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Effect of panel zone strength ratio on reduced beam section steel moment frame connections
Alexandria Engineering Journal (2018) xxx, xxx–xxx
H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
Effect of panel zone strength ratio on reduced beam section steel moment frame connections Amr A. Soliman, Omar A. Ibrahim *, Abdelaziz M. Ibrahim Dept. of Structural Engineering, Alexandria University, Lotfy El-Sied st. off Gamal Abd El-Naser – Alexandria, Alexandria Governorate 11432, Egypt Received 12 May 2018; revised 3 July 2018; accepted 18 July 2018
KEYWORDS Panel zone; Reduced beam section; Beam-to-column connection
Abstract The effect of different panel zone design ratios (Rv/Vpz) on reduced-beam-section connections as part of steel moment resisting frames under cyclic and monotonic loading is investigated. As design specifications suggest an overestimated value for the (Rv/Vpz) ratio in some cases. To achieve this objective, the balanced design proposed in the specifications is compared to other design concepts in the guidelines. Then a finite element (FE) analysis is conducted representing the beam-to-column connection assemblies under cyclic and monotonic loading to investigate the effect of different panel zone strength ratios. The FE simulation is validated and compared to test results from the literature, then a parametric study is carried out. The parameters included in the study are; the column flange thickness, the panel zone aspect ratio, and the strong column weak beam ratio. Each connection configuration is investigated according to; the amount of energy dissipation achieved, the participation in energy dissipation between the beams and the panel zone, the stable hysteretic behavior and its fracture potential. Results from the analytical study show that for assemblies with thick column flanges the design specifications overestimate the panel zone strength. Therefore, a range for the validity of the panel zone design strength formula is suggested. Ó 2018 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction In response to the brittle fractures that occurred in steel moment resisting frames (MRFs) after the 1994 Northridge earthquake, the steel design specifications AISC 341-02 [1] imposed a balanced design for the panel zone. Such that, the panel zone and the beam participate together in the MRF * Corresponding author. E-mail addresses: [email protected] (A.A. Soliman), omar. [email protected] (O.A. Ibrahim). Peer review under responsibility of Faculty of Engineering, Alexandria University.
inelastic deformation under large story drifts. As it was found that connections with excessively weak panel zones undergo large shear deformation of the panel zone, causing local kinks in the column flanges, and increasing the stress and strain demands in this sensitive area resulting in brittle fractures [2–4]. On the other hand, in order to avoid these problems and to comply with the balanced panel zone design required by the specifications (AISC 341-02) [1], thick doubler plates are used; resulting in high residual stresses around the joint which increases the potential for crack initiation and fracture at these locations in the column section [5,6]. Furthermore, the required balanced design forces most of the inelastic deformation to occur in the beam, causing lateral or local buckling
https://doi.org/10.1016/j.aej.2018.07.017 1110-0168 Ó 2018 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: A.A. Soliman et al., Effect of panel zone strength ratio on reduced beam section steel moment frame connections, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.07.017
2 of the beam, thus causing unbalanced hysteretic behavior of the assembly, and large strength degradation [7,8]. Accordingly, this study aims to determine the balanced panel zone design for different beam to column configurations such that, the maximum energy dissipation is achieved taking into account the potential for fracture. In the 1970s it was found that beam to column connections in special MRF provide significant ductility; as they have large reserve strength beyond yielding without strength degradation [9–13]. Since the design specifications (AISC 341-02) [1] require the design using the strong column weak beam approach, then most of the inelastic deformation of the MRF occurs at the beam and the panel zone. Moreover it was found that using strong panel zones with thick doubler plates leads to elastic behavior of the panel zone and forces all of the inelastic deformation to the beam [5,12,14]. Consequently, attempts were made to use weak panel zones as it was found that panel zones have a stable hysteretic behavior and develop large cyclic strain hardening, therefore, dissipating more energy [2,12,14]. Krawinkler (1978) [2] proposed a mathematical model for the panel zone stiffness and strength calculations taking into account the resistance of the surrounding elements and the thickness of the flanges of the column. As a result, the design codes such as UBC 1988 [15], and AISC 1990 [16] increased the panel zone strength and reduced the shear demand; they allowed the yielding of the panel zone prior to the full development of the strength of the beam. On 1994, the Northridge earthquake caused no structural collapses but resulted in a large number of brittle fractures at beam to column connections at low levels of plastic demands [17–19]. Among the reasons for the brittle failures that occurred during the 1994 Northridge earthquake, was the use of excessively weak panel zones; leading to the formation of local kinks in the column flanges, thus increasing the stress and strain demands in this area and making it more susceptible for brittle fracture [17– 19]. In response to these brittle fractures a balanced panel zone design is proposed in specifications AISC 341-02 [1]; AISC [1] requires the panel zone strength to resist the shear force resulting from the moment at column face projected from the flexural strength of the connected beams at the plastic hinge location in order to assure balanced design of the panel zone and beam strength, such that they participate together in dissipating the energy from cyclic loading. Moreover, a variety of beam to column connections were proposed to be used in MRFs [7,8,20] in order to improve the behavior of MRF. One of the most effective connections proposed is to use a reduced beam section (RBS); testing programs were conducted by Jones et al. [8], Zhang et al. [7], as well as Lee et al. [3] to evaluate the behavior of RBS beam to column connections and the effect of panel zone strength on its performance. The results of these tests suggested that assemblies with strong panel zone endured unstable inelastic behavior due to the concentration of inelastic deformation at the beam RBS, thus causing local and lateral torsional buckling. Furthermore, weak panel zones were also not recommended as they cause local kinks in the column flanges. Therefore balanced design criteria for the panel zone were proposed in order to avoid the problems associated with the use of either a strong or a weak panel zone [3,7]. It is worth mentioning that the balanced panel zone specimens experienced yielding at the panel zone, and at the RBS, yielding and local buckling were experienced, thus most of the inelastic energy is dissipated by the beam [7,8].
