Numerical Validation on Noval Replaceable Reduced Beam Section Connections for Moment- Resisting Frames


 After a severe seismic activation, the buildings designed based on seismic specifications are expected to have damages without any local and global collapse. The key parameters that influence re-occupancy of the damaged buildings are workmanship cost and time. In order to circumvent shortcomings of these crucial parameters, replaceable fuse members with high energy dissipation capacity have been developed up to date. Moment resisting frames (MRFs) are one of the most preferred lateral load resisting systems in terms of architectural versatility and high energy dissipation capacity. Even though many beam-to-column connection details have been investigated over the years, none of them has addressed assembly difficulties when replacing the damaged fuse members under the residual drift ratio occurred after an earthquake. Therefore, this study presents replaceable reduced beam sections with connection detail for MRFs under residual drift. The proposed detail includes end-plated mid-spliced reduced beam sections. Pursuant to this goal, the proposed detail has been investigated under cyclic loading protocol required by AISC 341-16 by using ABAQUS finite element program. Seismic response of the proposed connection detail was compared from PEEQ and Rupture Index standpoint. The obtained findings indicate that the proposed mid-spliced replaceable reduced beam section satisfies all requirements mandated by AISC 341-16.


Introduction
Lateral loads acting on the structures due to wind and earthquake are resisted by lateral load resisting systems. Moment resisting frames (MRFs) and concentrically braced frames (CBFs) are the most preferred systems developed up to date. As opposed to CBFs, MRFs composed of beams, columns and rigidly connected beam to column connections have high energy dissipation capacity thanks to plastic deformations which, in turn, result in plastic hinges on the ends of the beams of MRFs under seismic loads. Therefore, all structural members other than the ends of the beams of MRFs need to be designed to remain fully elastic. On the other hand, unexpected material hardening of the beams and lack of beam to column connections may lead to brittle failures. In order to avoid the undesired behavior of MRFs, reduced beam sections adjacent to beam-to-column connections are employed. Reduced beam section (RBS) concept was rst mentioned in the Plumier studies (Plumier, 1997). More than 150 buildings where MRFs were utilized as lateral load resisting systems encountered brittle failures at the beam to column connections in 1994 Northridge and 1995 Kobe earthquakes (Shen et al., 2011). Two strategies which are strengthening beam-to-column connections and weakening beam sections arose in order to promote poor seismic behavior of MRFs after these EQs. RBSs that diminish or eliminate plastic deformation of the beam-to-column connections by producing plastic hinge in the reduced beam section domain present the most e cient connection facility from a seismic response standpoint. RBS area is produced by cutting both top and column anges of the beam segment adjacent to beam to column connections. Tahamouli After a severe earthquake, the fuse members of the lateral load resisting systems are expected to be damaged but not fractured. Therefore, the buildings which have damaged structural members due to the seismic event need to be retro tted as soon as possible to reoccupy. In order to recover the damaged structure where MRFs are employed, replaceability of the yielded segment of the existing beam members may be su cient. However, torch cutting and site welding need to be applied to replace the damaged beam segment with the new ones. These operations bring about costly solutions, time-consuming and poor quality (Mahmoudi et al., 2019;Shen et al., 2011). It is crucial to develop new strategies to reduce the repair and retro tting costs as well as reoccupy damaged buildings as soon as possible (Piluso et al., 2014). In order to overcome these problems, replaceable fuse members have been developed over the years.
The concept of replaceable members has been used especially in MRFs and eccentrically braced frames (EBFs). For EBFs, Stratan and Dubina (Stratan and Dubina, 2004) proposed the rst replaceable links which can be easily replaced after an earthquake. Dubina (Nikoukalam and Dolatshahi, 2015) proposed replaceable link connections for MRFs. To evaluate the performance of the connections, a numerical investigation was carried out by using ABAQUS software under cyclic loading. The ndings showed that the proposed connections exhibited much more ductility than the conventional connections. Mahmoudi et al. (Mahmoudi et al., 2019) subsequently conducted an experimental program to validate and evaluate the seismic performance of the replaceable link connections proposed by Nikoukalama and Dolatshahi (Nikoukalam and Dolatshahi, 2015). This experimental study proved that the proposed connection can be an alternative connection for MRFs. Replaceable beam to column connection detail utilizing pin connections (Pongiglione et al., 2021), buckling-restrained steel plates and mechanic pin connections (Peng et al., 2020), perforated shear links (Mirghaderi et al., 2021)   After a seismic event, the damaged reduced beam sections need to be replaced as soon as possible to recover the damaged buildings to initial ductility and strength capacity. In most cases, however, uneconomical methods are followed because of long and heavy beams. In order to avoid the aforementioned disadvantage, the replaceable RBSs have also been recommended by Özkılıç (Ozkilic, 2020). In the proposed detail, as shown in Fig. 1a, RBS is connected to a column with end plate whereas it is connected to a beam with splice connection. Therefore, thanks to the gap formed between the beams in splice detail, the RBS which is expected to yield under the earthquake load can be separated from the main beam with no need for torch cutting and hydraulic piston. However, the proposed detail does not allow the replacement of the RBS under the residual drift. The disadvantage of the proposed connection detail due to residual drift is aimed to be eliminated with the novel connection detail developed in the scope of this study. The proposed detail provides end-plated connection to connect RBS to column and side-plated connection to connect RBS to the main beam The side plated connection detail was inspired by the detail used in the mid-splice replaceable link in EBF proposed by Özkılıç et al. (Fig. 1b) (Ozkilic, 2021).
Due to the side plated connection, the proposed RBS detail allows easy replaceability even under the certain amount of residual drift expected after an earthquake (Fig. 2). Theoretically, the bending moment at mid-point of the link where the side plated connection is employed is zero in EBFs. However, in the region where the side-plated connection proposed in this study, the bending moment is close to M pr , which is plastic moment capacity of the RBS. Therefore, response of the side-plated connection in MRFs is different than that in EBFs which may affect global performance of MRF where the proposed detail is utilized. In order to investigate seismic response of the replaceable RBS where side-plated connection is used, a numerical study was undertaken. In the proposed side-plated connection detail, slip critical and bearing typed bolted connections and welded connections were taken into account as prime variables. In order to facilitate easy replaceability, bolted connections were applied as slotted and site drilled. All specimens were subjected to loading protocol mandated by AISC 341-16 (Aisc, 2016). Numerical studies indicated the potential of the proposed replaceable RBS used in MRFs.

