Seismic performance of steel MRFs with partially-restrained bolted beam-to-column connections through FE simulations

E. Brunesi1, R. Nascimbene2 and G.A. Rassati3

1ROSE Programme, UME School, IUSS Pavia, Institute for Advanced Study, Via Ferrata 1, 27100 Pavia, Italy, PH (+39)-0382-5169893; FAX (+39)-0382-529131; email: emanuele.brunesi@eucentre.it 2EUCENTRE, European Centre for Training and Research in Earthquake Engineering, Via Ferrata 1, 27100 Pavia, Italy, PH (+39)-0382-5169827; FAX (+39)-0382-529131; email: roberto.nascimbene@eucentre.it 3School of Advanced Structures, University of Cincinnati, 765 Baldwin Hall, Cincinnati, OH 45221-0071 USA, PH (513)-556-3696; FAX (513)-556-2599; email: Gian.Rassati@uc.edu ABSTRACT Even though partially-restrained bolted beam-to-column connection systems are not explicitly certified to be used for moment resistance in current building specification jurisdictions, they represent a promising solution in modern steel moment resisting frames (MRFs), showing their significant potential to be able to mitigate some of the major drawbacks inherently related to the geometry of welded connections. In order to quantify the influence of this attractive solution, applicable both to new construction and to the retrofitting of existing structures, on the global response of whole MRF buildings under seismic loads, a numerical procedure, based both on refined three-dimensional solid and one-dimensional fiber-based finite element (FE) models, has been developed and validated using past experimental results. This validated numerical approach has been used to assess the seismic performance of T-stub connection systems within entire MRFs, in comparison with the response of other top-and-seat angle joints; a series of conventional and adaptive pushover and incremental dynamic analyses, accounting for material and geometric nonlinearities, has been carried out to quantify behavioral changes as a consequence of geometric variations in the connection system. INTRODUCTION Field observations in the aftermath of 1994 Northridge and 1995 Kobe earthquakes had revealed the poor performance of traditional fully welded moment connections, whose geometry promotes large strain demand in critical areas such as those close to the weld access holes (Swanson and Leon, 2000). In addition, both economic reasons and performance-based design (Wijesundara et al., 2011) force the lateral resistance of modern MRFs to be concentrated in a limited number of connections (Nascimbene et al., 2011). Therefore, the need of large rotational ductility under

loading reversals, in combination with larger shear demands induced by deeper beams used to control interstorey drifts, have suggested the adoption of bolted connections as an alternative solution, feasible both for new and existing constructions. Through the years, both top-and-seat angle and T-stub connections have undergone extensive campaigns of experimental tests (Swanson and Leon, 2000; Girão Coelho et al., 2004; Maggi et al., 2005; Piluso and Rizzano, 2008) to assess their response under pseudo-static cyclic loads. FE simulation, in compliance with experimental validation, has revealed to be a promising technique for accurately predicting their cyclic behavior (Swanson et al., 2002; Citipitioglu et al., 2002; Brunesi et al., 2013a). The influence of some of the main design assumptions, such as bolt-plates gap, bolt prestress and friction coefficient, has been quantified in terms of global force-displacement curves and local strain demand in the connection components, as well as behavioral changes as consequence of geometric variations in the connection system. In light of this scenario, this paper shows a series of numerical investigations, carried out with the aim of determining the capabilities of such types of connection systems, when included in the lateral-force resisting system (LFRS) of current MRF buildings. In particular, a procedure, based both on detailed three-dimensional solid and one-dimensional fiber-based FE models, has been used and validated by past experimental results. Examples of full-scale T-stub connection systems, tested in past programs (Schrauben, 1999; Swanson and Leon, 2000), have been analyzed, both at local and global scale. Inelastic force-based fiber elements, combined with nonlinear links, have been employed to reproduce the experimental test protocols. In addition, refined solid models, rationally accounting for the influence of friction, pretension of bolts, relative slippage of faying surfaces, prying and clamping actions through a well-established general nonlinear contact scheme, have been created to ensure that all possible failure modes are considered within the simplified FE idealization proposed. NONLINEAR FE ANALYSES OF FULL-SCALE CONNECTION SYSTEMS In particular, the high-definition FE analyses presented herein focus on two full-scale T-stub connections, tested by Schrauben (1999), namely FS-09 and FS-10. Specimen FS-09(TC-01) consists of a W27x84 beam bolted to a W14x145 column by a 15”x5-1/4”x1/2” shear tab and T-stubs cut from a W33x169. The fasteners used to bolt the flanges of each T-stub to the column flange (tension bolts) are eight 7/8” diameter, 3-1/2” long A490 high-strength bolts with one washer. Twelve 7/8” diameter, 3” long A490 bolts with three washers are used to fasten each T-stub stem to the flange of the beam and five 7/8” diameter, 2-1/4” long A490 bolts with one washer are used to fasten the beam web to the shear tab. Specimen FS-10(TC-09) is similar to specimen FS-09(TC-01) except 1” diameter A490 high-strength bolts are used, in combination with two washers instead of one. In Figure 1, the connection geometry is sketched and bolt nomenclature, used in the up-coming discussion of the FE results, is introduced. A mesh of 10-node isoparametric, displacement-based solid elements is employed to model all the connection components and the contact conditions, as shown in Figure 1, are explicitly recognized in the framework of a