A.A. Soliman et al. The testing program established by Zhang et al. [7] consisted of six full scale internal RBS beam to column connections in a perimeter MRF. All tests included a composite reinforced concrete (RC) slab except test number SPEC 6. [Zhang et al. [7,21]] found that in some cases the proposed panel zone design criteria in AISC 341-02 [1] overestimates the panel zone strength for test utilizing a deep column. The objective of this paper is to investigate the effect of different parameters of the RBS beam to column connections on the behavior of the panel zone for different beam to column configurations and to evaluate the optimal panel zone strength for each assembly taking into account parameters such as (1) column flange thickness (tcf), (2) aspect ratio (db/dc), and (3) strong column weak beam ratio (Mpc/Mpb). Moreover, in this research the range of validity of the panel zone strength to demand ratio proposed by specifications AISC 341-16 [22] is determined. 2. Methodology for investigating panel zone strength In order to determine the optimal panel zone strength for beam to column configurations, a finite element analysis of the beam to column connection in a steel MRF is carried out through the analysis of a typical internal MRF joint under lateral drift. For multi bay MRF the inflection points are assumed to be at midspan of the beams and mid-height of the columns. Therefore, a cruciform assemblage is used for analysis. The dimension of the beam to column assembly configuration are adopted from SPEC 6 of the test performed by Zhang et al. [7] as shown in Fig. 1. The boundary conditions of the test are composed of a pin connection at the end of the column, while the ends of the beams are supported by rigid links that allow horizontal movement to simulate inflection points. The ends of the beams and columns are laterally braced to prevent twisting and out of plane movement, and additional lateral bracing at the ends of the RBS as shown in Fig. 1. The specimens were tested by imposing a quasi-static cyclic story drift according to the loading protocol defined by Appendix S in AISC 341-02 [1]. The steel grade used for SPEC 6 sections was steel A992 ASTM [23] grade 50 (yield stress fy = 345 MPa). A parametric study is presented herein, with the purpose of investigating the effect of the panel zone strength on RBS beam to column connection behavior. The parametric study is conducted; in order to evaluate the panel zone strength ratio in different beam to column configurations, the studied configurations are analyzed under cyclic and monotonic loading in order to evaluate their performance. The sizes of beams are selected to ensure strong column weak beam configuration in order to comply with AISC 341-16 [22]. RBS connections are designed according to AISC 358-16 [24] with a circular radius cut of 50% of the beam flange removed at the center of the RBS, at about 200 mm from the column face according to the beam section. The panel zones are designed according to AISC 341-16 [22]. 3. Parametric study matrix The parametric study includes eight beam-to-column configurations with different panel zone strength ratios (Rv/Vpz) through varying the doubler plate thickness for each configuration. The analysis matrix for this analytical study is summarized in Tables 1 and 2, the eight configurations are chosen to
Please cite this article in press as: A.A. Soliman et al., Effect of panel zone strength ratio on reduced beam section steel moment frame connections, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.07.017
Effect of panel zone strength ratio
3
Fig. 1
Table 1
Test Setup according to Zhang et al. [7].
Parametric analysis matrix assemblies (A to D).
Assembly No
Column section
Beam section
Doubler Pl (mm)
Rv/Vpz
db/dc
tcf (mm)
Mpc/Mpb
A
1 2 3 4 5 6
W920X253 (W36X170)
W840X252 (W33X169)
6 8 10 11 12 15
0.84 0.91 0.98 1.01 1.05 1.15
0.94
27.9
1.32
B
1 2 3 4 5
W920X201 (W36X135)
W530X197 (W21X132)
6 7 10 12 14
0.84 0.88 0.99 1.07 1.15
0.62
20.1
2.02
C
1 2 3 4 5 6 7 8 9 10
W360X347 (W14X233)
W760X161 (W30X108)
0 6 10 14 17 20 25 30 32 35
0.77 0.91 1.00 1.09 1.15 1.22 1.33 1.44 1.49 1.55
1.87
43.7
1.50
D
1 2 3 4 5 6 7 8 9 10 11
W360X422 (W14X283)
W530X219 (W21X147)
6 9 14 18 22 26 30 35 40 45 50
0.86 0.91 0.99 1.05 1.12 1.18 1.25 1.33 1.41 1.49 1.57
1.32
52.6
1.93
(AISC)
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A.A. Soliman et al. Table 2
Parametric analysis matrix assemblies (E to H).
Assembly No
Column section
Beam section
Doubler Pl (mm)
Rv/Vpz
db/dc
tcf (mm)
Mpc/Mpb
E
1 2 3 4 5 6 7
W610X195 (W24X131)
W760X161 (W30X108)
6 7 9 10 13 15 17
0.77 0.81 0.88 0.91 1.01 1.08 1.15
1.22
24.4
1.27
F
1 2 3 4 5 6 7
W610X140 (W24X94)
W610X125 (W24X84)
6 7 8 9 10 12 14
0.82 0.86 0.91 0.95 0.99 1.07 1.15
1.00
22.2
1.41
G
1 2 3 4 5 6
W690X323 (W27X217)
W690X265 (W27X178)
10 14 18 22 26 30
0.81 0.91 1.00 1.10 1.19 1.28
0.98
38.1
1.63
H
1 2 3 4 5 6
W690X289 (W27X194)
W610X174 (W24X117)
0 6 8 10 14 16
0.75 0.96 1.03 1.09 1.23 1.30
0.86
34.0
2.49
represent the range of sections used in practice in the design of MRF for low-rise and medium-rise buildings, except assembly group (B), where the column section W36X135 does not meet the requirements of highly ductile sections used in special moment frames (SMF), however it is used herein for the purpose of comparison and to provide the required range of column flange thickness and aspect ratio. Moreover, secondary parameters are studied including: (1) Column flange thickness (tcf) (2) Aspect ratio (db/dc) (3) Strong column weak beam (SCWB) ratio (Mpc/Mpb). Thus, the assemblies are chosen to have variable column flange thicknesses (20–53 mm), variable aspect ratios (0.6–1.9) and variable SCWB ratios (1.3–2.5). 3.1. Panel zone design Panel zones are designed to provide a range of panel zone strengths (weak, balanced, and strong). The panel zones strength is calculated according to the AISC 2016 [22,25] which matches the design in AISC 2002 [1]; the panel zone strength is calculated from Eq. (1) taking into account the stiffness of the elements surrounding the panel zone as suggested by Krawinkler [2]. ! 3 bcf t2cf Rv ¼ 0:6 Fyc dc tw 1 þ ð1Þ db dc tw where Fyc is the yield stress of the column material, dc is the depth of the column, tw is the summation of thickness of the web and the doubler plate, bcf is the width of the column flange, tcf is the thickness of the column flange and db is the depth of the beam. The panel zone shear demand is calculated according to AISC 341-16 [22] as shown in Eq. (2).
(AISC)
Vpz ¼ 2 Mf =db V
ð2Þ
where Mf is the moment at column face resulting from the projection of the expected plastic moment at RBS, db is the beam depth (assuming two symmetrical beams) and V is the shear developed in the column at the point where the moment reaches its expected plastic value at the RBS. 4. Finite element modelling In order to conduct the parametric study, three-dimensional nonlinear finite element models are created to study the assemblies shown in Tables 1 and 2 using the ABAQUS software [26]. Two models are created for each assembly, a global model representing a cruciform assembly to evaluate the global behavior of the beam to column connection, and a submodel representing the region of the beam flange to the column flange connection subjected to tension in order to evaluate the potential for fracture as shown in Fig. 2. In the global model the beams, column, and the connection attachments are modeled as 4 nodes shell element (S4R). Initial geometrical imperfections are taken into consideration as a combination of the lowest buckling modes. The bottom of the column is pinned at the centroid of the section, the ends of the beams are supported only in the vertical direction, and a rigid body constraint is provided at the column top and bottom and the beam end surfaces to simulate the actual load transfer to the support. Material nonlinearity is considered by using a metal plasticity model in the ABAQUS material library based on Von Mises yield criterion assuming nonlinear combined isotropic kinematic hardening rule. The values used for the
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Effect of panel zone strength ratio
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Fig. 2 Finite element simulation for the global assembly and the sub-model.
