Experimental investigation of link beams with perforated web section in eccentrically braced frames

Abstract

Eccentrically braced frame (EBF) system is one of the most effective lateral loads resisting systems for steel structures. In these systems, links are designed in such a way that they yield in shear not only to provide high ductility and rigidity but also to provide a high energy dissipation capacity. In particular, as the internal forces to be considered for the design of the members outside of the links must be calculated with the amplification factor based on the yielding of the links, the magnitude of the internal forces may become so large that they may not be met by the adjacent members. Therefore, it is challenging to develop an economic design for adjacent members and connections because of the high level of design loads obtained by the amplification factor. This paper studies the effect of the perforation arrangement in the web of shear link beams in eccentrically braced frames. Both experimental and numerical investigation were conducted to demonstrate the effectiveness of the link beam with slotted perforations in the web portion. Seven equivalent isolated link beam specimens with various slot-hole patterns were tested under quasi-static cyclic loading. The results of the study indicate that using slot-holes in the web portion reduces the link shear capacity significantly. The results also show that the failure mechanism of reduced link sections was controlled by fracture at end of the slot-holes and inelastic rotation capacities were varying between 0.025 rad and 0.065 rad depending on the slot-hole patterns.

Keywords

eccentrically braced frame cyclic loading perforated section link beam shear links

Introduction

In recent years, there has been an increasing interest in Eccentrically Braced Frame (EBF) systems. There have been many studies in the literature reporting that EBF systems provide a high level of stiffness, ductility, and seismic energy dissipation capacity to the structure (Hjelmstad and Popov, 1983b). In EBFs, the benefits of moment frames and concentrically braced frames are combined into one structural system (Hjelmstad and Popov, 1983a; Popov and Malley, 1983). Link beams are considered as fuse elements which will yield primarily with large inelastic deformation level. Seismic energy is dissipated through the yielding of the link beam and also inelastic deformation of the structure confined on the link (Hjelmstad and Popov, 1983a, 1983b, 1984; Malley and Popov, 1984; Manheim and Popov, 1984; Popov and Malley, 1983). The yield behavior which is determined by the length of the member can be classified into three categories: shear, flexural, both shear and flexural yielding (AISC341-16, 2016; Engelhardt and Popov, 1989). Many researchers state that link beams which yield primarily in shear provide excellent ductility and energy dissipation capacity to the structure rather than moment-shear and flexural links (Kasai and Popov, 1986b; Popov et al., 1987).

The capacity design principle requires that connections, columns, braces and beam outside of the link must resist the forces induced by the yielding of link beams and these elements must remain essentially elastic. In order to achieve this, connections and adjacent members must be designed to resist the forces developed by fully yielded and strain hardened links (Popov and Malley, 1983). For design forces to be resisted by the elements expected to remain essentially elastic, the capacity of the link beam must be amplified by the overstrength factor. The maximum shear force developed by a link V_max, is calculated as follows

V_{max} = Ω R_{y} V_{n}

(1)

where Ω is the overstrength factor due to the strain hardening, R_y is the ratio of the expected yield stress to the specified minimum yield stress, and V_n is the nominal shear capacity of the link. A number of studies have found that an overstrength factor of 1.5 is reasonable for short links (Malley and Popov, 1984; Della Corte et al., 2013). Ji et al. (2016) has demonstrated that very short shear links can develop overstrength of 1.9 on average. Due to the large overstrength factor, it is difficult to design link-to-column connections and surrounding elements in the most economical way.

Another significant problem is to deal with the large inelastic rotation demand in the connection region when the link beam attached to the column are employed. Link-to-column connections are subject to excessive stress concentrations that may lead to a fracture in the connection region due to the large inelastic rotation demand. Link-to-column connections have less inelastic rotation capacity due to the tendency of fracture in the flange (Engelhardt and Popov, 1989). Typical moment connection details commonly used in the moment frames perform poorly when it is used for a link-to-column connection. No any prequalified link-to-column connection is specified in AISC Seismic Provision for EBF systems (AISC341-16, 2016). Extensive experimental and analytical studies of link-to-column connections have indicated that promising connection details are very limited and researches are on-going (Okazaki, 2004; Okazaki et al., 2004, 2015).