general nonlinear contact scheme, including the combined effects of slip and friction. Bolt-plates gap is represented, in a phenomenological sense, by the contact algorithm. Large displacement-large strain kinematics, with automatic switching between updated Lagrangian Hencky (ULH) and updated Lagrangian Jaumann (ULJ) formulations are used. The Von Mises yielding criterion with a combination of isotropic and kinematic strain hardening is assumed to reproduce the cyclic stress-strain relationship of the steel members, accounting for both translations and expansions/contractions of the yielding surface to predict the permanent deformations exhibited by plastic materials during the loading-unloading history.

Figure 1. Connection geometry and details of FE mesh and contact regions The series of numerical investigations makes use of a method for applying pretension in the bolts, allowing for frictional force transfer by clamping plates together with the bolts. Advantage is taken of orthotropic thermal expansion coefficients, allowing for thermal expansion/contraction only along the longitudinal axis of the bolt, while a second phase is adopted to monotonically and cyclically load the connection system, by applying a prescribed displacement. An implicit solution strategy, with an energy-normalized convergence criterion, whose limit is set to 10-3, is assumed to reproduce the experimental loading protocol, proposed in the SAC Project (Swanson and Leon, 2000). NX Nastran solver is adopted to play out the detailed FE approach proposed, using FEMAP as the pre- and post-processing software. Comparison between experimental and FE predictions is shown in Figure 2, in terms of both monotonic and cyclic actuator load-tip displacement capacity curves, while Figure 3 depicts the evolution of Von Mises stress in the connection components of specimen FS-09 during monotonic loading. Numerical simulations reveal an accurate agreement with experimental results in terms of failure mechanism, initial stiffness, displacement and rotation ductilities, shear and bending resistances. The response is observed to be governed by a pronounced slippage of the connection components at large drift levels. More in detail, both specimens behave almost elastically in the first three steps of the loading protocol, while initial slip between the T-stub stem and the beam flange occurs at roughly 1% drift. More manifest slip appears at 1.5% drift cycles, for actuator loads of about 180 kN; at approximately 2% drift, major slip leads the shear bolts into bearing, resulting into visible load and stiffness increments. Except for the observed slippage, the connections behavior is

almost linear. Initial yielding of both T-stubs and beam is caused by the application of 3% drift cycles. In particular, yielding in the beam is localized in the flanges extending at roughly 45° angles from the last two rows of bolts, referred as “d”. The 4% drift causes yielding to extend into the beam web beyond the shear bolts, with yield lines perpendicular to the beam flanges. Large local strains are induced in the T-stubs and beam flanges and the slight bending of the T-stub flange denotes a weak form of prying action. Failure occurs at approximately 4.5% drift, by a sudden fracture of the T-stub tension bolts, as confirmed by the Von Mises stress distributions observed in the bolts of the T-stub connections investigated (Figure 4). The ultimate actuator load is approximately 430 kN (97 ksi), thus implying a bending moment slightly lower than 2000 kNm (1475 kip-ft). Prior to failure, yielding has propagated further into the web and some slight local bucking of the top beam flange occurred near the end of the T-stub stem.