Replaceable Reduced Beam Section Concept
The proposed connection detail employed to connect the RBS to the main beam presents a replaceable RBS for MRFs. In this detail, in order to provide bolted connection, end plate is welded to one end of the RBS whereas the channel section is welded to the other end of the RBS. Channel sections can be selected from hot-rolled sections or they can be produced as a built-up section. While the replaceable RBS is connected to the column with end-plated connection, it is connected to the main beam with side-plated connection. The gap provided between the main beam and replaceable RBS facilitates easy removal of the damaged RBS after an earthquake. In addition, due to the site drilled, site welded and slotted connection types recommended in the side-plated joint detail, it is possible to install the new RBS easily even under residual drifts. Since residual drifts do not exist in the new construction, bolted connection with standard holes and alternatively slotted holes can be utilized for the side plated connections. While the bolted connection with standard holes can be designed as bearing type and slip critical type, the bolted connection with slotted holes has to be designed as slip critical type to eliminate relative slip between the RBS and the main beam. After a seismic event, site drilled or site welded connection types need to be used for easy replacement of the damaged RBS where standard holes are used in the sideplated connection. On the other hand, as the slot lengths are designed according to the amount of residual drifts of the structure where slotted holes are used in the side-plated connection, the same slotted connection design is used when the damaged RBS is replaced. It is recommended that the slots, which provide easy replacement, should be formed vertically on the side plates and horizontally in the channel sections. However, the bidirectional slot used in the connection causes to reduce the strength of the sideplated connection which in turn increases the number of bolts required. Therefore, since the vertical slots of the side plates are not needed in the design of the new building, it is recommended to use only horizontal slots in the channel sections to increase the strength of the connection. However, even if the side plates are not damaged at all after an earthquake, in order to easily replacement of the damaged RBS under residual drift, the side plates without vertical slots should be replaced with the side plates with vertical slots.
Two different methods can be followed for the channel sections, as shown in Fig. 3. In the rst option, the depth of the channel sections should be greater than the ange width of the main beam. Therefore, the bolts are easily installed in the main beams with narrow ange width. In this detail, an eccentricity which is indicated by "f" in Fig. 3b between the side plates and the beam anges occurs. Yielding may occur in the web of the channel sections due to signi cant bending moment and shear forces resulted from this eccentricity. In order to circumvent this undesired yielding which in turn pinching behavior of the proposed connection, the stiffeners that connect the anges of the channel sections are proposed to be used (Fig.  3b). In the second second option, as shown in Fig. 3c, the anges of the channel sections are welded directly to the anges of the main beam and the replaceable RBS. Therefore, the eccentricity and the signi cant amount of the bending moment caused by this eccentricity in the rst option are eliminated. However, this option can only be preferred in the beam sections with wide anges for easy installation of the bolts used in the side-plated connection.
The limit values of the parameters of "a", "b", "c" in the proposed replaceable RBS are similar to the parameters given for RBS de ned in AISC 358-16 (Ansi) (Eqn. (1), (2), and (3). Moreover, it is recommended the parameter of "e", indicated in Fig. 3, to be at least 10 mm longer than the ange of the channel section in order to keep the RBS away from heat affected zone occurred during to welding process.

