Proposing two new methods to decrease lateral-torsional buckling in reduced beam section connections

Abstract

Reduced web section (RWS) connections can prevent lateral-torsional buckling and web local buckling experienced by reduced beam section (RBS) connections. In RWS connections, removing a large portion of web can result in shear demand intolerance induced to plastic hinge region. The present study aims to resolve the problems of RBS and RWS connections by proposing two new connections: (1) RBS with stiffener (RBS-ST) and (2) RBS with reduced web (RW-RBS) connections. In the first connection (RBS-ST), a series of stiffeners is connected to the beam in the reduced flange region, while the second connection (RW-RBS) considers both a reduction in flanges and a reduction in web. Five beam-to-column joints with three different connections, including RBS, RBS-ST, and RW-RBS connections were considered and simulated in ABAQUS. According to the results, RBS-ST and RW-RBS connections can decrease or even eliminate lateral-torsional buckling and web local buckling in RBS connection. It is important to note that RW-RBS connection is more effective in long beams with smaller shear demands in the plastic hinge region. Moreover, results showed that RBS and RW-RBS connections experienced strength degradation at 4% to 5% drift, while no strength degradation was observed in RBS-ST connection until 8% drift.

Graphical abstract

Keywords

RBS / RBS-ST / RW-RBS / lateral-torsional buckling / cyclic performance

1 Introduction

Steel Special Moment Resisting Frames (SMRFs) with rigid beam-to-column connections, generally provided by Complete Joint Penetration (CJP), Partial Joint Penetration (PJP), and fillet welds, have been widely used for lateral load resistance systems in high seismic risk regions. In the 1994 Northridge and 1995 Kobe earthquakes, unexpected damage was found in these connections, which confirmed their inappropriate application [1,2]. Consequently, certain methods, such as reinforcing the beam at the column face [3–6] and weakening the beam section at a certain distance from the column face [7], were proposed. Significantly, weakening the beam section was achieved through reducing the beam flanges or cutting parts of the beam web.

Plumier was the first researcher who proposed the method of beam section reduction [8]. In this regard, extensive experimental and theoretical research have been conducted to determine the best cut configuration. Finally, it was found that the radius cut used to reduce the beam flanges indicated the best seismic behavior, known as the Reduced Beam Section (RBS) connection [9,10]. The investigations have indicated that RBS connections experience common failure modes, such as web local buckling, flange local buckling, and lateral-torsional buckling [11,12]. The studies conducted by Zhang and Ricles [13], and Chi and Uang [14] showed that the use of RBS connections in deep-columns can result in lateral-torsional buckling. Moreover, strength degradation was observed in a study performed by Li et al. [15]. They concluded that local instabilities resulted in the strength degradation. Additionally, Morshedi et al. [16] proposed two adjacent radius cuts in RBS connections to improve the ductile behavior and energy dissipation capacity.

As mentioned, RBS connections may experience the degradation of torsional stiffness, decrease in the lateral stiffness, lateral-torsional buckling, and web local buckling. Moreover, regarding the key role of beam flanges in the resistance of bending moments, the reduction in the beam web with various configurations, such as circular or elliptical opening, and the two semi-circular voids [17–20], have been proposed. The connections with a reduction in the beam web are considered RWS connections. The ability of RWS connections to overcome the disadvantages of RBS connections is expected. Horton et al. [21] numerically investigated 90 beams with different flange reductions to develop a more effective design method for RBS connections. They found that the depth and width parameters of RBS cut would significantly affect the seismic behavior of RBS connections.

Unlike numerous investigations conducted on RBS connections, limited studies have been carried out to evaluate the performance of RWS connections. In this sense, Yang et al. [22] experimentally and analytically investigated the effect of a circular opening created in the beam web, concluding that this method enhanced the seismic behavior of MRFs. Furthermore, Momenzadeh et al. [23] proposed rectangular-opening RWS connections with stiffeners and indicated that this connection detail can be used as a pre-qualified connection in Special Moment Resisting Frames (SMRFs). Additionally, RWS connections with two-parallel horizontal-openings were introduced by Hedayat and Celikag [18]. They concluded that this method can locate the plastic hinges away from the column face, while proposing a step-by-step design procedure. Davarpanah et al. [24] and Nazaralizadeh et al. [25] indicated that RWS connections with elliptical-shaped or vertical-slits can provide suitable cyclic behavior and locate the plastic hinge away from the column face. In this regard, Imanpour et al. [20] and Mirghaderi et al. [26] evaluated accordion-web reduced beam connection subjected to the cyclic loading. Results indicated that this connection type is able to form the plastic hinge at the reduced area and prevent yielding at the welded beam-to-column connection.