material parameters are; E = 2e+05 MPa, Fy = 345 MPa, C = 3378 MPa, c = 20, Q1 = 90 MPa, b = 12 [27]. In order to evaluate the behavior of the assembly, the two models are evaluated. From the global model the peak strength, the strength degradation, the energy dissipation and the total rotation are determined. From the sub-model the potential for fracture is evaluated; an effective criterion for comparing various connections for fracture potential is through calculating the Rupture Index (RI) [4,7] as shown in Eq. (3) RI ¼
PEEQ e1:5T
ð3Þ
where T is the triaxiality ratio (ratio between the hydrostatic stress and effective stress) as follows: rhydrostatic ð4Þ T¼ reff And PEEQ is the plastic equivalent strain as follows: rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 pl pl e e PEEQ ¼ ð5Þ 3 ij ij where epl ij are the plastic strain components in directions i and j, it is a measure of local ductility. The validation of the finite element simulation is discussed in the following section. 4.1. Finite element analysis validation In order to evaluate the FE model, the results are compared with the aforementioned SPEC 6 of the test performed by
Fig. 3
Zhang et al. [7] representing a bare steel beam to column connection assembly tested under quasi-static cyclic story drift according to the loading protocol defined in Appendix S in AISC 341-02 [1]. As the story drift increased, no local buckling occurred in the beam flanges nor beam web, the panel zone dissipated most of the energy, no deterioration in specimen capacity occurred until fracture initiated at the west side beam bottom flange heat affected zone (HAZ) near the weld root at the end of the first 5% story drift cycle. The FE model is found to be in good agreement with the test results, it captured the panel zone yielding, beam yielding, and the peak strength. The FE model reached 95% of the peak strength of the test as shown in Fig. 3(a). Furthermore, the FE model dissipated 103% of the energy dissipated by the test. Minor local buckling in the beam web at RBS occurred at the first cycle of 5% story drift same as the test. Additionally, the FE model predictions are in good agreement with the panel zone and the beam rotations as shown in Fig. 3(b and c) respectively. Consequently, the discussed finite element analysis is used to establish the parametric study. The results of the parametric study are discussed in the following section. 5. Results and discussion The parametric study, established to investigate the effect of the panel zone strength on the connection performance, is evaluated according to global behavior and local behavior of the assembly. The global behavior results include total story drift, energy dissipation, and stability of the assemblies and is discussed in Section 5.1. The global energy dissipation is calculated for each assembly as the area under the curve of loaddeflection, such that the load acting on the assembly is increasing. Furthermore, the participation of each element in the energy dissipation is calculated using the same method as the global dissipation by calculating the area under their curves using the deflection due to the rotation of each element. Moreover, the local behavior results include the comparison of the potential for fracture of the connections and is discussed in Section 5.2. A discussion of the results is presented in Section 5.3. 5.1. Global behavior In order to evaluate the effect of the panel zone strength on the cyclic behavior of the studied assemblies and to determine the panel zone strength ratio that achieves the best performance, the participation of each element in the energy dissipation is evaluated as explained earlier. An example of the effect of
Comparison of the analytical results with experimental results from Zhang et al. [7].
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A.A. Soliman et al.
Fig. 4
Mises Stress Distribution for Different PZ Strength Assemblies.
panel zone strength is shown in Fig. 4, for Assembly group C. It is found that in Fig. 4(a), having a panel zone strength ratio of 1, the panel zone endures large effective stress, while the beam yielding occurs in the beam flanges only, thus it behaves as weak panel zone, where the panel zone dissipates most of the energy. In Fig. 4(b), by increasing the panel zone strength ratio to 1.22, yielding propagates in parts of the beam web. Fig. 4(c) shows the effect of having a panel zone strength ratio of 1.44 on the performance of Assembly C, yielding propagates in the panel zone, as well as a large portion of the beam section at the RBS; resulting in the best behavior in this case, and the largest energy dissipation. In Fig. 4(d) with strong panel zone with strength ratio of 1.55, the beam endures large stresses, and undergoes local buckling, thus causing strength degradation, and less energy dissipation than that shown in Fig. 4(c). A summary of the response of the studied assemblies is presented; for Assembly group A, for weak panel zones, the panel zone dissipates most of the inelastic energy, and the beam remains almost elastic, no local buckling occurs, thus no strength degradation occurs. As a result, the lateral load capacity, and the energy dissipated by each assembly increase as the panel zone strength increases. Assembly A-5, having a panel zone strength of 1.05 according to AISC 341-16 [22], has the most energy dissipation as shown in Fig. 5(a), and has the most participation of panel zone and beam in energy dissipation. Therefore, the AISC panel zone strength formula is valid in this case. Minor beam local buckling occurs, therefore small strength degradation occurs as shown in Fig. 6(a), however, it continued until 6% story drift. In Assembly A-6, having a strong panel zone, the beam suffers local buckling resulting in gradual capacity deterioration as the story drift increases, thus dissipating less energy, it achieves one cycle of
6% story drift then severe degradation occurs up to below 80% of the peak strength. Assembly B behaves the same as Assembly A, as the panel zone strength increases the lateral load capacity increases, and the energy dissipation increases. Moreover, no local buckling takes place at the beams, even for strong panel zone assemblies. Assembly B-5, having a panel zone strength 1.15 according to AISC 341-16 [22], achieves the maximum energy dissipation as shown in Fig. 5(b). Therefore, in this assembly, the AISC formula for panel zone strength overestimates the strength. All assemblies in this group reached the second cycle of 6% story drift without strength degradation as shown in Fig. 6(b). It was found that, in this configuration all of the assemblies experience a stable behavior, no local buckling occurs, even for strong panel zone assemblies. For Assembly C, it was found that the panel zone strength is overestimated in the design specifications AISC 341-16 [22]. As the panel zone strength increases the assembly strength and energy dissipation increases. Assembly C-8, having a panel zone strength 1.44 according to AISC 341-16 [22], achieves the largest energy dissipation as shown in Fig. 5(c), and the best participation of the beam and panel zone in the inelastic deformation. As the panel zone strength increases the beam suffers local buckling, and consequently, less energy is dissipated by the assembly. All the assemblies achieve two cycles of 6% story drift without strength degradation as shown in Fig. 6(c), except Assembly C-10 where, severe strength degradation occurs after the first cycle of 6% story drift to below 80% of the peak strength. Therefore, in this assembly also, the AISC panel zone strength is inadequate and requires refinement. Assembly D is almost similar to Assembly C; however, no local buckling occurs in the beams. The energy dissipation
Please cite this article in press as: A.A. Soliman et al., Effect of panel zone strength ratio on reduced beam section steel moment frame connections, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.07.017
Effect of panel zone strength ratio
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Fig. 5
Total energy dissipation for the assemblies.
increases as the panel zone strength increases. Assembly D-10, having a panel zone strength 1.49 according to AISC 341-16 [22], achieves the most energy dissipation as shown in Fig. 5 (d), although the poor panel zone participation. Therefore, in this assembly, the AISC formula for panel zone strength overestimates the strength. It was found that for Assembly D
the beam (W21x147) achieves very large plastic rotations without the occurrence of local buckling, thus more energy is dissipated by the beam as it undergoes large inelastic rotation. All the assemblies successfully fulfilled the second cycle of 6% story drift and had a stable behavior without the occurrence of strength degradation as shown in Fig. 6(d).
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A.A. Soliman et al.
Fig. 6
Load-deflection of assemblies with maximum energy dissipation.
