LOW-CYCLE FATIGUE BEHAVIOUR OF PULL-PUSH SPECIMENS WITH HEADED STUD SHEAR CONNECTORS

Transcription

1 LOW-CYCLE FATIGUE BEHAVIOUR OF PULL-PUSH SPECIMENS WITH HEADED STUD SHEAR CONNECTORS Silvano Erlicher, Oreste S. Bursi and Riccardo Zandonini Department of Mechanical and Structural Engineering, University of Trento, Italy. Abstract Two series of pull-push specimens with 16 mm and 22 mm diameter headed stud shear connectors were built and tested as part of a general investigation on seismic design of steel-concrete composite beams with full and partial shear connection. In order to assess the shear connector performances from a seismic and damage standpoint, pull-push specimens have been exposed to series of variable, random and constant reversed slips. Main results are commented upon and evaluated in terms of yielding and maximum shear strength capacity as well as ultimate slip ductility. A comparison between experimental and prediction strengths derived by relevant design code provisions provides an estimate of their accuracy. Finally, a low-cycle fatigue damage model is investigated to establish damage limit domains for headed studs. 1. Introduction The earthquake resistant design of steel-concrete composite structures is still hindered by inadequate design code provisions. As a matter of fact, the part of Eurocode 8 (EC8) dealing with steel-concrete composite systems still appears as an informative Annex owing to lack of data [1]. Hence, extensive experimental and numerical research into the seismic resistance of composite members and structures under simulated-earthquake conditions is under way [2]. On the North-American side, a major step taken in recent years was the development of the provisions for the seismic design of composite structures [3]. With regard to composite beams of special moment frames, these provisions require both proper welding of shear connectors and additional connectors beyond those required in AISC LRFD [4] for dissipative zones. Nonetheless, there are several situations in which the required composite action between the steel beam and the concrete deck is rather low [5] and, thereby, full shear connection is needless. Eurocode 4 (EC4) [6] and AISC specifications [4] permit partial shear connection where the interface slip between the steel beam and the concrete deck cannot be ignored. In these 1303

2 conditions, the connector ability to exhibit ductility and dissipate energy depends mainly on its capability to withstand low-cycle fatigue during the seismic event. Thereby, if members embodying composite dissipative zones need to be designed, a better understanding of the cyclic behaviour of shear connection is required. The analysis of the low-cycle fatigue behaviour of shear connectors requires the availability of data for connectors loaded cyclically to failure. The vast majority of available useful data, however, is for connectors loaded monotonically. As far as the experimental analysis of push-type specimens exposed to cyclic loading is concerned, few exceptions are the recent works of Astaneh et al. [7] and Aribert et al. [8]. The study presented in this paper extends the recent research work conducted on 16 mm diameter headed stud shear connectors by Bursi and Gramola [9] to the cyclic behaviour and analysis of 22 mm headed stud shear connectors. Thereby, experimental data relevant to pull-push specimens subjected to monotonic, variable and random reversed displacements are evaluated with regard to their seismic performance in terms of strength and slip ductility. Moreover, a comparison between experimental and predicted strengths based on EC4 [6] and AISC specifications [4] provides some design indications. Finally, an energy-based fatigue model is calibrated on experimental data to establish damage limit domains for headed stud connectors. As a result, low statistical correlation among the experimental data has been found. 2. Experimental investigation The investigation focused on the determination of the seismic performance of headed stud shear connectors. To comply with the connector ductility requirements suggested for buildings in the EC4 specifications [6], connectors with 16 and 22 mm diameter and with an overall length after welding not less than 4 times the shank diameter have been considered. Thereby, eighteen elemental push-type specimens divided into two series Table 1. Nomenclature and test procedures of specimens with 16 mm shear connectors (Series I) Table 2. Nomenclature and test procedures of specimens with 22 mm shear connectors (Series II) Specimen Test protocol NPM-01 Monotonic NPM-02 Monotonic NPC-01 ECCS NPC-02 ECCS NPC-03 ATC (10 e y ) NPC-04 ECCS type NPC-05 ATC (40 e y ) Specimen Test protocol RPM-01 Monotonic RPM-02 Monotonic RPC-01 ECCS RPC-02 ATC (3 e y ) RPC-03 ATC (6 e y ) RPC-04 ATC (9 e y ) RPC-05 ATC type RPC-06 ATC type RPC-07 ATC type RPC-08 Random RPC-09 Random 1304

