfavourable material quality combination was chosen for dissipative (fy = ) and non-dissipative (fy = fnom ) joint members, Fig. 21. In 1.25 fnom y y order to provide realistic and representative material stress–strain curves for beam and connection plates, reference uniaxial stress–strain material curves from material tests were adopted. In order to provide fully consistent response evaluation of all the joints, the stiffened connections were designed with the stiffened cross-section check utilisation factor close to 0.90. Normalised values of rib-stiffener and cover-plate thicknesses according to the applied design procedure for complete range of IPE, HEA and HEB beam profiles are depicted in Fig. 22. The performance of the designed 16 full strength RS and CP beamto-column joints was first checked under monotonic loading. In all the cases complete joint plastic response was concentrated in plastic hinge zone beyond the stiffened region of the beam. All the columns remained in elastic state, with total column rotation (column elastic bending together with column panel zone deformation) not more than 0.007 rad. Particularly of interest is the plastic strain demand on stiffened connection components (reinforcing plates, welds) at the face of the column and at the end of the stiffener, which can be observed from Fig. 23. The plastic equivalent strain PEEQ is plotted over the

Fig. 20. I and H cross-sections used for the beams (actual relative geometric ratio preserved).

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Table 3 RS and CP joints used for the complementary numerical study. Member cross-section

I

H

Stiffened joint type

Beam

Column

IPE270 IPE360 IPE400 IPE500 HEA400 HEB240 HEB400 HEB800

HEB240 RS and CP HEB300 HEB340 HEB400 HEM340 HEM280 HEM450 HEM1000

Loading

Tot no. of simulations

Cyclic 16 (ANSI/AISC 341-10)

deformed mesh of a particular joint. According to the purpose of the applied design procedure, reinforcing plates of all the simulated stiffened joints remain essentially in elastic state, although some plastic strain concentrations can also be observed at the end of the rib-stiffener and at the stiffened region close to the column flange.

5.2. Prediction of LCF joint response To facilitate consistency in comparison between the responses of all the sixteen stiffened beam-to-column joints, the same loading protocol according to ANSI/AISC-341-10 [6] was used for the simulation of cyclic loading. The cyclic response in terms of the moment calculated to the plastic hinge centreline, and normalised with the nominal beam plastic moment Mh/Mnom pl,b , as a function of the total beam rotation θb is presented in Fig. 24 for the selected six stiffened joints. Response of each stiffened joint is presented for all the simulated cycles, which is different for each particular joint, Table 4. In case of all the stiffened full-strength beam-to-column joints, plastic hinge occurred in the unstiffened beam section beyond the end of the stiffened region. Accordingly, the critical site with crack initiation appeared in the beam flange at either the end of the stiffener or away from it in the most buckled region of the beam flange, depending on the configuration of the stiffened joint, as presented and discussed hereinafter. Further evaluation and comparison of the cyclic response of the joints in terms of low-cycle fatigue life prediction until crack initiation phase is presented and discussed below. Beside the proposed crack initiation based LCF failure criterion, see Fig. 15 and Eq. (4), hereinafter referred to as crit.a, effective damage concept for the prediction of ductile cracking onset proposed by Ohata and Toyoda [5] in conjunction with damage curve from Bleck et al. and Feldmann et al. [4,20], referred to as crit.b, was used. The results in terms of consecutive critical cycle number and location with identified LCF crack initiation for all the stiffened joints are gathered in Table 4.

Fig. 22. Normalised stiffening plate thicknesses for complete range of I and H beam profiles.

In relation to the estimation of the LCF crack initiation in the joints, presented in Table 4, both applied criteria provided almost the same results for RS and CP joints in case of all the IPE beams. At the same time, somewhat non-conservative result can be observed in case of the effective damage concept, crit.b, for the same group of joints. However, for all the other RS and CP joints, comprising beams HEA and HEB, crit. b did not provide consistent results at all, as effective cracking criterion was not even met for the applied number of cycles. On the other hand, the proposed criterion crit.a appears to provide fully consistent and logical results for all the 16 analysed RS and CP joints. Based on the above discussion, only results obtained on the basis of the proposed criterion crit.a are presented and discussed in detail below. In Table 4 the observed differences in the number of cycles to the LCF crack initiation between RS and CP joints comprising IPE beams are negligible and thus the performance of this group of joints appears to be fully comparable, see also Fig. 25. However, in case of all the RS joints comprising H beam profiles (HEA, HEB), the LCF crack initiation mechanism was triggered substantially earlier compared to all the CP joints, Table 4 and Fig. 25. The comparison of cyclic performance between selected RS and CP joint configurations with HEA400 beam in terms of equivalent plastic strain PEEQ plotted over the deformed shape for the critical step with the identified LCF crack occurrence, according to crit.a, is depicted in Fig. 26. From the comparison of the deformed shapes presented in Fig. 26 it is clear that the RS joint detail is critical in terms of the large plastic strain concentrations in much localised region on the beam flange at the end of the rib-stiffener. On the other hand, no such intense stress/ plastic strain concentrations were observed in case of CP joints: in the