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Figure 2. Experimental vs. FE monotonic and cyclic capacity curves (FS-09)

Figure 3. Evolution of Von Mises stress under monotonic loading (FS-09)

Severe yielding of the beam flanges takes place, as well as the regularity of slip plateau, with load picking up following slip as the bolts begin to bear in the oversized holes. Finally, Figure 4 compares the numerically predicted Von Mises

stress distributions at ultimate conditions in the bolts of the two T-stubs analyzed. Both specimen FS-09 and FS-10 collapse by a tension bolt failure, after local buckling of the beam and the formation of a plastic hinge. The Von Mises stress profiles depict the behavior previously described in terms of resisting mechanisms provided by the connection system; stress concentrations, up to approximately 1100 MPa (160 ksi), are observed in the tension bolts of the top T-stub, namely “1a”. The bending moment developed in the beam is resisted by a pair of opposite forces induced in the bolt lines at the interface between T-stubs and beam flanges, referred as “3” and “4” respectively. Their fairly anti-symmetric distributions, with peaks lower than that observed in the tension bolts and opposite each other, identify this transfer mechanism. In addition, bolt “4d” is characterized by a peak larger than “4a”, “4b” and “4c” and uplifted in respect to them, thus revealing yielding in that zone of the beam flange. Yielding of the beam web, due to the shear force transfer in the shear bolts, is confirmed by looking at “5a”, whose distribution presents more evident damage throughout the entire length of the bolt, in comparison with “5b” and “5c”. Similar trends may be observed for specimen FS-10. Von Mises maximum stress is again predicted in “1a”; however, a peak lower than that obtained for FS-09 is observed; this is due to the larger diameter bolt used in this connection. A similar mechanism is evidenced, even though less damage is predicted in the shear bolts. By contrast, a more visible stress concentration is experienced in “2a”, in combination with the contribution of “4a” and “4d”.

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Figure 4. FS-09 vs. FS-10: Von Mises stress in the bolts, at ultimate conditions Since the advanced FE solid models developed are time-consuming, when applied to predict the cyclic response of these bolted connections, thus forcing this approach to be unfeasible if entire MRFs has to be assessed, the contribution of such connections can be easily incorporated into a fiber-based FE model by means of bi- or tri-linear links (Rassati et al., 2004), capable of representing the interaction among connection components into an equivalent manner. This simplified approach is additionally used to assess the two T-stub systems; although not nearly complex enough to provide a perfect match, particularly in terms of slip, this approach is proven to allow for effective predictions of the connection behavior at the global scale (Figure 2). A slight overestimation (5%) of the ultimate capacity is accountable at the design stage and, in addition, the design target of a MRF is not pushed to such a large drift level.

SEISMIC PERFORMANCE OF BOLTED CONNECTIONS WITHIN MRFs In light of this, the procedure proposed by Rassati et al. (2004) is adopted in order to assess the seismic performance of the T-stubs, previously studied at local scale, when included in the LFRS of modern MRF. A Comparison is provided with the response of two top-and-seat angle systems, numerically analyzed by Brunesi et al. (2013b). Herein, further details related to the geometry of the connections, named FS-01 and FS-02, and accuracy of their calibration can be found. Both 4- and 8-storey MRFs, with these 4 partially-restrained bolted beam-to-column connections, have been assessed both in static and dynamic fashion. Conventional pushover analysis, by applying uniform (U) and first-mode (F) force distribution, and first-mode displacement-based adaptive pushover (1-DAP) analysis have been tried in comparison with a series of incremental dynamic analyses (IDA), carried out by assuming the ATC63 far-field (ATC63-FF) set of recorded ground motions (FEMA P-695, 2009) as seismic input. The records of this suite originate from severe events of moment magnitude between 6.5 and 7.6 and closest distance to fault rupture larger than 10 km; only strike-slip and reverse sources are considered. All 44 records of this set (two records from 22 earthquakes), recorded on NEHRP site classes C (soft rock) and D (stiff soil) (FEMA 368, 2000), are used. W14x145 columns have a constant inter-storey height of 3.5 m and 6 m is assumed as beam span for all bays, while the out-of-plane span is 8 m. Dead and live loads are assumed to be 5 kN/m2 and 3 kN/m2, respectively. MRFs are identified in the following by the label of their connections, assumed to remain those experimentally tested and numerically assessed at local scale by detailed FE models. Therefore, W18x40 beams are used for FS01 and FS02, while W27x84 profiles are adopted as framing beams of FS-09 and FS-10. In accordance with Priestley and Grant (2005) tangent stiffness-proportional Rayleigh damping, calibrated on the natural periods, shown in Table 1, is employed to perform nonlinear dynamic simulations.