Saleh et al. [27] and Zahrai et al. [28] proposed the Tubular Web RBS connection (TW-RBS), a type of accordion-web RBS connection where one or two steel tubes are placed at the expected length of the plastic hinge instead of a part of the flat beam web. Their results showed that the TW-RBS connection would lead to the formation of a ductile fuse far from the beam-to-column connection, as well as the improvement of the lateral-torsional buckling stability of the beam. Moreover, Mansouri et al. [29] introduced and evaluated two new types of corrugated web RBS connections, called the curved cell web RBS (CW-RBS) and hexagonal cell web RBS (HW-RBS). They indicated that the proposed connections can result in stable hysteretic response, lower strength degradation, higher ductility, and lower maximum equivalent plastic strains compared to the conventional RBS connection. Furthermore, Vahedi et al. [30] numerically evaluated the seismic performance of TW-RBS connections under different parameters, including diameter, thickness, and location of the tube. They concluded that tube location is an important parameter when determining the seismic performance of TW-RBS connections, while diameter and thickness of the tube were insignificant.

The current study proposes two new connections for beam-to-column joints in SMRFs to reduce or eliminate lateral-torsional buckling and web local buckling, recognized as the failure modes in RBS connections. The first proposed connection is constructed by adding the stiffeners to the reduced flange region in RBS connections, named as RBS with stiffeners (RBS-ST) connection. The second proposed connection consists of both the reduction in beam flange and beam web so that the resulting plastic modulus is equal to that obtained from the equivalent RBS connection. This study selected RBS with reduced web (RW-RBS) connection as the second proposed connection and provided its corresponding design procedure. Three connection types, specifically RBS, RBS-ST, and RW-RBS connections were considered in five beam-to-column joint models. In all five models, the cyclic performance of the proposed connections was compared to that of the RBS connection using verified nonlinear finite element models.

2 Introducing two novel connections

As mentioned, many extensive experimental and numerical studies have confirmed that RBS connections can form the plastic hinges far from the column face. However, certain failure modes, such as lateral-torsional buckling and web local buckling, may occur in this connection. Accordingly, the aim of this study is to decrease or eliminate these failure modes and improve the cyclic performance of RBS connections by proposing two new connections.

2.1 Reduced beam section with stiffener connection

The first proposed connection, as shown in Fig.1, is constructed by adding the stiffeners to the reduced flange region in RBS connections at four locations. Two of the stiffeners should be installed at the two ends of the reduced flange region and the remaining two at 1/4 of the reduced flange region length (b) from its ends b/4. Consequently, no stiffener is installed at the middle portion of the reduced flange region with the length of b/2. Note that many studies [31,32] have shown that the plastic hinge is formed at the middle portion of the reduced flange region. Hence, the plastic modulus of this location should not be increased by installing stiffeners. Therefore, no stiffener should be installed at the middle portion of the reduced flange region.

The a, b, and c parameters in Fig.1 should be determined in accordance with AISC-358 [33] recommendations for the radius cut profile of RBS connections. In addition, the stiffener dimensions are calculated based on the requirements specified in AISC seismic provisions [34] for link beam stiffeners of eccentrically braced frames. Hence, full-depth web stiffeners should be connected to both sides of the reduced flange region at the specified locations. Additionally, the stiffener thickness, t_{\mathrm{s}\mathrm{t}}, should be determined to be larger than \text{0.}75 t_{\mathrm{w}}, and 10 mm, where t_{\mathrm{w}} is the beam web thickness. These parameters are defined in Section 3.