Fig. 21. Steel material stress–strain curves applied in the complementary numerical analysis: a) dissipative and b) non-dissipative components, c) monotonic and kinematic cyclic hardening curves.

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Fig. 23. RS and CP joints with IPE400 beam: column a) instance of maximum flexural strength, column b) deformed shape corresponding to 20% fall of the maximum moment resistance. Deformation scale factor 1.0.

Fig. 24. Cyclic response of RS and CP joints: IPE400 (14 cycles), HEA400 and HEB 400 (16 cycles).

latter case the critical region is shifted away from the welded detail at the end of the cover-plate in the most buckled plastic hinge region of the beam flange. Based on the experimental test results, the latter situation is the preferred one, due to the larger LCF resistance of the parent

Table 4 Complete number of simulated cycles with LCF crack initiation onset identification (critical cycle). Beam

IPE270 IPE360 IPE400 IPE500 HEA400 HEB240 HEB400 HEB800

LCF crack initiation (critical cycle, Ncrack)

No. of simulated cycles RS 15 15 14 14 16 18 16 15

steel material in the unstiffened beam compared to the material in the weld HAZ at the end of the stiffener. The reason for quite early attained mechanical conditions under which the crack initiation mechanism would operate in case of RS HEA and HEB joints may be also due to the detail at the end of the ribstiffener considered in the FE models. Namely, the fillet weld was present in the FE model of all the RS joints comprising IPE beams, while for

RS CP

crit.

CP a

13(2), I 13(1), I 12(2), I 12(1), I 9(1), II 10(2), II 8(2), II 8(2), II

crit.

b

15(1), I 14(2), I 14(1), I 14(1), I Not met Not met Not met Not met

crit.a

crit.b

14(2), I 13(2), I 13(1), I 13(1), I 15(2), I 18(2), I 16(2), I 14(2), I

15(2), I 14(2), I 14(1), I 14(1), I Not met Not met Not met Not met

crit.a: Proposed crack initiation based LCF failure criterion. crit.b: Effective damage concept according to Ohata and Toyoda [5]. cycle No.(1/2): crack initiation observed in the first, (1), or the second half, (2), of the reported critical cycle. Critical location on the beam flange: away from the end of the stiffener, I, at the end of the stiffener, II.

Fig. 25. Number of cycles to LCF crack initiation according to the proposed criterion crit.a, see also Table 4.

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Fig. 26. Deformed shape of RS and CP joints with beam HEA400. Predicted instance of LCF crack initiation according to the proposed criteria crit.a. Deformation scale factor 1.0.

the case of all RS joints with HEA and HEB beams it was not included in order to simulate the actual geometry where butt weld is used to join the rib-plate to the beam and the column flange. In the latter case the sharper end of the stiffened region certainly led to somewhat increased stress/strain concentrations in the nearby region of the beam. The final comparison between all the experimental test results and the simulated joint response in this research work is gathered in Fig. 27. The low-cycle fatigue endurance till the first crack occurrence in the joints is presented in terms of standard S-N curve approach. Linear regression line was obtained by fitting the data obtained from cyclic tests and is presented as solid line. Scatter bands at ± two times the standard deviation are shown as dashed lines. The following conclusions can be drawn. Results form all the simulated CP joints and RS joints comprising IPE beams may be considered as very well predicted by the regression line obtained from the experimental cyclic tests, although somewhat non-conservative values are obtained with the proposed LCF failure criterion. Again, clearly evident drawback in case of RS joints with HEA and HEB beams can be observed. Unfavourable much localised stress/strain concentrations at the end of the rib-stiffener, Fig. 26, lead this type of connection to behave in less ductile manner. According to the above discussions, the CP joint was found superior to the RS joint. 6. Conclusions and outlook Advanced finite-element model has been developed in Abaqus to analyse low-cycle fatigue behaviour of beam-to-column joints under arbitrary cyclic loading conditions. The test results with additional experimental data from literature were used to verify the numerical model, which was employed for further complementary study on rib-stiffened (RS) and cover-plate (CP) connections subjected to monotonic and cyclic loading.