Table 1. Reference MRFs: natural periods from eigenvalue analysis 4-storey 8-storey

FS01 FS02 FS09 FS10 FS01 FS02 FS09 FS10

T1 [s] 1.167 1.176 0.938 0.941 2.461 2.483 1.895 1.902

According to experimental test observations (Schrauben, 1999), failure of the MRF is assumed to occur when rotation demand in the first connection exceeds 0.03 rad for FS-01 and FS-02, or 0.025 rad, for FS-09 and FS-10. Therefore, having established the ultimate capacity in a conservative way, each record is scaled by 16 uniform load factors (LFs), in order to represent the increasing seismic intensity. Results have been collected and shown in the following in terms of base shear-top displacement capacity curves, rotation demand and inter-storey drift profiles at ultimate conditions (i.e. LF = 100%), as well as their evolution at increasing LFs. To quantify differences in the MRFs response caused by variations in connection geometry, comparison is given by ratios of the parameters involved (i.e. FS-02 vs. FS-01 and FS-10 vs. FS-09).

Four-storey MRF models The majority of the IDA curves under-estimates the total base shear determined from nonlinear static conventional (NLS) and adaptive pushover analyses (1-DAP). In detail, NLS U over-predicts NLS F by roughly 20%; 1-DAP diverges from NLS F at large displacement levels that correspond to displacement ductility of about 3, for FS-01 and FS-02, thus resulting into a 10% lower capacity. By contrast, 1-DAP sudden deviates at yielding displacement, presenting a fairly constant discrepancy of approximately 5%, for both FS-09 and FS-10. As expected, MRFs with T-stubs reveal capacity almost 3 times larger than that observed for MRFs with top-and-seat angle connections, at 20% larger displacement. However, some records induce large dynamic amplification, thus resulting into base shear larger than that obtained by adaptive and, in some cases, even by conventional pushover analysis with uniform lateral force distribution, for all 4 MRFs. Increments of about 40% and 30% are obtained for FS-01 and FS-09, respectively (see Figure 5).

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Figure 5. Base shear-top displacement capacity curves (4-storey MRFs) If the average of the 44 records is considered, rotation demand peaks are localized in the beam-to-column connections of the first storey and, hence, the related maxima of the inter-storey drift profiles are obtained between first and second floor, as shown in Figure 6. This trend is observed for all the earthquakes for both FS-09 and FS-10,

while MRFs with clip angles present some cases where the rotation and inter-storey drift maxima are placed in the upper floors, indicating higher mode contributions. Quite a large scatter is detected at the top two levels, particularly for FS-02. Furthermore, the exceedance of the plastic rotation capacity induces drift peaks of about 4.3%, 4.0%, 6.1% and 5.8% for FS-01, FS-02, FS-09 and FS-10, respectively. At ultimate condition, FS-02 is observed to be stiffer than FS-01 at the base, while, as the height increases, this discrepancy tends to vanish; opposite trend results from comparison between FS-10 and FS-09.