3 were fabricated. The nomenclature that identifies the specimens is reported in Column 1 of Tables 1 and 2, whilst the relevant geometrical characteristics are depicted in Figs. 1 and 2, respectively. Both geometrical and mechanical characteristics of Series I specimens are similar to those of the companion steel-concrete composite beams exposed to cyclic and pseudodynamic loading [10]. In detail, shear studs are placed in two rows with large spacing as illustrated in Figs. 1 and 2, to allow stud shear loads within the concrete slabs to be redistributed. The reinforcement consists of a mesh of φ 12 whilst transverse rebars are designed against slab longitudinal splitting. TRW Nelson studs have a shank diameter of 16 mm and a mean height of 102 mm in Series I whilst Series II comprises Nelson studs with a shank diameter of 22 mm and a mean height of 126 mm. By using a TRW Nelson welding system a mean welded height of 4.5 mm has been obtained. The mechanical properties of concrete and shear studs are listed in Table 3. Specimens of all series were monotonically (push regime) and cyclically (pull-push regime) loaded in a quasi-static fashion, by means of a series of representative slip histories. Due to the random nature of seismic loading, several test protocols comprised between the extremes of constant-amplitude and random-amplitude slip reversals were applied to the specimens: i) the so-called Complete Testing Procedure proposed by the ECCS [11]; ii) the Cumulative Damage Testing Program suggested by the ATC [12]; iii) test procedures characterized by large slip reversals superimposed upon constant amplitude slips; iv) test protocols endowed with slip reversals of random amplitude. The first type of procedure is adopted to acquire data relevant to the maximum shear strength, the ultimate slip ductility, etc. Conversely, the second type of procedure provides the basis for developing fatigue-life relationships. The test program is described in Column 2 of the Tables 1 and 2, respectively. It comprises two classical monotonic tests to develop the backbone force-slip envelope for each specimen response. As a matter of fact, some seismic damage models use strength and deformation quantities derived from monotonic tests to normalize and/or formulate damage expressions. In addition, a slip elastic limit e y and the corresponding yield shear strength P y were determined as illustrated in Fig. 3. The ECCS test protocol [11], applied to the NPC-01 and RPC-01 specimens and depicted in Fig. 4, is characterized by sets of equi-amplitude slip (1k)e y, (k = 0,...,n). This sequence would provide a convenient benchmark against which to compare specimen performances subjected to variable amplitude testing. The ATC test protocol [12] with a set of equi-amplitude constant slips at 10e y is applied to the NPC-03 specimen and is illustrated in Fig. 5. This test protocol has been applied to the specimens NPC-05, RPC-02, RPC-03 and RPC-04 with equi-amplitude slip at 40e y, 3e y, 6e y and 9e y, respectively, and provides the basis for developing fatigue-life relationships. Table 3. Material properties of push-type specimens Series Displacement test procedure Concrete Shear stud f cm f ctm E cm f y f u (Mpa) (Mpa) (Mpa) (Mpa) (Mpa) I Mon. & cyclic II Mon. & cyclic

4 Figure 1: Geometrical characteristics of Series I specimens Figure 2: Geometrical characteristics of Series II specimens P (P max,e max ) (P y,e y ) (P p,e p ) K e,r K h (P u,e u ) e/e y ECCS, 1986 (P e,e e ) K e Figure 3: Bi- and trilinear fits of a shear force-slip envelope Envelope Trilinear approx. Bilinear approx. e CYCLE NUMBER Figure 4: ECCS test protocol with constant and variable cycles e/e y ATC (1992) CYCLE NUMBER Figure 5: ATC test protocol with constant amplitude cycles e/e y RANDOM CYCLE NUMBER Figure 6: Test protocol with random amplitude cycles 1306