Assembly E behaved opposite to the previous groups; relatively weak panel zones have a better performance, more energy dissipation, and stable hysteretic behavior. Although less beam participation in the energy dissipation. Assembly E-3, having a panel zone strength 0.88 according to AISC 341-16 [22], dissipates the most energy, as shown in Fig. 5(e), where the panel zone endures large inelastic deformation, it undergoes a stable behavior as shown in Fig. 6(e). Therefore, in this assembly, the AISC formula for panel zone strength underestimates the strength. As the panel zone strength increases the beams undergo larger inelastic deformation and are subjected to local buckling causing strength degradation. Therefore, Assemblies E-5, E-6, and E-7 with balanced and relatively strong panel zones experience beam local buckling, and gradual strength degradation, thus unstable behavior, and they didn’t achieve the target displacement of 2 cycles of 6% due to severe strength deterioration. For Assembly F, assemblies with weak panel zones have a stable behavior and large inelastic panel zone distortion. Assembly F-5, having a panel zone strength 0.99 according to AISC 341-16 [22], has minor beam local buckling, although, it dissipates more energy than the others as shown in Fig. 5(f) and accomplishes two cycles of 6% story drift as shown in Fig. 6f. Therefore, the AISC panel zone strength is valid in this case. Assemblies with strong panel zones suffer large local buckling, and strength degradation, therefore they suffer severe strength deterioration after the second cycle of 5% story drift to below 80% of the peak strength. In Assembly G, Assembly G-4, having a panel zone strength 1.1 according to AISC 341-16 [22], dissipates the most energy as shown in Fig. 5(g), it has a stable hysteretic behavior as shown in Fig. 6(g). Additionally, it has a balanced behavior; as the panel zone and beam share the inelastic deformation. For assemblies with strong panel zones the beam undergoes minor local buckling, resulting in a reduction in energy dissipation. For Assembly H, Assembly H-2, having a panel zone strength 0.96 according to AISC 341-16[22], dissipates the
most energy as shown in Fig. 5(h), it undergoes a stable behavior as shown in Fig. 6(h), it has a balanced behavior; as the panel zone and beam share the inelastic deformation. Therefore, the AISC panel zone strength is valid in this case. For assemblies with strong panel zone the beam undergoes minor local buckling, resulting in a reduction in energy dissipation. 5.2. Local behavior A summary of the maximum values of RI measured at 6% story drift at the critical locations in the sub-models is shown in Fig. 7. It was found that the beam flange complete joint penetration CJP groove weld is the most critical location; at which the largest plastic strain and triaxial stress occurs. In all beam to column configurations weak panel zones had the largest RI, due to the large plastic strain and high triaxiality ratio at the flange CJP groove weld resulting from the large panel zone distortion, thus more potential for fracture. It was found that assemblies with balanced panel zones, designed according to specifications AISC 341-16 [22], had 1.8–3.2 times less RI than that of assemblies with weak panel zones. For assemblies with strong panel zones, most of the inelastic deformation occurs in the beam, thus the panel zone endures small inelastic distortions, therefore, less plastic strain and less triaxiality at the beam flange CJP groove weld. Thus, the assemblies with strong panel zones had 5–13 times less RI compared to the weak panel zone assemblies. 5.3. Results discussion From the parametric study results, it is found that in weak panel zone RBS beam to column connections, the panel zone sustains most of the inelastic deformation, thus it dissipates most of the energy, resulting in a stable hysteretic behavior. However, weak panel zone connections have less lateral load capacity, and have significantly higher potential for fracture.
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Effect of panel zone strength ratio
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Fig. 7
Parametric Study Rupture Index (RI).
On the other hand, in strong panel zone connections the beam endures large inelastic rotations causing local buckling, which results in strength degradation. Additionally, strong panel zone connections have less potential for fracture. The panel zone design strength according to AISC 341-16 [22] for each beam to column configuration at which the maximum energy dissipation is achieved as shown in Table 3. It is found that the panel zone design strength from AISC 360-16 [25] overestimates the panel zone strength in the cases
Table 3
of thick column flanges (larger than 34 mm). Therefore, in assemblies designed as balanced the panel zone undergoes large inelastic deformation and dissipates most of the energy, while beams remain almost elastic. While assemblies designed as strong panel zones have a balanced behavior; as the beams and the panel zone participate together in the energy dissipation. Consequently, a larger panel zone strength is required for thick column flange connections. As shown in Fig. 8 the balanced panel zone design with panel zone strength ranging
Summary of assemblies that achieved the maximum energy dissipation.
Assembly No
Column flange thickness (tcf)
Aspect ratio (db/dc)
SCWB ratio (Mc/Mb)
PZ design ratio Rv/Vpz
Assembly Assembly Assembly Assembly Assembly Assembly Assembly Assembly
27.9 20.1 43.7 52.6 24.4 22.2 38.1 34
0.94 0.62 1.87 1.32 1.22 1.00 0.98 0.86
1.32 2.02 1.50 1.93 1.27 1.41 1.63 2.49
1.05 1.15 1.44 1.49 0.88 0.99 1.1 0.96
A B C D E F G H
Fig. 8
(AISC)
Effect of Column Flange Thickness on the PZ Design Strength.
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A.A. Soliman et al.
Fig. 9
Fig. 10
Effect of SCWB Ratio on the PZ Design Strength.
Effect of aspect ratio on the PZ design strength.