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Figure 6. Inter-storey drift profiles at ultimate condition (4-storey MRFs) Eight-storey MRF models Figure 7 shows the capacity curves obtained from the IDA performed on the 8-storey MRFs, in comparison with pushover curves. Trends similar to those observed for the 4-storey MRFs emerge from the 3 NLS approaches, while the series of IDA reveal a much more pronounced dynamic amplification, undergone by all the 4 structures. In fact, 44% and 52% increments with respect to 1-DAP are respectively experienced by FS-01 and FS-02, while even doubled base shear is observed for FS-09 and FS-10, in the case of the most severe record. As shown in Figure 8, rotation peaks are obtained in the connections of the first floor for both T-stub and clip angle structures, even if the contraflexure point, present but not so prominent, in the average profile, approximately equals or exceeds the rotation

demand at the first storey, in the case of the worst event. This trend is more visible and frequent in the MRFs with top-and-seat angle connections, while both FS-09 and FS-10 are approximately characterized by two linear piecewise curves.

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Figure 7. Base shear-top displacement capacity curves (8-storey MRFs)

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Figure 8. Rotation demands at failure in FS-01 and FS-09 (8-storey MRFs) Therefore, these MRFs are observed to be robustly ductile, reaching levels of global displacement ductility of about 3 in the case of clip angles MRFs and approximately 2.5 for structures with T-stub connections. In particular, FS-02 is roughly 20% more ductile than FS-01, while FS-10 is only 10% less than FS-09. Large plastic rotation capacity results in a significant potential to be able to accommodate large inter-storey

drifts, as evidenced in Figure 9 that shows the drift profiles at ultimate conditions, for the 4 MRFs. Peaks of about 4.1%, 3.8%, 5.9% and 5.7% are respectively predicted for FS-01, FS-02, FS-09 and FS-10, at the second inter-storey.

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Figure 9. Inter-storey drift profiles at ultimate condition (8-storey MRFs) Even if FS-02 has larger rotational ductility than FS-01 in its connections, their lower force transfer capability implies an anticipated exceedance of their common ultimate rotation, thus allowing for accommodating lower drifts. As height increases, the ratio between the drifts, observed in FS-02 and FS-01, increases almost linearly from 0.94 to approximately a unit value. Similarly, FS-10 is capable of accommodating drifts lower than those experienced in the lower floors of FS-09, at ultimate condition, since the former is simply less ductile than the latter, for similar strength levels. Finally, in Figure 10, the evolving profiles of rotational demand for increasing seismic intensities are shown in FS-01 and FS-09, taken as reference of MRFs with top-and-seat angle and T-stub connections, in order to quantify these trends at increasing load levels; curves are built by the average of the rotation profiles in the connections. FS-02 demands larger rotations than FS-01, for all normalized load levels, particularly in the upper floors; in some cases, even a 60% increase is observed. Furthermore, for LFs equal to 25% and 37%, corresponding to the slippage activation and subsequent drop in stiffness connections of FS-02, the peak occurs at first and second floor. Almost an opposite trend emerges from the comparison between FS-10 and FS-09, as the connections of the former are observed

to work for larger rotations in their elastic range (i.e. LF of 25% and 37%). As LF increases, the rotational demand ratio becomes lower, due to a different activation of connections slippage. This reduction is evident for medium load levels (i.e. LF of 50%, 62% and 75%) in the lower floors, while the minimum uplifts from second to third storey at larger LFs (i.e. from 87% to 100%).

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Figure 10. Evolution of rotation demand for increasing LFs (8-storey MRFs) CONCLUSIONS This paper focuses on the cyclic response of T-stub connections, investigated at local scale by high-definition FE simulations, reproducing experimental observations and, then included in the LFRS of modern MRFs, to assess their seismic performance at increasing intensities, via fiber-based models, accounting for material and geometric nonlinearities. A comparison is provided with the behavior of other semi-rigid joints. If properly detailed, bolted partially-restrained connections have been demonstrated to be effective to ensure an optimum combination of strength, stiffness and ductility. In addition, the response of current MRFs is proven to be significantly dependent on the behavior of beam-to-column joints. Trends have been discussed in terms of capacity curves, rotation and inter-storey drift profiles, at increased excitation. Hence, global-structural variations as consequence of local changes in connection capabilities have been quantified following different geometric features of their detailing.

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