5 Moreover, additional procedures were conceived to analyze the slip sequence effects on cumulative damage. In detail, the test protocols applied to the RPC-05, RPC-06 and RPC-07 specimens are characterized by large slip reversals reproducing seismic pulses superimposed upon constant amplitude slips. Finally, the last two protocols applied to the specimens RPC-08 and RPC-09 were tracked from pseudo-dynamic tests on composite substructures exposed to the N69W component of the 1952 Taft earthquake [10]. In detail, the procedure applied to the RPC-09 specimen, depicted in Fig. 6, traces over slips from composite substructures with full shear connection. As a matter of fact, an amplified slip peak level greater than 6e y brings the specimens of Series II to collapse. This type of sequence provides a benchmark against which to compare random amplitude testing. 3. Main results and code comparison For brevity, hereinafter only the most significant results are commented upon. As far as the Series I is concerned, the monotonic shear force-slip (P e) response of the NPM-02 specimen is depicted in Fig. 7. The observed inelastic behaviour is governed by stud yielding and concrete cracking. The specimen collapse was governed by local concrete crushing. With regard to the corresponding cyclic behaviour, the response of the NPC-02 specimen is plotted in the same figure. In this test, both stiffness and strength of stud connectors reduce at all stages owing to stud cyclic yielding and fatigue as well as to propagation and coalescence of micro-cracks in concrete. However, failure was governed by local concrete crushing. As far as Series II is concerned, the shear force-slip response relevant both to the RPM- 01 and the RPC-01 specimen are plotted in Fig. 8. The inelastic behaviour and failure are governed by stud shearing. With regard to the cyclic response, the RPC-01 specimen exhibits both stiffness and strength reduction owing to shear yielding and low-cycle fatigue in the studs. Reversed displacement cycles cause a limited reduction of the shear strength owing to the high concrete strength (see Column 3 of Table 3) whilst the ultimate slip reduction is evident. Due to the relatively high value of concrete strength collapse is governed by low-cycle fatigue of studs. Moreover, the pinching phenomena are evident, and the plateau corresponding to the minimum reloading force can be observed in the Figs. 7 and 8. The amount of the plateau may be related to the friction between concrete slab and steel flange. To extend our knowledge on stud connector seismic performances, they are compared from a cyclic standpoint. Thereby, a conventional elastic limit state characterized by the displacement e y and the corresponding force P y can be defined on the first part of each skeleton curve as schematically illustrated in Fig. 3. To determine these values the trilinear approximation of each curve, is determined on the basis of best-fitting and of the equivalence of the dissipated energy between the actual non-linear response and the idealized trilinear approximation up to (e max, P max ). Then, the linear elastic approximation with slope K e and the linear strain-hardening approximation with slope K h define the coordinates (e y, P y ). Imposing the condition P = P y = P u the ultimate slip capacity e u can be identified. Thereby, the stud seismic performances can be 1307

6 evaluated also by means of the ultimate slip ductility factor e u /e y. The Columns 4 and 5 of Table 4 allow the slip reduction exhibited by the specimens subjected to cyclic loading with respect to those exposed to monotonic loading to be quantified. The minimum ductility ratio (e u /e y ) NPC-02 /(e u /e y ) NPM-02 is about 55.4 per cent if ATC [12] tests at equi-constant amplitude and the ECCS [11] test protocol with unloading are disregarded. From the Columns 6 and 7 of the same table, the maximum shear strength reduction can be assessed. The strength ratio P max,npc-02 /P max,npm-02 reaches 71.8 per cent according to Column 7 of Table 4. At present, design codes do not predict the stud shear strength of connectors under cyclic loading and therefore, it is worthwhile to quantify their accuracy in such conditions. To verify the capabilities of headed stud strength provisions calibrated on monotonic loading, stud strength calculations according to EC4 [6] and AISC [4] are applied to the specimens under exam. These values have been evaluated with and without partial safety factors γ or reduction factors φ, respectively, using measured rather than nominal material properties. Predictions for individual connectors are indicated in Fig. 9 for Series I specimens. In the same figure, the experimental strength values P max are indicated too. It can be observed that codes predict correctly the failure mode, viz. concrete cracking and crushing. However, owing to reversed slip effects predicted strength values are non-conservative under cyclic loading. More specifically, test and predicted strength values draw the conclusion that the design resistance of headed stud shear connectors in dissipative zones can be obtained from the design resistance provided by EC4 [6] applying a concrete penalty factor equal to This value agrees with the reduction factor proposed in the draft of the Eurocode 8 [1] regarding specific rules for steel-concrete composite buildings [13]. Conversely, a reduction factor of 0.55 is suggested for the AISC specifications [4], to achieve the same safety level of EC4 [6]. As far as slip is concerned, the slip capacity of the specimens NPC-01 and NPC-02 subjected to the ECCS test protocol [11] has been examined. Slip values collected in Table 4 bring to the conclusion that the minimum cyclic slip capacity is at least half of the slip capacity, i.e. 6 mm, required from EC4 [6] for ductile connectors. Similar conclusions can be drawn for Series II specimens with regard to strength (see Fig. 10) and cyclic slip capacity. 4. Seismic damage assessment Several of the pull-push specimens subjected to cyclic loading failed owing to low-cycle fatigue, viz. a damage process which results from a limited number of excursion well into the inelastic range. Therefore, a damage assessment of test results was conducted to provide a new quantitative evaluation strategy to the demand versus capacity. More specifically, additional limit states associated with low-cycle fatigue, viz. damage control (Damage index D i << 1) and low-cycle fatigue failure (D i = 1) can be defined, and the damageability of components can be predicted by means of non-linear dynamic computational analyses. In view of a damage model validation, it is deemed to be necessary to define failure, viz. to evaluate the cycle number N f that entails collapse. 1308