Side-plated Connection Design
The design of the side-plated connection employed to connect the replaceable RBS to the main beam is based on the probable maximum moment capacity of the RBS computed by using Equation (4). Therefore, unlike the similar connection type used in the mid-spliced end-plated replaceable link concept (Ozkilic, 2021), the connection aforementioned is subjected to a signi cant amount of bending moment.
The probable maximum moment at the center of the RBS M pr is calculated as follows: M pr = C pr R y F y Z RBS (4) Where, C pr is a coe cient and equal to (F y +F u )/2F y ≤1.2, R y is the ratio of expected yield stress to speci ed minimum yield stress, F y is the yield stress and Z RBS is the plastic section modulus at the center of the reduced beam section and calculated as follows: Where, Z x is the plastic section modulus about x-axis for full beam cross section The bending moment, M s acting on the connection is computed by using the geometrical relationship of the moment diagram depicted in Fig. 4.
The side-plated connection is also subjected to the shear force obtained by the required shear force at the center of the RBS which is calculated by Equation (6).
where, w is uniform beam gravity load that is calculated by considering the load combination of 1.2D+0.5L+0.2S.
In summary, the required bending moment M s and the required shear force V s shown in the free body diagram of the proposed connection region (Fig. 5) are calculated by using Equation (7) and (8)

Numerical Study
The use of nite element programs has been increased with the development of computer technology. The parametric numerical analyses were conducted using the nite element tool, ABAQUS. Geometric and material nonlinearities were taken into account. Different numerical models were generated to prove the concept of the proposed connection.