Prinz and Richards (2009) performed an analytical study in which they suggested the improvement in the link-to-column connections by putting circular holes in the link web. To determine the effectiveness of reduced web section, nineteen models with various hole patterns were numerically investigated. Berman et al. (2010) conducted analytical analyses on the Reduced Link Section (RLS) similar to the reduced beam section (RBS) beam-to-column connection. The results of the analyses show that flange plastic strains at the link end are reduced by implementing RLS concept on link beam. However, it should be noted that fracture was not modeled in the aforementioned study. Experimental investigation is needed to better understand the failure mechanisms of reduced link sections. Similarly, Naserifar and Danesh (2016) found that Reduced Link Section (RLS) concept can be used to protect link connection from negative effect of stress concentration in long link beams.

This paper examines the use of shear links with slot-hole perforations in web portions and intends to provide knowledge regarding the behavior of link beam having web with slot perforations to reduce amplification factor for more economical design of link-to-column connections and surrounding elements. For this purpose, a total of seven isolated link beams were constructed from IPE200 hot rolled European steel shape with the material of S275 grade structural steel. Six various slot-hole patterns with the same amount of section removed were introduced in the web of link beams. Specimens were subject to quasi-static cyclic loading following the loading protocol specified in AISC Seismic Provision (AISC341-16, 2016). The paper describes both experimental and numerical investigation of the link beams with perforated web section, then results are presented and discussed.

Experimental program

Test setup

Detailed views of the test setup are illustrated in Figures 1 and 2. The test setup consists of an isolated link beam (specimen), loading (upper) beam, lower beam, and columns. Isolated link beams were attached to the loading and lower beams with fully pre-tensioned bolts of 8 × M20-8.8. Each column was fixed to the strong floor through the 40 mm thick base plates using 7 × M40 anchor bolts. Out-of-plane movement was prevented through the frames with HE200B that surround the loading beam. Two hydraulic actuators with a load capacity of 250 kN and an available stroke of ±300 mm, were attached to the loading beam with 8×M20-8.8 bolts for each actuator.

Figure 1.

Test setup: (a) general view, (b) details (All dimensions are in mm).

Figure 2.

View of the test setup.

Lower beam having vertical slotted bolt holes at both ends was fastened to the columns by four M20 bolts in snug tight condition to allow vertical movement of the lower beam and thereby minimize axial force associated with vertical length change. Based on the measurements during the tests and analysis results of the finite element model, axial shortenings of the reference specimen were obtained 3.60 mm and 3.13 mm, respectively.

As shown in Figures 1 and 2, roller supports were provided at two points of the test setup to allow for the horizontal movement of the upper beam. These two supports were located at the top of the columns. At each support point, upper beam was supported through four round bars and eight bearings that allow free motion on the longitudinal axis of upper beam, while limiting vertical and out-of-plane motion. The diameter and length of the round bars were 50 mm and 250 mm, respectively, outer diameter, inner diameter, and thickness of the bearings were 52 mm, 20 mm, and 15 mm, respectively. In order to minimize the friction between the surfaces in contact with each other, grease oil was applied to the surfaces of round bars and bearings.

As seen in Figure 1, linear variable differential transformer (LVDT) displacement transducer T1 was installed to measure the applied displacement of the upper link end, and displacement transducers T2 and T3 were used to measure displacements at the lower end of the link beam. Remaining displacement transducers were used to monitor the vertical displacements of the link beam end-plate (by T4 and T5), lower beam (by T6 and T7), and loading beam (by T8 and T9) and thus the rotation of these elements.

Possible out-of-plane movement of the test setup and interface slip between link ends and beams were monitored for only reference specimen which is subjected to largest shear force. The value of maximum out-of-plane displacement and the value of slippage were 2 mm and 0.28 mm, respectively. Because the values were found negligible, no measurement was taken for those in the subsequent tests.

The loading protocol specified in the Seismic Provision (AISC341-16, 2016) was adopted to apply quasi-static cyclic loading (Figure 3). The loading is controlled by the link rotation angle. The link rotation angle (γ) was calculated as the relative displacement divided by the link length. Relative displacement was computed as a difference between T1 and the average of T2 and T3.

Figure 3.

Loading protocol.

Test specimens

In order to investigate the effect of the perforation arrangements in the web of shear link beams in eccentrically braced frames, a total of seven isolated shear links were tested under quasi-static cyclic loading. Due to the limitations of available equipment in the laboratory, IPE200 hot rolled European steel shape with the material of S275 was selected as a reference specimen. Based on the coupon test results, the measured yield stress and tensile strength values for S275 grade structural steel are given in Table 1. As shown in Figure 4, full depth stiffeners with the thickness of 10 mm were placed on both sides of the link web and spacing between the stiffeners was 125 mm. The thickness of stiffeners and the spacing were determined according to the Seismic Provision (AISC341-16, 2016). Stiffeners welded to the flange sections and web section. 40 mm thick end-plates were shop-welded to both ends through all around fillet welds. The throats of the fillet welds connecting the end-plates to the link beam were sized by taking them equal to the thickness of the connected link flange and web as suggested by Okazaki and Engelhardt (2007).