from (0.9–1.05) according to AISC 341-16 [22] is proposed as it gives the best performance. While for assemblies with thick column flanges (larger than 34 mm), they contradict with this design, as the design specifications AISC 360-16 [25] overestimates the panel zone strength. Except for Assembly B, which doesn’t match this design concept, this is caused by the low slenderness ratios of the beam used (W21X132), therefore no local buckling occurred at the beam even for strong panel zone assemblies, resulting in a stable hysteretic behavior and larger energy dissipation. The SCWB ratio and the aspect ratio of the panel zone have no effect on the proposed panel zone design ratio, as shown in Figs. 9 and 10 respectively, as the large scatter in the results implies that the proposed panel zone design ratio is not affected by these configuration variables. 6. Conclusion and recommendations A parametric study is conducted in order to study the effect of panel zone strength on the performance of RBS steel MRF connection, and to evaluate the panel zone design concepts in design specifications and guidelines for different beam to column configurations in order to achieve the best performance; to increase the energy dissipated, to have a stable hysteretic behavior, and to reduce the potential for fracture. Furthermore, this study presents a range for the validity of the panel zone design strength formula suggested by the AISC 360-16 [25]. Moreover, the effect of other parameters such as
the column flange thickness, SCWB ratio, and aspect ratio on the assembly behavior is presented. From the analytical study results the following observations are concluded: It was found in most of the cases that panel zone design according to AISC 341-16 [22] is accurate, and results in the best performance regarding the stable behavior, large energy dissipation, and potential for fracture. In assemblies with weak panel zones, the panel zone undergoes large inelastic deformation, having a stable hysteretic behavior. The panel zone dissipates most of the inelastic energy while the beam remains almost elastic. The weak panel zone assemblies have less lateral load capacity, and a significantly higher potential for fracture. While assemblies with strong panel zones the beams endure large inelastic rotation, causing local buckling of the beam web at the RBS, resulting in strength degradation and having an unstable behavior. Furthermore assemblies with strong panel zones have less potential for fracture A proposed panel zone design strength validity range is suggested for AISC formula according to the thickness of the column flanges; in order to achieve the best performance and to avoid the problems of weak and strong panel zones. It was found that for thick column flanges (larger than 34 mm) the design specifications AISC [22,25] overestimate the panel zone strength. As such, AISC 360-16 [25] formula for panel zone strength is only valid for assemblies with column flange of thickness less than 34 mm. Therefore the
Please cite this article in press as: A.A. Soliman et al., Effect of panel zone strength ratio on reduced beam section steel moment frame connections, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.07.017
Effect of panel zone strength ratio panel zone design strength according to AISC 360-16 [25] requires further refinement in the cases of thick column flanges in order to achieve the best performance. All beam to column configurations agree with the proposed design concept except Assembly B, as in Assembly B when increasing the panel zone strength, the energy dissipation increases, and it has a stable behavior even for strong panel zone assemblies. This is caused by the low beam slenderness ratio; thus, the beam has a large inelastic rotation capacity without the occurrence of local buckling. Therefore, the beam slenderness ratio needs to be taken into consideration in order to determine the optimal panel zone design. It was found that the SCWB ratio and the aspect ratio have no effect on the behavior of the assembly, whereas the panel zone behavior is affected by other variables. Further studies are required to properly estimate the panel zone strength in the case of thick column flanges, besides the beam slenderness ratio should be taken into account while designing the RBS beam to column connection. Acknowledgement The authors gratefully acknowledge the support of Prof. Dimitrios Lignos, who provided advice and assistance on this research. References [1] AISC, Seismic Provisions for Structural Steel Buildings, Chicago, Illinois, ANSI/AISC 341, 2002. [2] H. Krawinkler, Shear in beam-column joints in seismic design of steel frames, Eng. J., AISC 15 (1978) 82–91. [3] C.-H. Lee, S.-W. Jeon, J.-H. Kim, C.-M. Uang, Effects of panel zone strength and beam web connection method on seismic performance of reduced beam section steel moment connections, J. Struct. Eng. 131 (2005) 1854–1865. [4] S. El-Tawil, E. Vidarsson, T. Mikesell, S.K. Kunnath, Inelastic behavior and design of steel panel zones, J. Struct. Eng. 125 (1999) 183–193. [5] E.P. Popov, Seismic Moment Connections for MomentResisting Steel Frames, Earthquake Engineering Research Center: University of California Berkeley, 1983. [6] V. Nikolaidou, C.A. Rogers, D.G. Lignos, Influence of welding of doubler plates to ASTM A913 450 MPa grade columns. Naples (Italy): Eurosteel, 2014. [7] X. Zhang, J.M. Ricles, L.-W. Lu, J.W. Fisher, Development of seismic guidelines for deep-column, Steel Moment Connect. (2004).
11 [8] S.L. Jones, G.T. Fry, M.D. Engelhardt, Experimental evaluation of cyclically loaded reduced beam section moment connections, J. Struct. Eng. 128 (2002) 441–451. [9] H. Krawinkler, V.V. Bertero, E.P. Popov, Inelastic Behavior of Steel Beam-to-Column Subassemblages, University of California, Berkeley, 1971. [10] L.D. Carpenter, L.-W. Lu, Reversed and repeated lost tests of full-scale steel frames, Am. Iron Steel Inst. (1973). [11] R. Becker, Panel zone effect on the strength and stiffness of steel rigid frames, Eng. J., AISC. 12 (1975) 19–29. [12] H. Krawinkler, S. Mohasseb, Effects of panel zone deformations on seismic response, J. Constr. Steel Res. 8 (1987) 233–250. [13] J.S.H. David Fielding, Shear in steel beam-to-column connections, Weld. Res. Suppl. J. (1971) 14. [14] E.P. Popov, N.R. Amin, J.J. Louie, R.M. Stephen, Cyclic behavior of large beam-column assemblies, Earthq. Spectra 1 (1985) 203–238. [15] UBC, Uniform Building Code. Whittier, California: International Conference of Building Officials, 1988. [16] AISC, Specification for Structural Steel Buildings, Chicago, Illinois: ANSI/AISC 360, 1990. [17] D.K. Miller, Lessons learned from the Northridge earthquake, Eng. Struct. 20 (1998) 249–260. [18] T.-S. Yang, E.P. Popov, Behavior of PRE-NORTHRIDGE MOMENT RESISTING STEEL Connections, Earthquake Engineering Research Center, University of California, 1995. [19] FEMA-350, Recommended Seismic Design Criteria for New Steel Moment Frame Buildings, FEMA 350. Washington, DC: Federal Emergency Management Agency, 2000. [20] M.D. Engelhardt, T. Winneberger, A.J. Zekany, T.J. Potyraj, The dogbone connection: Part II, Modern Steel Const. 36 (1996) 46–55. [21] X. Zhang, J.M. Ricles, Experimental evaluation of reduced beam section connections to deep columns, J. Struct. Eng. 132 (2006) 346–357. [22] AISC, Seismic Provisions for Structural Steel Buildings, Chicago, Illinois, ANSI/AISC 341, 2016. [23] ASTM, A992/A992M-11, Standard Specification for Structural Steel Shapes, ASTM International, West Conshohocken, PA, 2015. [24] AISC, Prequalified Connections for Special and Intermediate Steel Moment Frames for Seismic Applications. Chicago, Illinois, ANSI/AISC 358, 2016. [25] AISC, Specification for Structural Steel Buildings, Chicago, Illinois: ANSI/AISC 360, 2016. [26] Hibbitt, Karlsson, Sorensen, ABAQUS/Explicit: user’s manual: Hibbitt, Karlsson and Sorenson Incorporated, 2001. [27] A. Elkady, Collapse Risk Assessment of Steel Moment Resisting Frames Designed with Deep Wide-Flange Columns in Seismic Regions, McGill University Libraries, 2016.
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H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
Effect of panel zone strength ratio on reduced beam section steel moment frame connections Amr A. Soliman, Omar A. Ibrahim *, Abdelaziz M. Ibrahim Dept. of Structural Engineering, Alexandria University, Lotfy El-Sied st. off Gamal Abd El-Naser – Alexandria, Alexandria Governorate 11432, Egypt Received 12 May 2018; revised 3 July 2018; accepted 18 July 2018
KEYWORDS Panel zone; Reduced beam section; Beam-to-column connection
Abstract The effect of different panel zone design ratios (Rv/Vpz) on reduced-beam-section connections as part of steel moment resisting frames under cyclic and monotonic loading is investigated. As design specifications suggest an overestimated value for the (Rv/Vpz) ratio in some cases. To achieve this objective, the balanced design proposed in the specifications is compared to other design concepts in the guidelines. Then a finite element (FE) analysis is conducted representing the beam-to-column connection assemblies under cyclic and monotonic loading to investigate the effect of different panel zone strength ratios. The FE simulation is validated and compared to test results from the literature, then a parametric study is carried out. The parameters included in the study are; the column flange thickness, the panel zone aspect ratio, and the strong column weak beam ratio. Each connection configuration is investigated according to; the amount of energy dissipation achieved, the participation in energy dissipation between the beams and the panel zone, the stable hysteretic behavior and its fracture potential. Results from the analytical study show that for assemblies with thick column flanges the design specifications overestimate the panel zone strength. Therefore, a range for the validity of the panel zone design strength formula is suggested. Ó 2018 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction In response to the brittle fractures that occurred in steel moment resisting frames (MRFs) after the 1994 Northridge earthquake, the steel design specifications AISC 341-02 [1] imposed a balanced design for the panel zone. Such that, the panel zone and the beam participate together in the MRF * Corresponding author. E-mail addresses: [email protected] (A.A. Soliman), omar. [email protected] (O.A. Ibrahim). Peer review under responsibility of Faculty of Engineering, Alexandria University.