Finite Element Modeling Details
All members were modeled utilizing C3D8R elements, eight-node brick elements with reduced integration.
Four layers of elements were applied for all members in order to accurately simulate buckling and bending behavior (Ozkilic, 2020). Finer mesh size was selected for the proposed connection while coarser mesh size was applied for the rest of the beam. The mesh con guration is shown in Fig. 7.
The column was modeled explicitly. A region of the column ange where the end-plated bolted to the column was implanted. All degrees of freedom were restrained at lower surface of the column face. The interactions between the side plate and bolts, channel section and side plate, channel section and bolts, end-plate and bolts were simulated by de ning surface-to-surface interaction. Multi-point constraint (MPC) was de ned to a reference point located at center of the beam end. The loading was applied through this point. Cyclic loading based on the loading protocol mandated by AISC exposed to the all beams. A lateral bracing was applied to the anges of beams where 250 mm away from the connection. Tangential behavior with the coe cient of friction (µ) of 0.3 was considered. Welding was not implanted explicitly; instead, tie constrain was utilized to connect the welded members. The pretension force was applied utilizing "Bolt Load" option in ABAQUS.
Nonlinear isotropic and kinematic hardening material model was introduced based on the studies of Elkady and Lignos (Elkady and Lignos, 2015) and Özkılıç (Ozkilic, 2020). Nonlinear isotropic and kinematic hardening parameters were de ned using Eqns. (9-10). α = C F y (σ − α)ε pl − γαε pl (9) σ = F y + Q ∞ (1 − e − bε pl ) (10) where α is the backstress, C is the initial kinematic hardening modulus, F y is yield stress of plate, σ is the equivalent yield stress at zero plastic strain, ε pl is cumulative plastic strain, γ is the rate at which C decreases with cumulative plastic strain ε pl , 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 deformation develops.
where PEEQ is the plastic equivalent strain and calculated as ratio of effective plastic strain to yield strain. PEEQ measures local plastic strain demand and higher value of PEEQ indicates potential damage and vulnerability. p and q are hydrostatic pressure and von Mises stress, respectively. The calculation of PEEQ, p and q are given in Eqs. (12)(13)(14).  (14) where p ij stand for the plastic strain in direction i and j, σ ij is Cauchy stress and S ij is deviatoric stress.

Veri cation
In order to verify the assumptions in the numerical section, an experiment on reduced beam section conducted by Özkılıç (Ozkilic, 2020) was simulated. The specimen was HEA240 section with a length of 1650 mm. The specimen had a of 152 mm, b of 166 mm, c of 45 mm and R of 94 mm. The specimen was laterally supported and connected to the column with the use of a bolted end-plated connection. Cyclic loading protocol mandated by AISC 341 exposed to the specimen. The specimen successfully completed 0.06 rad rotation and failed at 0.07 rad rotation due to excessive buckling of anges. The hysteresis behavior of the experimental and numerical results are compared in Fig. 8. It is seen that the numerical model captured strength degradation due to buckling of the anges. Moreover, the load difference between numerical results and experimental ndings is less than 3%. Fig. 9 demonstrates the failure modes observed in the numerical model and experimented specimen. The numerical model successfully simulated the buckling behavior of the anges.

Validation of Proposed Connection Concept
The numerical models were exposed to cyclic loading according to the AISC 341. Six cycles were repeated at 0.00375 rad, 0.005 rad, and 0.0075 rad, then four cycles were repeated at 0.01rad, later two cycles were repeated at 0.015 rad and 0.02 rad. Following cycles were repeated two times with increments of 0.01 rad. A beam should complete 0.04 rad and sustain a moment at the column face above 0.8 times the moment capacity of the beam in order to satisfy AISC 341 criteria.
( ) √ √ For this section, section of HEA240 was utilized. Reduced section had a of 120 mm, b of 150 mm and c of 60 mm. Lateral support was utilized after reduced section. Initially, reference beam without any proposed connection was analyzed. Here, the reference beam was utilized with and without end-plate connection and hysteresis behavior of them were compared in Fig. 10. On the other hand, Fig. 11 illustrates PEEQ and RI distributions of the reference beam. It is seen that these beams exhibited similar seismic behavior. These beams completed 0.08 rad rotation and failed at 0.09 rad rotation since the moment reduced 0.08 moment capacity.
In the scope of this study, bearing and slip-critical typed connections were utilized for the numerical study. For bearing typed connections, straight and staggered bolted connections were adopted for mid-spliced connections. Standard sized holes and vertical and/or horizontal slotted holes were investigated for slipcritical connections. Moreover, the model with slip-critical connection with residual drifts was studied as well. Hysteresis behaviors, PEEQ and RI distributions are compared in the following sections.