Table 1.

Measured material properties.

Portion of IPE200	Yield stress F_y [MPa]	Tensile strength F_u [MPa]	F_u/F_y	Max elongation%
Flange	343	479	1.40	32
Web	392	504	1.29	30

Figure 4.

Detailed view of the reference specimen (All dimensions are in mm).

The length of the specimens was 500 mm. Measured thickness of web and flanges are 5.68 mm and 8.57 mm, respectively. The bolts specified for the link end-plate connection were M20 8.8 which has a nominal yield strength of 640 MPa and a nominal tensile strength of 800 MPa.

Seven specimens whose details are tabulated in Table 2 and illustrated in Figure 5, were produced to perform the experimental study. One of these specimens was a reference model and six specimens were developed with various slot-hole dimensions and slot-hole patterns. Slot-holes were cut in the link web by the machining method. The ratio of removed portions to the web area was held constant for each specimen. Therefore, all those specimens with reduced web section had a similar amount of web area removed, which is 12% of the link total web area.

Table 2.

Detail of specimens.

Spec. No.	Tag	n×m [Quantity]	h_s [mm]	h_e [mm]	h_h [mm]	l_s [mm]	Reduction in the web area [%]
1	IPE200	Reference specimen
2	P42_1260	4 × 2	48	64	12	60	12
3	P46_0460	4 × 6	19	40.5	4	60
4	P44_0660	4 × 4	29	44.5	6	60
5	P46_0440	4 × 6	19	40.5	4	40
6	P26_0440	2 × 6	19	40.5	4	40
7	P26_0460	2 × 6	19	40.5	4	60

n: number of horizontal slot-holes (longitudinal direction), m: number of vertical slot-holes, h_h: height of the slot-holes, h_s: height of the parts between two slot-holes, h_e: height of the parts between slot-hole and edge, l_s: length of the slot-holes(center-to-center), l_se: total length of the slot-holes (l_se= l_s+ h_h)

Figure 5.

Detailed view of the specimens (a) reference specimen, (b) P12_60, (c) P46_0460, (d) P44_0660, (e) P46_0440, (f) P26_0440, (g) P26_0460 (All dimensions are in mm).

Estimation of shear strength

The methodology to estimate the shear strength at yielding of the link beam with perforated web portion is based on the summation of the shear strength of one end of each segment (sub-link). Two sub-links with T-shape cross-section are located on outer sides of I-shaped beam, and depending on the hole pattern, m-1 number of sub-links exist within the inner side of the web. Each sub-link can be considered as a beam member whose shear strength is governed by either shear or flexural capacity. By computing shear strength of sub-links separately and combining them, the shear strength at yielding can be estimated as follows

V_{ne} = \sum_{i = 1}^{m + 1} \min [V_{pi}; \frac{(2 M_{pi})}{l_{se}}]

(2)

where V_pi is the plastic shear strength of a sub-link and M_pi is the plastic bending moment of a sub-link.

Finite element model (FEM)

The purpose of the finite element study was to facilitate a comparison with experimental results, predict the cyclic behavior of the specimens and investigate the consistency of the results from the tests and the analyses. Finite element models of the reference specimen and two different specimens (P46_0440 and P26_0460) with the largest rotational capacity in the 4P and 2P groups, which exhibited better performance than the others, were prepared by utilizing ABAQUS/CAE 2019 software (ABAQUS, 2019). Four-node shell element (S4R: A 4-node doubly curved thin or thick shell, reduced integration, hourglass control, and finite membrane strains) (ABAQUS, 2014) was employed to define stiffeners, web, and flange of link beam. The centerline dimensions were used to model the link beam geometry. The nonlinear behavior of the steel material was accounted for by a Von-Mises yield surface and an associated flow rule. Engineering stress (σ)–engineering strain (ε) values obtained from the results of the coupon tests were converted into to the true stress (σ_true)–true strain (ε_true) (Scheider et al., 2004). The hardening behavior of the material was introduced using a combined isotropic-kinematic hardening plasticity. Nonlinear isotropic and kinematic hardening model constituting combined material hardening model is based on the work done by Lemaitré and Chaboche (1990) (ABAQUS, 2014). The kinematic component of the model is characterized by Ziegler law (ABAQUS, 2014). Material hardening model parameters were calibrated in such a way that the curve of numerical results is best fit to that of the experimental test results of reference specimen. These parameters are tabulated in Table 3.