7 REACTION FORCE (kn) SHEAR STRENGTH (kn) PUSH -60 NPM-02 PULL NPC SLIP (mm) Figure 7: Monotonic shear force vs. controlled slip and hysteresis loops of Series I specimens Cyclic Monotonic LRFD (φ = 1) LRFD (φ = 0.85) EC4 (γ υ = 1) EC4 (γ = 1.25) f ' c, f ck (MPa) Figure 9: Connector maximum strengths and code predictions of Series I specimens υ REACTION FORCE (kn) PULL PUSH -120 RPM-01 RPC SLIP (mm) Figure 8: Monotonic shear force vs. controlled slip and hysteresis loops of Series II specimens SHEAR STRENGTH (kn) LRFD (φ = 1) LRFD ( φ= 0.85) EC4 EC4 (γ = 1) (γ = 1.25) υ 100 Cyclic 90 Monotonic f ' c, f ck (MPa) Figure 10: Connector maximum strengths and code predictions of Series II specimens υ E h / P y e u,m 4.0 NPC NPC NPC-03 NPC NPC Monotonic Cyclic NPM Di = 1.0 NPM-01 R 2 = e u / e u,m Figure 11: Damage limit domain of Series I specimens E h / P y e u,m 2.5 Monotonic RPC-02 RPC-03 Cyclic 2.0 RPC-01 RPC-04 RPC-07 RPC RPC-09 RPM-01 RPC D i = 1.0 RPM-02 R 2 = e u / e u,m Figure 12: Damage limit domain of Series II specimens 1309

8 Table 4. Connector shear force-slip response parameters of Series I specimens Specimen K e e y e u /e y P y (kn/mm) (mm) (mm) (kn) (kn) NPM NPM NPC NPC NPC NPC NPC Due to the large uncertainty in the failure definition, different criteria have been adopted in this study. However, for the sake of brevity only two of them are discussed hereinafter. Firstly, Calado and Castiglioni [14] propose the use of the ratio η f / η 0 α with α = 0.5. This quantity is defined as the ratio η f between the absorbed energy at the last cycle before failure and the energy that might be absorbed in the same cycle if the component would exhibit an elastic-perfectly-plastic behaviour over the same ratio η 0, with reference to the first cycle in the inelastic range. Moreover, the criterion of Chai et al. [15] has been adopted. It relies on the design assumption that failure happens when the deteriorated resistance P approaches the plastic failure resistance P u = P y depicted in Fig. 3. All the above-mentioned criteria have been applied to the specimens under investigation. With regard to the response provided by the ECCS procedure [11], a cycle number N f of about 50 for Series I and of about 15 for Series II was estimated, respectively. Once failure is defined, it is appropriate to associate the final state of the specimen under cyclic loading to a unique point of an equivalent monotonic response. More specifically, it is deemed to be necessary the definition of a damage indicator, viz. a state variable that enables a one-to-one correspondence from any damaged state caused by cyclic loading to a unique point of a monotonic specimen response. In these conditions, the safety assessment is straightforward being unique the distance from failure. More specifically, a damage index D i is introduced, viz. a normalized damage indicator such that zero corresponds to the virgin state and one to the achievement of collapse, in agreement with the assumed failure criterion. Different choices relevant to damage indicators are available. Anew for brevity, only the damage model proposed by Chai et al. [15] and derived from the widely used model of Park and Ang [16] is discussed. In detail, this model takes into account the energy absorbed by the component during a monotonic loading process, labelled E hm, and only the surplus of cumulative energy (E h E hm ) is considered significant to damage, E h being the absorbed total energy. In these conditions, the damage index reads * em β ( Eh Ehm ) Di = (1) e P e um y e u um P max 1310