An important part of the study was dedicated to the development of a new crack initiation based LCF failure criterion for structural steel components subjected to low-cycle fatigue loading with arbitrary loading conditions. The two-parameter criterion in which total accumulated plastic strain εpl and stress triaxiality h were adopted as mechanical parameters that control the LCF cracking was applied to define a new damage curve. The criterion is based on the use of nonlinear isotropic/ kinematic hardening cyclic constitutive model to describe cyclic plasticity of metals. No user-defined subroutines in general purpose finite-element (FE) method packages are needed to account for damage effects. It was found highly consistent with the experimental test results and provides easy and fully applicable methodology for engineering problems, e.g. to support and validate detailing rules and design procedures for structural steel components and members. The primary objective of numerical study was to explore any potentially adverse beam member type and size effects on the cyclic response of the two full-strength joint configurations. To this aim, a set of eight practically applicable I and H European beam profiles were considered for the joints. The proposed methodology to account for low-cycle fatigue response in the complementary study served for consistent comparison of cyclic response evaluation of all the analysed joints in terms of damage evolution till the predicted cycle with the onset of cracking. All the stiffened joints subjected to cyclic loading simulations with stepwisely increasing loading amplitude according to the ANSI/AISC 341-10 possessed sufficient degree of overstrength to allow for the development of the full beam plastic rotation capacity. However, from the subsequent analysis important difference in fatigue behaviour between RS and CP joints was found. In case of CP joints, mechanical conditions under which the crack initiation mechanism would operate were always met after the overall joint flexural strength degradation, characterised by well-developed beam local buckling in the plastic

Fig. 27. Low-cycle fatigue assessment of the experimental and the simulated stiffened joint response.

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hinge zone. The response of all the RS joints comprising IPE beams was found fully comparable to the aforementioned fatigue response of the CP joints. On the other hand, in case of all the RS joints comprising H beam profiles (HEA, HEB), crack initiation mechanism was triggered substantially earlier compared to the corresponding CP joints and before the onset of the overall joint flexural strength degradation due to the local beam buckling. RS joint detail was found critical in terms of large plastic strain concentrations in much localised region on the beam flange at the end of the rib-stiffener. Consequently, CP joint configuration was found to behave superior to RS connection. Acknowledgements The first author sincerely thanks the late Professor Darko Beg for his guidance, professional and energetic support, and most of all for the encouragement during his PhD study. Funding for this research was provided by the Slovenian Research Agency and Research Fund for Coal and Steel within project HSS-SERF (RFSR-CT-2009-00024). References [1] B. Čermelj, D. Beg, Cyclic behaviour of welded stiffened beam-to-column joints — experimental tests, Steel Constr. 7 (2014) 221–229. [2] D.K. Miller, Lessons learned from the Northridge earthquake, Eng. Struct. 20 (1998) 249–260. [3] M. Nakashima, K. Inoue, M. Tada, Classification of damage to steel buildings observed in the 1995 Hyogoken-Nanbu earthquake, Eng. Struct. 20 (1998) 271–281. [4] W. Bleck, W. Dahl, A. Nonn, L. Amlung, M. Feldmann, D. Schafer, B. Eichler, Numerical and experimental analyses of damage behaviour of steel moment connection, Eng. Fract. Mech. 76 (2009) 1531–1547. [5] M. Ohata, M. Toyoda, Damage concept for evaluating ductile cracking of steel structure subjected to large-scale cyclic loading, Sci. Technol. Adv. Mater. 5 (2004) 241–249. [6] ANSI/AISC, Seismic provisions for structural steel buildings, American Institute of Steel Construction, Chicago, Illinois, 2010. [7] SIMULIA, Abaqus Online Documentation: Version 6.12-2, in, Dessault Systèmes, 2012. [8] CEN, Eurocode 3, Design of steel structures — Part 1–5, Plated structural elements, EN 1993-1-5, European Committe for Standardisation, Brussels, 2007.

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