Table 3.

Nonlinear isotropic and kinematic hardening model parameters.

Parameter	Value
Q _∞	80
B	4
C ₁	5500
γ₁	25

The ductile damage model was used to capture the behavior with fractures for the specimens with reduced web section. Geometrical imperfection was not introduced to the FEM model. Nonlinear geometry, “nlgeom,” option in ABAQUS was utilized to account for the large displacement effects (ABAQUS, 2014). In studies conducted by Mohebkhah and Chegeni (2014), and Richards and Uang (2005), it was inferred that ABAQUS can capture inelastic local buckling consistently without assigning an initial imperfection.

Figure 6 presents the boundary conditions on the finite element model of link beam. Boundary conditions were implemented on reference points with the help of rigid body constraints. At each end of the link beam, rigid body constraint is defined to constrain the motion of all edge nodes to each reference point which is specified on the mid-height of the web edge at each end of the link. As can be seen in Figure 6, all rotations were restrained at both ends. Translation along the longitudinal axis was permitted at the left end as well as translation in direction two at the right end.

Figure 6.

Boundary conditions of finite element model of reference specimen.

Assessment of the results

The cyclic responses of all specimens are shown in Figure 7. The results obtained from the experimental study of link beams with slotted perforations in the web portion are summarized in Table 4. As Figure 8 indicates, maximum rotation, γ_max, was defined as previous full cycle rotation where the measured link shear force was equivalent to 80% of maximum measured shear force during the test. Inelastic link rotation, γ_p, was calculated by subtracting the elastic portion of the rotation from the total link rotation. The yield forces and corresponding link rotations were determined considering the point where the initial stiffness line intersected the tangential stiffness line having the slope of 10% of the initial stiffness (Stratan and Dubina, 2004).

Figure 7.

Hysteresis loops of all specimens.

Table 4.

Test results.

No	Group	Specimen	Elastic stiffness, K_e, % of IPE200	Yielding strength, V_y [kN]	Estimated shear strength, V_ne [kN]	Maximum shear strength, V_max [kN]	Plastic link rotation, γ_p [rad]	Total link rotation, γ [rad]	Overstrength factor, Ω	Failure mode
1		IPE200	100	252	241	392	0.124	0.13	1.56	Fracture at link flange
2	4P	P42_1260	92.3	192	180	257	0.045	0.05	1.34	Fracture at slot ends
3		P46_0460	56.8	130	115	167	0.065	0.07	1.28	Fracture at slot ends
4		P44_0660	75.0	133	136	194	0.065	0.07	1.46	Fracture at slot ends
5		P46_0440	78.2	139	129	200	0.065	0.07	1.44	Fracture at slot ends
6	2P	P26_0440	82.7	188	129	222	0.025	0.03	1.18	Fracture at slot ends
7	2P	P26_0460	66.7	131	115	155	0.035	0.04	1.18	Fracture at slot ends

Figure 8.

Parameters for the assessment of link beam behavior in shear.

Behavior of the reference specimen

As shown in Figures 9 and 10, the results of finite element analysis were in a good agreement with those obtained from the experimental study in terms of both their deformation patterns and hysteretic behavior. Agreement in experimental and numerical results indicate that a combined isotropic-kinematic hardening is the best fit hardening model for shear links similar to that from earlier studies conducted by Kasai and Popov (1986a), and Ricles and Popov (1987). The reference specimen at the end of the test is illustrated in Figure 10(b). At 0.0075 rad, yielding was started when the shear force was 252 kN and flaking of the whitewash was observed at web panels. Subsequently, the flange near the end began to yield at a total link rotation angle of 0.015 rad. At 0.07 rad cycle, a severe flaking of the white wash at web panels occurred and yielding was clear at the flange near the end, additionally minor buckling was noted in the flange near the end.

Figure 9.

Cyclic responses of reference specimen, Test result and FEM analysis.

Figure 10.

Reference specimen: (a) fracture of link flange, (b) deformed shape by the test, (c) deformed shape by the FEM analysis.