2.2 Reduced beam section with reduced web connection

The second proposed connection, as shown in Fig.2, includes both the reduction in beam flanges and reduction in beam web, and is named the RBS with reduced web (RW-RBS) connection. The amount of reduction in beam flanges and web should be determined in accordance with the following criteria. The first criterion is that the reduced beam web should be able to tolerate the maximum expected shear demand induced on the plastic hinge of the beam with RBS connection. The second criterion is that the reduction amounts in the beam flanges and web should result in a plastic modulus equal to that obtained from an equivalent RBS connection. Accordingly, this study proposes a step-by-step design procedure for RW-RBS connection, as follows.

Step 1: calculating the maximum expected shear demand, V_{\mathrm{e}\mathrm{x}\mathrm{p}}, induced on the beam plastic hinge with RBS connection.

Step 2: determining the required amount of beam web through considering V_{\mathrm{e}\mathrm{x}\mathrm{p}} and the beam web thickness. Note that the required amount of beam web is identical to the reduced beam web shown in Fig.2 with the depth of 2\left({\displaystyle \frac{d_{\mathrm{b}}}{2}}-{\displaystyle \frac{d}{2}}\right)=d_{\mathrm{b}}- d.

Step 3: calculating the amount of the beam web that can be removed with respect to the beam web depth, d_{\mathrm{b}}, and the required amount of beam web, d_{\mathrm{b}}-d. The removed beam web with the maximum depth of d is shown in Fig.2. Regarding Fig.2, b is the length of the reduced beam flanges determined in accordance with RBS connections. Consequently, an elliptical opening with diameters of d and b should form in the beam web.

Step 4: calculating the plastic modulus of the equivalent RBS connection corresponding to the section where the beam flanges have the least width, Z_{\mathrm{R}\mathrm{B}\mathrm{S}}.

Step 5: determining the required plastic modulus of the reduced beam flanges, Z_{\mathrm{R}-\mathrm{F}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}}, considering Z_{\mathrm{R}\mathrm{B}\mathrm{S}} and the plastic modulus, which results from the reduced beam web, Z_{\mathrm{R}-\mathrm{W}\mathrm{e}\mathrm{b}} as Z_{\mathrm{R}-\mathrm{F}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}}=Z_{\mathrm{R}\mathrm{B}\mathrm{S}}-Z_{\mathrm{R}-\mathrm{W}\mathrm{e}\mathrm{b}}.

Step 6: calculating the reduction amount of the beam flanges, e, according to Z_{\mathrm{R}-\mathrm{F}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}}.

Note that the parameters of a and b in Fig.2 should be determined in accordance with AISC-358 [33] recommendations for the radius cut profile of RBS connections. These parameters are defined in Section 3. In addition, the parameters of d and e in Fig.2 should be computed according to the design procedure provided for RW-RBS connections in this study.

3 Models in numerical study

Five beam-to-column joint models are considered for three different connection types, specifically RBS, RBS-ST, and RW-RBS connections. The models were full-scale T-subassemblies whose geometrical details are shown in Fig.3 and Tab.1. Moreover, the beams and columns were assumed to be fabricated from Iranian steel profile sections. The strong column-weak beam limitations in accordance with the AISC seismic provisions [34] was used to determine the beam and column dimensions. The continuity plate thickness was considered equivalent to the beam flange thickness. All components of the fifteen models were constructed from St-37 steel with a nominal yield stress of 240 \mathrm{M}\mathrm{P}\mathrm{a} and an ultimate stress of 370\mathrm{M}\mathrm{P}\mathrm{a}.

Typical characteristics of RBS connections with radius cut profile are shown in Fig.4. The parameters of the radius cut profile in RBS connections recommended by AISC-358 [33] are tabulated in Tab.2.

Regarding Tab.2, b_{\mathrm{b}} is the beam flange width and d_{\mathrm{b}} is the beam depth. Tab.3 shows the considered values for the parameters of a, b, c, and t_{\mathrm{s}\mathrm{t}} in five beam-to-column joint models with two different connection types, namely RBS and RBS-ST connections. In addition, Tab.4 shows the considered values for the parameters of a, b, V_{\mathrm{e}\mathrm{x}\mathrm{p}}, (d_{\mathrm{b}}- d), d, Z_{\mathrm{R}\mathrm{B}\mathrm{S}}, Z_{\mathrm{R}-\mathrm{W}\mathrm{e}\mathrm{b}}, Z_{\mathrm{R}-\mathrm{F}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}}, and e explained in Subsection 2.2 and Fig.2 for five beam-to-column joint models with RW-RBS connection.