inelastic deformation under large story drifts. As it was found that connections with excessively weak panel zones undergo large shear deformation of the panel zone, causing local kinks in the column flanges, and increasing the stress and strain demands in this sensitive area resulting in brittle fractures [2–4]. On the other hand, in order to avoid these problems and to comply with the balanced panel zone design required by the specifications (AISC 341-02) [1], thick doubler plates are used; resulting in high residual stresses around the joint which increases the potential for crack initiation and fracture at these locations in the column section [5,6]. Furthermore, the required balanced design forces most of the inelastic deformation to occur in the beam, causing lateral or local buckling
https://doi.org/10.1016/j.aej.2018.07.017 1110-0168 Ó 2018 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: A.A. Soliman et al., Effect of panel zone strength ratio on reduced beam section steel moment frame connections, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.07.017
2 of the beam, thus causing unbalanced hysteretic behavior of the assembly, and large strength degradation [7,8]. Accordingly, this study aims to determine the balanced panel zone design for different beam to column configurations such that, the maximum energy dissipation is achieved taking into account the potential for fracture. In the 1970s it was found that beam to column connections in special MRF provide significant ductility; as they have large reserve strength beyond yielding without strength degradation [9–13]. Since the design specifications (AISC 341-02) [1] require the design using the strong column weak beam approach, then most of the inelastic deformation of the MRF occurs at the beam and the panel zone. Moreover it was found that using strong panel zones with thick doubler plates leads to elastic behavior of the panel zone and forces all of the inelastic deformation to the beam [5,12,14]. Consequently, attempts were made to use weak panel zones as it was found that panel zones have a stable hysteretic behavior and develop large cyclic strain hardening, therefore, dissipating more energy [2,12,14]. Krawinkler (1978) [2] proposed a mathematical model for the panel zone stiffness and strength calculations taking into account the resistance of the surrounding elements and the thickness of the flanges of the column. As a result, the design codes such as UBC 1988 [15], and AISC 1990 [16] increased the panel zone strength and reduced the shear demand; they allowed the yielding of the panel zone prior to the full development of the strength of the beam. On 1994, the Northridge earthquake caused no structural collapses but resulted in a large number of brittle fractures at beam to column connections at low levels of plastic demands [17–19]. Among the reasons for the brittle failures that occurred during the 1994 Northridge earthquake, was the use of excessively weak panel zones; leading to the formation of local kinks in the column flanges, thus increasing the stress and strain demands in this area and making it more susceptible for brittle fracture [17– 19]. In response to these brittle fractures a balanced panel zone design is proposed in specifications AISC 341-02 [1]; AISC [1] requires the panel zone strength to resist the shear force resulting from the moment at column face projected from the flexural strength of the connected beams at the plastic hinge location in order to assure balanced design of the panel zone and beam strength, such that they participate together in dissipating the energy from cyclic loading. Moreover, a variety of beam to column connections were proposed to be used in MRFs [7,8,20] in order to improve the behavior of MRF. One of the most effective connections proposed is to use a reduced beam section (RBS); testing programs were conducted by Jones et al. [8], Zhang et al. [7], as well as Lee et al. [3] to evaluate the behavior of RBS beam to column connections and the effect of panel zone strength on its performance. The results of these tests suggested that assemblies with strong panel zone endured unstable inelastic behavior due to the concentration of inelastic deformation at the beam RBS, thus causing local and lateral torsional buckling. Furthermore, weak panel zones were also not recommended as they cause local kinks in the column flanges. Therefore balanced design criteria for the panel zone were proposed in order to avoid the problems associated with the use of either a strong or a weak panel zone [3,7]. It is worth mentioning that the balanced panel zone specimens experienced yielding at the panel zone, and at the RBS, yielding and local buckling were experienced, thus most of the inelastic energy is dissipated by the beam [7,8].
A.A. Soliman et al. The testing program established by Zhang et al. [7] consisted of six full scale internal RBS beam to column connections in a perimeter MRF. All tests included a composite reinforced concrete (RC) slab except test number SPEC 6. [Zhang et al. [7,21]] found that in some cases the proposed panel zone design criteria in AISC 341-02 [1] overestimates the panel zone strength for test utilizing a deep column. The objective of this paper is to investigate the effect of different parameters of the RBS beam to column connections on the behavior of the panel zone for different beam to column configurations and to evaluate the optimal panel zone strength for each assembly taking into account parameters such as (1) column flange thickness (tcf), (2) aspect ratio (db/dc), and (3) strong column weak beam ratio (Mpc/Mpb). Moreover, in this research the range of validity of the panel zone strength to demand ratio proposed by specifications AISC 341-16 [22] is determined. 2. Methodology for investigating panel zone strength In order to determine the optimal panel zone strength for beam to column configurations, a finite element analysis of the beam to column connection in a steel MRF is carried out through the analysis of a typical internal MRF joint under lateral drift. For multi bay MRF the inflection points are assumed to be at midspan of the beams and mid-height of the columns. Therefore, a cruciform assemblage is used for analysis. The dimension of the beam to column assembly configuration are adopted from SPEC 6 of the test performed by Zhang et al. [7] as shown in Fig. 1. The boundary conditions of the test are composed of a pin connection at the end of the column, while the ends of the beams are supported by rigid links that allow horizontal movement to simulate inflection points. The ends of the beams and columns are laterally braced to prevent twisting and out of plane movement, and additional lateral bracing at the ends of the RBS as shown in Fig. 1. The specimens were tested by imposing a quasi-static cyclic story drift according to the loading protocol defined by Appendix S in AISC 341-02 [1]. The steel grade used for SPEC 6 sections was steel A992 ASTM [23] grade 50 (yield stress fy = 345 MPa). A parametric study is presented herein, with the purpose of investigating the effect of the panel zone strength on RBS beam to column connection behavior. The parametric study is conducted; in order to evaluate the panel zone strength ratio in different beam to column configurations, the studied configurations are analyzed under cyclic and monotonic loading in order to evaluate their performance. The sizes of beams are selected to ensure strong column weak beam configuration in order to comply with AISC 341-16 [22]. RBS connections are designed according to AISC 358-16 [24] with a circular radius cut of 50% of the beam flange removed at the center of the RBS, at about 200 mm from the column face according to the beam section. The panel zones are designed according to AISC 341-16 [22]. 3. Parametric study matrix The parametric study includes eight beam-to-column configurations with different panel zone strength ratios (Rv/Vpz) through varying the doubler plate thickness for each configuration. The analysis matrix for this analytical study is summarized in Tables 1 and 2, the eight configurations are chosen to
Please cite this article in press as: A.A. Soliman et al., Effect of panel zone strength ratio on reduced beam section steel moment frame connections, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.07.017
Effect of panel zone strength ratio
3
Fig. 1
Table 1
Test Setup according to Zhang et al. [7].