Straight Bolt Con guration
Five different numerical models were investigated for the bearing typed connections with straight bolted connection, in which details are given in Fig. 12. Model A represents mid-spliced connection without stiffener. Stiffeners were included in Model B. On the other hand, channels were directly welded to the anges of the beam for Model C. For Models D and E, the stiffeners were welded above the channel. Moreover, distance of "e" was kept as 30 mm for Model E in order to reduce the weight of the replaceable part. Fig. 13 compares the hysteresis behavior of these models. The results showed that Model A, which does not have stiffeners, exhibited poor seismic performance when compared to the others. The reason for the inadequate performance can be explained with RI and PEEQ distributions which are shown in Fig.  16. Unlike Models B and C, Model A produced higher RI and PEEQ values at the connection of beam-tochannel. The channels were yielded followed by buckling due to the moment transferred by the main beam and this led to the transition of the damage from RBS to channel web. This problem was mitigated by two solutions. In the rst approach which represents Model B, stiffeners were employed by making use of welding between channel anges and web in order to prevent web buckling of the channels. In the second one referring Model C, the channel sections were welded directly to the beam. These two alternative connection details exhibited similar behavior. However, lower RI values were observed at the connection of beam-to-channel for Model B, which in turn caused a reduction in RI distributions at RBS compared to Model C. Buckling of RBS was detected at Model C which led to strength degradation at the last cycles. The effect of the stiffener location on the seismic response of the RBS were examined in Model D. In this Model, the stiffeners were placed above the channel in order to provide an easy erection. However, shifting the stiffeners away from the beam anges caused the shifting of the damage from RBS to the channel section which led to a reduction in the capacity. Model D and Model E are identical except that the length of the RBS in Model E was reduced in order to reduce the weight of the replaceable RBS. Since the proposed connection detail in Model E was subjected to more bending moment compared to the detail in other Model D, more poor seismic performance were obtained which indicated as the required bending moment increases, the seismic performance reduces.

Staggered Bolt Con guration
In order to decrease the height of the proposed connection detail, a staggered bolt con guration may be employed. Four different numerical models were investigated for bearing typed connections with the staggered bolted connection. Model A represents mid-spliced connection without stiffener whereas Model B includes stiffeners between anges and web of channels. On the other hand, channels were welded to the beam for Model C. For these three models, the height of the proposed connection is considered higher than the beam depth. In other words, one row bolts were included outer of the beam height due to increase the moment capacity of the connection. Model D is identical to Model C except that the bolts were kept within the beam height in order to come up with compact connection detail. The details of these models are depicted in Fig. 15. Figure 16 compares the hysteresis behavior of models having bearing typed connections with staggered bolted con guration. RI and PEEQ distributions are illustrated in Fig. 17. Although RBS members in Model B and C were buckled after 0.06 rad rotation, they exhibited excellent seismic performance by completing 0.09 rad rotation, which is much greater than the minimum rotation of 0.04 rad de ned in AISC 341, without any strength degradation. These models dissipated signi cantly higher energy than that of Models A and D. Due to the absence of the stiffeners in Model A, buckling of the channel was observed, which led to inadequate performance compared to Models B and C. The highest RI and PEEQ values were detected at the beam-channel connection. Adding stiffener or welding channel to the beam circumvent this problem. On the other hand, Model D performed a pinched behavior. Due to insu cient moment capacity, spliced connection detail exhibited in-plane rotation during the loading, which caused signi cant stiffness degradation.