It can be concluded from Tab.4 that RW-RBS connection in models with a beam length of 1500 mm results in a small value for d and, consequently, the value of e is determined to be almost equal to the value of c in RBS connection.

4 Finite element modeling

ABAQUS software [35] was used to simulate the models mentioned in Section 3. In this study, a three-dimensional deformable nonlinear model with geometric and material nonlinearities was employed. Considering the appropriate capability of shell elements in displaying the local buckling, four-node shell element with reduced integration (S4R) was used to simulate the steel components. It is worth mentioning that all steel components were fabricated from St-37 steel with Young’s modulus of 2\times {10}^5\mathrm{M}\mathrm{P}\mathrm{a}, Poisson’s ratio of 0.3, nominal yield stress of 240 \mathrm{M}\mathrm{P}\mathrm{a}, and ultimate stress of 370 \mathrm{M}\mathrm{P}\mathrm{a}. A bilinear kinematic hardening model, including true stress−true strain specifications for St-37 steel was used to simulate the plastic behavior of the steel material. Note that the ductile damage model included in ABAQUS shows the fracture locations in the numerical models. Given that some experimental studies [14,24] have indicated that no fracture occurred in RBS regions, the ductile damage model was not considered in finite element modeling. A static-general analysis with a default value of 0.0002 for specific dissipated energy fraction automatic stabilization was selected to apply the cyclic loading slowly. To determine the best mesh size for more accurate results, a mesh refinement study was carried out. The results showed that the obtained responses from a mesh size of 20 mm demonstrated appropriate accuracy. Additionally, structured quad meshes were used as mesh controls. A displacement-controlled loading protocol in accordance with AISC 341-16 [34], shown in Tab.5, was applied at the end of the beam. Fig.5 illustrates the boundary conditions considered for the models.

5 Verification of finite element modeling

The verification of finite element modeling was conducted by simulating two full-scale connections tested by Saneei Nia et al. [36] and Davarpanah et al. [24] in ABAQUS software.

5.1 Specimen DC-S tested by Saneei Nia et al. [36]

In the experimental study of Saneei Nia et al. [36], the connection between the box column and the built-up I-shaped beam was considered as a welded unreinforced flange (WUF) connection. In specimen DC-S, Saneei Nia et al. [36] considered a built-up I-shaped beam with a flange of 160 mm × 15 mm, web of 300 mm × 8 mm, and length of 2500 mm. Moreover, in specimen DC-S, the column was fabricated from a 300 mm × 300 mm × 15 mm box with a height of 3300 mm. Their experimental specimen was modeled in ABAQUS as shown in Fig.6. The comparison between the hysteresis response of the test results [36] and that of the finite element model is illustrated in Fig.7. Note that the load reported in the hysteresis response was obtained by extracting the force from the lateral displacement at the end of the beam. In addition, the rotation (or drift) of the hysteresis response can be calculated by dividing the lateral displacement applied to the end of the beam by the beam length. The comparison between the deformed shape of the specimen tested by Saneei Nia et al. [36] at 6% interstory drift and that of the modeled specimen in ABAQUS at the same drift is shown in Fig.8(a) and Fig.8(b).

5.2 Specimen radial-cutting reduced beam section tested by Davarpanah et al. [24]

Davarpanah et al. [24] tested a radial-cutting RBS (R-RBS) specimen with an IPE270 beam and IPB200 column. The beam length and column height were considered to be 1070 and 1500 mm, respectively. The values of 101, 216, and 27 mm were determined for the parameters of a, b, and c, respectively. Fig.9 shows the comparison between the hysteresis response of the R-RBS experimental specimen [24] and that of the finite element model. In addition, the deformed shape of the R-RBS specimen tested by Davarpanah et al. [24] is compared to that of the modeled specimen in ABAQUS in Fig.10(a) and Fig.10(b).