Parametric analysis matrix assemblies (A to D).
Assembly No
Column section
Beam section
Doubler Pl (mm)
Rv/Vpz
db/dc
tcf (mm)
Mpc/Mpb
A
1 2 3 4 5 6
W920X253 (W36X170)
W840X252 (W33X169)
6 8 10 11 12 15
0.84 0.91 0.98 1.01 1.05 1.15
0.94
27.9
1.32
B
1 2 3 4 5
W920X201 (W36X135)
W530X197 (W21X132)
6 7 10 12 14
0.84 0.88 0.99 1.07 1.15
0.62
20.1
2.02
C
1 2 3 4 5 6 7 8 9 10
W360X347 (W14X233)
W760X161 (W30X108)
0 6 10 14 17 20 25 30 32 35
0.77 0.91 1.00 1.09 1.15 1.22 1.33 1.44 1.49 1.55
1.87
43.7
1.50
D
1 2 3 4 5 6 7 8 9 10 11
W360X422 (W14X283)
W530X219 (W21X147)
6 9 14 18 22 26 30 35 40 45 50
0.86 0.91 0.99 1.05 1.12 1.18 1.25 1.33 1.41 1.49 1.57
1.32
52.6
1.93
(AISC)
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4
A.A. Soliman et al. Table 2
Parametric analysis matrix assemblies (E to H).
Assembly No
Column section
Beam section
Doubler Pl (mm)
Rv/Vpz
db/dc
tcf (mm)
Mpc/Mpb
E
1 2 3 4 5 6 7
W610X195 (W24X131)
W760X161 (W30X108)
6 7 9 10 13 15 17
0.77 0.81 0.88 0.91 1.01 1.08 1.15
1.22
24.4
1.27
F
1 2 3 4 5 6 7
W610X140 (W24X94)
W610X125 (W24X84)
6 7 8 9 10 12 14
0.82 0.86 0.91 0.95 0.99 1.07 1.15
1.00
22.2
1.41
G
1 2 3 4 5 6
W690X323 (W27X217)
W690X265 (W27X178)
10 14 18 22 26 30
0.81 0.91 1.00 1.10 1.19 1.28
0.98
38.1
1.63
H
1 2 3 4 5 6
W690X289 (W27X194)
W610X174 (W24X117)
0 6 8 10 14 16
0.75 0.96 1.03 1.09 1.23 1.30
0.86
34.0
2.49
represent the range of sections used in practice in the design of MRF for low-rise and medium-rise buildings, except assembly group (B), where the column section W36X135 does not meet the requirements of highly ductile sections used in special moment frames (SMF), however it is used herein for the purpose of comparison and to provide the required range of column flange thickness and aspect ratio. Moreover, secondary parameters are studied including: (1) Column flange thickness (tcf) (2) Aspect ratio (db/dc) (3) Strong column weak beam (SCWB) ratio (Mpc/Mpb). Thus, the assemblies are chosen to have variable column flange thicknesses (20–53 mm), variable aspect ratios (0.6–1.9) and variable SCWB ratios (1.3–2.5). 3.1. Panel zone design Panel zones are designed to provide a range of panel zone strengths (weak, balanced, and strong). The panel zones strength is calculated according to the AISC 2016 [22,25] which matches the design in AISC 2002 [1]; the panel zone strength is calculated from Eq. (1) taking into account the stiffness of the elements surrounding the panel zone as suggested by Krawinkler [2]. ! 3 bcf t2cf Rv ¼ 0:6 Fyc dc tw 1 þ ð1Þ db dc tw where Fyc is the yield stress of the column material, dc is the depth of the column, tw is the summation of thickness of the web and the doubler plate, bcf is the width of the column flange, tcf is the thickness of the column flange and db is the depth of the beam. The panel zone shear demand is calculated according to AISC 341-16 [22] as shown in Eq. (2).
(AISC)
Vpz ¼ 2 Mf =db V
ð2Þ
where Mf is the moment at column face resulting from the projection of the expected plastic moment at RBS, db is the beam depth (assuming two symmetrical beams) and V is the shear developed in the column at the point where the moment reaches its expected plastic value at the RBS. 4. Finite element modelling In order to conduct the parametric study, three-dimensional nonlinear finite element models are created to study the assemblies shown in Tables 1 and 2 using the ABAQUS software [26]. Two models are created for each assembly, a global model representing a cruciform assembly to evaluate the global behavior of the beam to column connection, and a submodel representing the region of the beam flange to the column flange connection subjected to tension in order to evaluate the potential for fracture as shown in Fig. 2. In the global model the beams, column, and the connection attachments are modeled as 4 nodes shell element (S4R). Initial geometrical imperfections are taken into consideration as a combination of the lowest buckling modes. The bottom of the column is pinned at the centroid of the section, the ends of the beams are supported only in the vertical direction, and a rigid body constraint is provided at the column top and bottom and the beam end surfaces to simulate the actual load transfer to the support. Material nonlinearity is considered by using a metal plasticity model in the ABAQUS material library based on Von Mises yield criterion assuming nonlinear combined isotropic kinematic hardening rule. The values used for the
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Effect of panel zone strength ratio
5
Fig. 2 Finite element simulation for the global assembly and the sub-model.
material parameters are; E = 2e+05 MPa, Fy = 345 MPa, C = 3378 MPa, c = 20, Q1 = 90 MPa, b = 12 [27]. In order to evaluate the behavior of the assembly, the two models are evaluated. From the global model the peak strength, the strength degradation, the energy dissipation and the total rotation are determined. From the sub-model the potential for fracture is evaluated; an effective criterion for comparing various connections for fracture potential is through calculating the Rupture Index (RI) [4,7] as shown in Eq. (3) RI ¼
PEEQ e1:5T
ð3Þ
where T is the triaxiality ratio (ratio between the hydrostatic stress and effective stress) as follows: rhydrostatic ð4Þ T¼ reff And PEEQ is the plastic equivalent strain as follows: rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 pl pl e e PEEQ ¼ ð5Þ 3 ij ij where epl ij are the plastic strain components in directions i and j, it is a measure of local ductility. The validation of the finite element simulation is discussed in the following section. 4.1. Finite element analysis validation In order to evaluate the FE model, the results are compared with the aforementioned SPEC 6 of the test performed by
Fig. 3
Zhang et al. [7] representing a bare steel beam to column connection assembly tested under quasi-static cyclic story drift according to the loading protocol defined in Appendix S in AISC 341-02 [1]. As the story drift increased, no local buckling occurred in the beam flanges nor beam web, the panel zone dissipated most of the energy, no deterioration in specimen capacity occurred until fracture initiated at the west side beam bottom flange heat affected zone (HAZ) near the weld root at the end of the first 5% story drift cycle. The FE model is found to be in good agreement with the test results, it captured the panel zone yielding, beam yielding, and the peak strength. The FE model reached 95% of the peak strength of the test as shown in Fig. 3(a). Furthermore, the FE model dissipated 103% of the energy dissipated by the test. Minor local buckling in the beam web at RBS occurred at the first cycle of 5% story drift same as the test. Additionally, the FE model predictions are in good agreement with the panel zone and the beam rotations as shown in Fig. 3(b and c) respectively. Consequently, the discussed finite element analysis is used to establish the parametric study. The results of the parametric study are discussed in the following section. 5. Results and discussion The parametric study, established to investigate the effect of the panel zone strength on the connection performance, is evaluated according to global behavior and local behavior of the assembly. The global behavior results include total story drift, energy dissipation, and stability of the assemblies and is discussed in Section 5.1. The global energy dissipation is calculated for each assembly as the area under the curve of loaddeflection, such that the load acting on the assembly is increasing. Furthermore, the participation of each element in the energy dissipation is calculated using the same method as the global dissipation by calculating the area under their curves using the deflection due to the rotation of each element. Moreover, the local behavior results include the comparison of the potential for fracture of the connections and is discussed in Section 5.2. A discussion of the results is presented in Section 5.3. 5.1. Global behavior In order to evaluate the effect of the panel zone strength on the cyclic behavior of the studied assemblies and to determine the panel zone strength ratio that achieves the best performance, the participation of each element in the energy dissipation is evaluated as explained earlier. An example of the effect of
Comparison of the analytical results with experimental results from Zhang et al. [7].