Response of the Slip-Critical Typed Connections
For slip-critical typed connection, both standard-sized holes and slotted holes were investigated. Forty M24 bolts were utilized for mid-spliced connection. The details of the slip-critical typed connection detail with standard-sized holes are displayed in Fig. 18. Three different numerical models were studied. No stiffener was utilized in Model A while stiffeners were introduced to Model B. On the other hand, anges of the channel section were directly welded to the beam in Model C.
Hysteresis behaviors of the numerical models are compared in Fig. 19 while PEEQ and RI distributions are shown in Fig. 20. Although Models B and C performed satisfactory seismic behavior, Model A showed poor performance due to buckling of the channel. A slight strength degradation due to buckling was observed at Models B and C but at the last cycle Model C exhibited signi cant strength degradation. No PEEQ and RI values were observed at the connection of channel-to-beam for Models B and C.
Three models were created to investigate the behavior of slip-critical with slotted holes connections providing easy replacement of damage RBS under residual drift. Models A and B represent the mid-spliced connection with only vertical slots at side plates. Unlike Model A, for Model B, 0.5% residual drift was applied for the same beam at Model A. On the other hand, horizontal slots were included in channels for Model C. For these models, forty M27 bolts were utilized. The details of the models are depicted in Fig.   21.
Hysteresis behaviors of the numerical models with slotted holes are compared in Fig. 22 while PEEQ and RI distributions are shown in Fig. 23. All three models exhibited almost similar seismic behavior. After 0.06 rad rotation, strength degradation due to buckling of the reduced section was observed for all three models. All models successfully completed 0.09 rad rotation.

Discussion Of The Analysis Results
The energy dissipation capacities and moment capacities of the proposed numerical models were normalized by those of the reference beam without end-plate connection. Fig. 24 demonstrates the normalized energy dissipation and moment capacities. Based on the obtained ndings, stiffener placed near the anges of the beam contributes to increasing the energy dissipation and moment capacities of the RBS with the proposed detail. The absence of stiffener resulted in stress concentration at the beam to channel connections which in turn causes local buckling of webs of channel sections. As an alternative to stiffeners, anges of channel sections may be directly welded anges of beam members. This approach also decreases the weight of the replaceable part of the proposed connection detail. Even though slip-critical typed connection increases the cost of the proposed connection detail, the RBS with the slip-critical typed connection has a higher energy dissipation capacity than the RBSs with bearing typed connection. Vertical and horizontal slots may be utilized for easy replacement of the damage RBSs under residual drift.

Conclusions
In this study, a connection detail in order to provide easy replacement of damaged RBS under residual drift taken place after an earthquake was proposed. The potential of the proposed connection detail was validated by performing a series of numerical analyses. Usage and location of the stiffener, type and con guration of the bolted connection are considered as prime variables. According to analyses, it should be stated that not only stiffeners but also their location plays an important role in terms of energy dissipation and moment capacity. If the stiffeners are not used, it is recommended to weld the anges of the channel sections directly to the anges of the beams. Staggered bolt con guration may be preferred to be used in order to reduce the number of the bolts used in the proposed connection detail. Numerical analyses employing PEEQ and RI as indicators showed that the proposed connection detail, where either bearing or slip-critical typed connection was used, satis ed all requirements mandated by AISC 341-16.  The proposed replaceable reduced beam section Free-body diagram between center of side-plated connection and face of column Flowchart for the design of bolted connections for side plates Figure 7 Mesh con guration.   PEEQ and RI distributions for reference beam Figure 12 Details of bearing type connection with straight bolt con guration.

Figure 13
Page 24/29 Comparison of hysteresis behavior for bearing typed connections with straight bolted connection  Details of bearing type connection with staggered bolt con guration.

Figure 16
Comparison of hysteresis behavior for bearing typed connections with staggered bolted con guration Details of Models having slip-critical typed connection with standard-sized holes.

Figure 19
Page 27/29 Comparison of hysteresis behavior for slip-critical typed connections with standard sized holes Figure 20 RI and PEEQ distributions of Models having slip-critical typed connection with standard sized holes.

Figure 21
Details of Models having slip-critical typed connection with slotted holes.

Figure 22
Comparison of hysteresis behavior for slip-critical typed connections with slotted holes Figure 23 PEEQ and RI distributions of models having slip-critical typed connection with slotted holes. Figure 24