From Fig.7–Fig.10, it is clear that there is a high level of agreement between the finite element and experimental results.

6 Comparison of two new proposed connections with reduced beam section connection

A numerical study was conducted on the models mentioned in Tab.1, Tab.3, and Tab.4. The responses of the two new proposed connections were compared to that of the RBS connection to evaluate their performance.

6.1 Hysteresis response

Fig.11(a)–Fig.11(e) show the comparison between the hysteresis response of models with RBS connection and that of the RBS-ST/ RW-RBS connection models.

Fig.11(a)−Fig.11(e) show that the stiffness and strength are approximately equal in RBS, RBS-ST, and RW-RBS connections, suggesting that RBS-ST and RW-RBS connections behave similarly to RBS connections. It can be concluded from Fig.11(a)−Fig.11(e) that strength degradation is observed at 4% to 5% drift in the RBS and RW-RBS connection models, while strength degradation does not occur until 8% drift in the RBS-ST connection models.

6.2 Energy dissipation capacity

The comparison between the cumulative energy dissipation of the RBS-ST and RW-RBS connection models and that of the RBS connection models is shown in Tab.6.

Tab.6 indicates that RBS-ST connection increases the dissipated seismic energy by 2% to 33% compared to RBS connection as a result of the non-occurrence of lateral-torsional buckling and web local buckling. In addition, the decrease in the dissipated seismic energy of RW-RBS connection is insignificant compared to RBS connection.

6.3 Lateral-torsional buckling

The key advantage of the two new proposed connections is to decrease or eliminate lateral-torsional buckling and web local buckling in RBS connection. Fig.12(a)–Fig.12(e) compare the beam lateral deformation in five models with RBS, RBS-ST, and RW-RBS connections.

As mentioned in Section 3, the use of RW-RBS connection in models with a beam length of 1500 mm (short beams) results in a small value for d, and consequently, the value of e is determined to be almost equal to the value of c in RBS connection. It is worth mentioning that the shear demand is the main demand in the short beams. Regarding the specific beam section, a larger shear demand is induced on the plastic hinge of the short beams compared to the long beams. Therefore, the value of d is smaller for the short beams compared to the long beams and the value of e is determined to be almost equal to the value of c in RBS connection. From this, we can conclude that using RW-RBS connection in the short beams will not significantly decrease lateral-torsional buckling, despite its ability to decrease or eliminate lateral-torsional buckling in the long beams with smaller shear demands.

Fig.12(a)–12(e) indicate that the lateral-torsional buckling, web local buckling, and flange local buckling are the common failure modes in models with RBS connection. In addition, it can be seen that RBS-ST connection can acceptably decrease or eliminate lateral-torsional buckling and the web local buckling. From Fig.12(a)–12(e), it is clear that RW-RBS connection demonstrated satisfactory performance in decreasing lateral-torsional buckling and web local buckling in the long beams. On the contrary, this connection cannot appropriately decrease the lateral-torsional buckling and web local buckling of short beams.

6.4 Equivalent plastic strain index

Fig.13(a)–13(e) compare the equivalent plastic strain (PEEQ) index values between RBS, RBS-ST, and RW-RBS connections at 6% drift. This figure also presents the distance between the plastic hinge zone and column face measured for models with RBS, RBS-ST, and RW-RBS connections. Fig.14(a)–14(e) show the maximum PEEQ index values at the end of 1% to 6% drifts in RBS, RBS-ST, and RW-RBS connections for five models.

It can be concluded from Fig.13(a)–Fig.13(e) that the PEEQ index values of the three different connections are similar. Moreover, Fig.13(a)–Fig.13(e) show that the distance between the plastic hinge zone and column face is approximately equal in the RBS, RBS-ST, and RW-RBS models. This means that RBS-ST and RW-RBS connections can form the plastic hinge at the same location, that the plastic hinge is formed in RBS connection. Fig.14(a)–Fig.14(e) indicate that the maximum PEEQ index values in models with RBS and RW-RBS connections are approximately similar. However, the maximum PEEQ index value increases by up to 27% in RBS-ST connection compared to RBS connection. This may be because that the stiffeners of RBS-ST connection have decreased or eliminated the plasticity and local buckling in the beam web, thus the plasticity concentrates in the beam flanges resulted in an increase in the PEEQ index.