9 in which e M defines the maximum slip reached by the component so far; e um is the maximum slip under monotonic loading, i.e. a measure of the maximum deformation capacity and β * an empirical factor evaluated on experimental basis. The application of the damage model expressed by Eq. (1) with D i = 1 to Series I specimens entails the damage limit domain illustrated in Fig. 11 with a slope of 1.76, an intercept equal to 3.34, P y = kn, e um = 12.3 mm and a determination (correlation) coefficient R 2 = The application of the same model to Series II is illustrated in Fig. 12. In detail, a slope of 1.13, an intercept equal to 2.24, P y = kn, e um = 10.2 mm and a determination coefficient R 2 = 0.57 has been obtained. The slopes of the damage limit domains are rather different both for Series I and II whilst the coefficient R 2 is small in both cases. The limited values of R 2 show that a damage analysis is not easily applicable to steel-concrete shear connectors. Therefore, the definition of a damage model based on a simple linear combination of energy and of displacement, as in Eq. (1), should be improved. Moreover, the damage model should be strongly related to the evolution both of strength and of stiffness, in order to trace the shear connection response through its whole range. 5. Conclusions Test results relevant to two series of pull-push specimens embodying headed stud shear connectors have been presented in this paper. These results were derived from specimens subjected to series of monotonic, variable and constant equi-amplitude slips. Then, they were re-evaluated and compared in terms of global parameters such as yield shear strength, maximum strength as well as slip ductility factors. Some considerations about pinching phenomena were reported. Test results of Series I and Series II point out that connector slip ductility is enhanced if the cyclic behaviour is governed by concrete cracking and crushing. Moreover, a comparison between experimental and predicted shear strength values provided by relevant code provisions indicates that design specifications calibrated upon monotonic loading overestimate actual stud shear strength. Thereby, strength penalty factors are required whilst an assessment of maximum cyclic slip is possible. Furthermore, the damage index proposed by Chai et al. [15] has been applied to pull-push specimens, showing that its application to the composite specimens could be satisfactory only for design. Further analyses are currently underway to develop an improved damage model, related to suitable stiffness and strength degradation rules over the full range of the shear connector response. Acknowledgements This research project is sponsored by grants from the Italian Ministry of the University and Scientific and Technological Research (M.U.R.S.T.) for which the authors are grateful. However, opinions expressed in this paper are those of the writers, and do not necessarily reflect the views of the sponsoring agency. 1311

10 References 1. CEN, 'ENV , Eurocode 8 - Design provisions for earthquake resistance of structures - Part 1-3: Specific rules for various materials and elements', Plumier, A., 'European research and code developments on seismic design of composite steel concrete structures', Paper 1147 Twelve World Conf. Earth. Eng. A., American Institute of Steel Construction, 'Seismic provisions for structural steel buildings', AISC, Chicago, IL, American Institute for Steel Construction, 'Load and Resistance Factor Design - Specifications for Structural Steel Building', 1. AISC, Chicago, IL, Civjan, S.A., Engelhardt, M.D. and Gross, J.L., 'Experimental program and proposed design method for the retrofit of steel moment connections', Paper 257 in Twelve World Conf. on Earthquake Eng., Auckland, CEN, 'ENV , Eurocode 4 - Design of composite steel and concrete structures - Part 1-1: General rules and rules for buildings', Astaneh-Asl, A., McMullin, K.M., Fenves, G.L. and Fukuzava, E., 'Innovative semi-rigid steel frames for control of the seismic response of buildings', Report UCB/EERC-93/03, Aribert, J.M. and Lachal, A., 'Comportement de connecteurs acier-beton sous chargement cyclique repete en vue du dimensionnement parasismique des connexions', Proc. of 5 th National Colloquium AFPS, Cachan, October 1999, 19-21, Bursi, O.S. and Gramola, G., 'Behaviour of headed shear connectors under lowcycle high amplitude displacements', Materials and Structures, RILEM, 32, , Bursi, O. S., and Gramola, G., 'Behaviour of composite substructures with full and partial shear connection under quasi-static cyclic and pseudo-dynamic displacements', Materials and Structures, RILEM, 33, , ECCS, 'Recommended testing procedures for assessing the behaviour of structural steel elements under cyclic loads', No. 45, Technical Committee 13, Applied Technology Council, 'Guidelines for cyclic testing of components of steel structures', 24, ICONS Topic 4 Extended Group, A., 'Draft of a 6 to Eurocode 8, Part 1.3. Specific rules for steel concrete composite buildings', ICONS Project Report, University of Liege, Calado, L. and Castiglioni, C.A., 'Steel beam-to-column connections under low cycle fatigue: experimental and numerical research', 11th WCCE, Acapulco, Paper No. 1227, Chai, Y. H., Romstad, K. M., and Bird, S. M.,'Energy-based linear damage model for high-intensity seismic loading', J. Struct. Engrg., ASCE, 121(5), , Park, Y. J, and Ang, A. H.-S., 'Mechanistic seismic damage model for reinforced concrete' J. Struct. Engrg., ASCE, 111(4), ,