As can be seen in Figures 10(a) and (b), the reference specimen failed due to the fracture of the link flange at a total link rotation angle 0.13 rad, while the measured ultimate link shear force, V_max, was 392 kN. When the link flange fracture occurred, panel buckling was noted in the first panel near the end. At the end of the test, the target inelastic rotation of 0.08 rad was exceeded. Measured yield strength was 252 kN while estimated yield strength of the non-perforated link beam based on the yield stress obtained from material test was 241 kN. According to the measured values, overstrength ratio was calculated as 1.56 that appears to be reasonable for shear links.

Behavior of specimens with reduced web section

Introducing the slot-holes in the web of the link beam substantially decreased the yielding strength and maximum shear strength. Yielding started at the both ends of the all sub-links, then plastic deformations concentrated at around of the slot-holes’ ends. Concentrated plastic deformations resulted in initiation of cracks at these regions. Cracks continued to propagate from slot edges at diagonal direction. The general failure mode of specimens with slot-hole perforations can be explained by which the fracture of web around slot-holes. As understood from the formation of the failure modes, slot-hole patterns did not significantly change the failure mechanism.

Figures 11(a) and 12(a) illustrate cyclic responses of specimens P46_0440 and P26_0460, based on the experimental and numerical studies. As can be seen in Figures 11(b) and 12(b), the deformed shape and failure mode of specimens obtained from the experimental study are similar to that obtained from finite element analysis.

Figure 11.

Specimen P46_0440, (a) cyclic response and (b) deformed shape.

Figure 12.

Specimen P26_0460, (a) cyclic response and (b) deformed shape.

All specimens with slot-hole perforations failed to meet the plastic rotation requirement due to fracture at the ends of the slot-holes. None of the specimens gave a promising behavior to satisfy the plastic rotation capacity of 0.08 rad required for shear links (AISC341-16, 2016). The 4P specimens, which are P42_1260, P46_0460, P44_0660 and P46_0440, achieved plastic rotation of 0.065 rad and had overstrength factors varied between 1.28 and 1.46. Many researchers (Della Corte et al., 2013; Ji et al., 2016; Malley and Popov, 1984) argued that the overstrength factor of the shear links are around value of 1.5 or larger. In the case of using reduced web section, lower overstrength factors can be obtained. Unfortunately, in this case, the value of the required plastic rotation was not satisfied. Overstrength factors for the 2P specimens of P26_0440 and P26_0460 were 1.18, these two specimens showed a dramatically poor performance with the plastic rotation of 0.025 rad and 0.035 rad, respectively.

As shown in Figures 11 and 12, the experimental results indicate that by introducing the slot-holes into all panels of the web portion rather than limited number of panels, plastic deformations around the hole ends spread to entire web portion of the link beam. That is why, the 4P specimens sustained larger plastic rotation capacity than the 2P specimens. Flexural behavior is more dominant than the behavior in shear if larger slot-hole lengths or closely spaced slot-holes are used. Using a several number of holes in vertical direction corresponding to the same amount of reduced area decreases the heights of sub-links. As can be seen from Table 4, specimens including longer slot-holes with the same hole pattern (P46_0440 vs. P46_0460 or P26_0440 vs. P26_0460) have less elastic stiffness. Similarly, the use of the smaller height of sub-links (P42_1260 vs. P44_0660 vs. P46_0460) with the same length decreases the elastic stiffness because of the flexural-dominated behavior of sub-links.

Summary and conclusions

The main objective of this study was to investigate the behavior of the slot perforated web portion in shear links. For this purpose, seven specimens were tested. Six of them had web portions with various slot-hole patterns, in which each reduction corresponds to 12% of the total web area and the rest one without perforations was used for reference. All specimens were subjected to quasi-static cyclic loading by following the loading protocol (AISC 341, 2016). Based on the results obtained from the experimental and numerical studies, due to the presence of stress concentrations around hole ends, which contributes to web fracture, link beams with perforated web portions are susceptible to strength degradation, regardless of the slot holes pattern. The maximum inelastic rotation of 4P specimens reached a value twice as large as the inelastic rotation of 2P specimens. Because of fracture occurred at the ends of the sub-links, the rotation capacity of 0.08 rad specified for shear links has not been achieved, whereas amplification factor has been reduced.

Footnotes

Author’s Contribution

Haluk Emre Alçiçek: Investigation, Validation, Writing.

Cüneyt Vatansever: Methodology, Project administration, Supervision, Review & editing.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by Research Fund of the Istanbul Technical University. Project Number: 41905.

ORCID iD

Haluk Emre Alçiçek

Appendix

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