7 Comparison of reduced web section and reduced beam section with reduced web connections

RBS connections may experience a degradation in torsional stiffness, decrease in lateral stiffness, lateral-torsional buckling, and web local buckling. Moreover, the beam flanges play a key role in resisting the bending moments, thus the reduction in beam web with various configurations has been proposed. According to research on RWS connections, a relatively large opening is required to create a weak section and move the local buckling and plasticity far from the column face. Additionally, it is possible that the large openings cause the early beam section fractures, resulting in shear-flexure interactions in the remaining sections at the top and bottom of these large openings.

Herein, models 1, 4, and 5, whose characteristics are presented in Tab.1, are considered as RWS connection with elliptical opening (E-RWS) and designed based on the study performed by Davarpanah et al. [24]. The details of E-RWS connection proposed by Davarpanah et al. [24] are shown in Fig.15 and Tab.7.

Tab.8 shows the considered values for the parameters of a, b, and h in models 1, 4, and 5 with E-RWS connection.

Fig.16(a)–Fig.16(c) compare the behavior and hysteresis curve of the models with E-RWS connection to that of models with RW-RBS connection.

From Fig.16(a)–Fig.16(c), it can be concluded that in E-RWS connection, proposed by Davarpanah et al. [24], local buckling and plasticity occur near the column face, while RW-RBS connection moves the local buckling and plasticity far from the column face. The comparison between the hysteresis curves of E-RWS connection and those of RW-RBS connection shows that E-RWS connection demonstrates higher strength levels compared to RW-RBS connection. Note that in E-RWS connection, plasticity and local buckling are concentrated near the column face where the plastic module is larger. The larger plastic module also results in larger plastic bending moments, thus the strength levels in E-RWS connection become higher than those in RW-RBS connection.

8 Conclusions

Many studies have shown that RBS connections may experience lateral-torsional buckling and web local buckling, which are two common failure modes in RBS connections. Therefore, RWS connections are more attractive options due to their ability to prevent lateral-torsional buckling and web local buckling. However, removing a large portion of the beam web in RWS connections can result in shear demand intolerance induced on the plastic hinge region. In this study, two new steel moment connections are introduced to resolve the problems of RBS and RWS connections. The first proposed connection, fabricated by adding the stiffeners to the reduced flange region in RBS connections, is considered as RBS-ST connection. The second proposed connection, regarded as the RW-RBS connection, consists of both the reduction in the beam flange and beam web. In this sense, the plastic modulus resulting from these reductions is equal to that obtained from the equivalent RBS connection. Thereafter, a step-by-step design procedure is presented for RW-RBS connection. Accordingly, five beam-to-column joint models with three different connections, including RBS, RBS-ST, and RW-RBS connections were considered and evaluated under cyclic loading. The results indicated that.

1) Strength degradation occurred in the models with RBS and RW-RBS connections at 4% to 5% drift, while the models with RBS-ST connection did not experience strength degradation until 8% drift.

2) The RBS-ST connection increased the dissipated seismic energy by 2% to 33% compared to RBS connection.

3) The decrease in dissipated seismic energy of the models with RW-RBS connection is insignificantly compared to that of RBS connection models.

4) Due to the large shear demand in the short beams, a small value is computed for d, thus the value of e is determined to be almost equal to the value of c in RBS connection. Consequently, using RW-RBS connection is an appropriate way for long beams since they have smaller shear demands.

5) The RBS-ST connection can decrease or eliminate lateral-torsional buckling and web local buckling to a certain extent.

6) The performance of RW-RBS connection is acceptable in long beams, decreasing the lateral-torsional buckling and web local buckling. On the contrary, this connection cannot appropriately decrease lateral-torsional buckling and web local buckling in short beams.

7) In the future studies, the performance and feasibility of the proposed connections should be experimentally investigated prior to real life applications.

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