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6
A.A. Soliman et al.
Fig. 4
Mises Stress Distribution for Different PZ Strength Assemblies.
panel zone strength is shown in Fig. 4, for Assembly group C. It is found that in Fig. 4(a), having a panel zone strength ratio of 1, the panel zone endures large effective stress, while the beam yielding occurs in the beam flanges only, thus it behaves as weak panel zone, where the panel zone dissipates most of the energy. In Fig. 4(b), by increasing the panel zone strength ratio to 1.22, yielding propagates in parts of the beam web. Fig. 4(c) shows the effect of having a panel zone strength ratio of 1.44 on the performance of Assembly C, yielding propagates in the panel zone, as well as a large portion of the beam section at the RBS; resulting in the best behavior in this case, and the largest energy dissipation. In Fig. 4(d) with strong panel zone with strength ratio of 1.55, the beam endures large stresses, and undergoes local buckling, thus causing strength degradation, and less energy dissipation than that shown in Fig. 4(c). A summary of the response of the studied assemblies is presented; for Assembly group A, for weak panel zones, the panel zone dissipates most of the inelastic energy, and the beam remains almost elastic, no local buckling occurs, thus no strength degradation occurs. As a result, the lateral load capacity, and the energy dissipated by each assembly increase as the panel zone strength increases. Assembly A-5, having a panel zone strength of 1.05 according to AISC 341-16 [22], has the most energy dissipation as shown in Fig. 5(a), and has the most participation of panel zone and beam in energy dissipation. Therefore, the AISC panel zone strength formula is valid in this case. Minor beam local buckling occurs, therefore small strength degradation occurs as shown in Fig. 6(a), however, it continued until 6% story drift. In Assembly A-6, having a strong panel zone, the beam suffers local buckling resulting in gradual capacity deterioration as the story drift increases, thus dissipating less energy, it achieves one cycle of
6% story drift then severe degradation occurs up to below 80% of the peak strength. Assembly B behaves the same as Assembly A, as the panel zone strength increases the lateral load capacity increases, and the energy dissipation increases. Moreover, no local buckling takes place at the beams, even for strong panel zone assemblies. Assembly B-5, having a panel zone strength 1.15 according to AISC 341-16 [22], achieves the maximum energy dissipation as shown in Fig. 5(b). Therefore, in this assembly, the AISC formula for panel zone strength overestimates the strength. All assemblies in this group reached the second cycle of 6% story drift without strength degradation as shown in Fig. 6(b). It was found that, in this configuration all of the assemblies experience a stable behavior, no local buckling occurs, even for strong panel zone assemblies. For Assembly C, it was found that the panel zone strength is overestimated in the design specifications AISC 341-16 [22]. As the panel zone strength increases the assembly strength and energy dissipation increases. Assembly C-8, having a panel zone strength 1.44 according to AISC 341-16 [22], achieves the largest energy dissipation as shown in Fig. 5(c), and the best participation of the beam and panel zone in the inelastic deformation. As the panel zone strength increases the beam suffers local buckling, and consequently, less energy is dissipated by the assembly. All the assemblies achieve two cycles of 6% story drift without strength degradation as shown in Fig. 6(c), except Assembly C-10 where, severe strength degradation occurs after the first cycle of 6% story drift to below 80% of the peak strength. Therefore, in this assembly also, the AISC panel zone strength is inadequate and requires refinement. Assembly D is almost similar to Assembly C; however, no local buckling occurs in the beams. The energy dissipation
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Effect of panel zone strength ratio
7
Fig. 5
Total energy dissipation for the assemblies.
increases as the panel zone strength increases. Assembly D-10, having a panel zone strength 1.49 according to AISC 341-16 [22], achieves the most energy dissipation as shown in Fig. 5 (d), although the poor panel zone participation. Therefore, in this assembly, the AISC formula for panel zone strength overestimates the strength. It was found that for Assembly D
the beam (W21x147) achieves very large plastic rotations without the occurrence of local buckling, thus more energy is dissipated by the beam as it undergoes large inelastic rotation. All the assemblies successfully fulfilled the second cycle of 6% story drift and had a stable behavior without the occurrence of strength degradation as shown in Fig. 6(d).
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Fig. 6
Load-deflection of assemblies with maximum energy dissipation.
Assembly E behaved opposite to the previous groups; relatively weak panel zones have a better performance, more energy dissipation, and stable hysteretic behavior. Although less beam participation in the energy dissipation. Assembly E-3, having a panel zone strength 0.88 according to AISC 341-16 [22], dissipates the most energy, as shown in Fig. 5(e), where the panel zone endures large inelastic deformation, it undergoes a stable behavior as shown in Fig. 6(e). Therefore, in this assembly, the AISC formula for panel zone strength underestimates the strength. As the panel zone strength increases the beams undergo larger inelastic deformation and are subjected to local buckling causing strength degradation. Therefore, Assemblies E-5, E-6, and E-7 with balanced and relatively strong panel zones experience beam local buckling, and gradual strength degradation, thus unstable behavior, and they didn’t achieve the target displacement of 2 cycles of 6% due to severe strength deterioration. For Assembly F, assemblies with weak panel zones have a stable behavior and large inelastic panel zone distortion. Assembly F-5, having a panel zone strength 0.99 according to AISC 341-16 [22], has minor beam local buckling, although, it dissipates more energy than the others as shown in Fig. 5(f) and accomplishes two cycles of 6% story drift as shown in Fig. 6f. Therefore, the AISC panel zone strength is valid in this case. Assemblies with strong panel zones suffer large local buckling, and strength degradation, therefore they suffer severe strength deterioration after the second cycle of 5% story drift to below 80% of the peak strength. In Assembly G, Assembly G-4, having a panel zone strength 1.1 according to AISC 341-16 [22], dissipates the most energy as shown in Fig. 5(g), it has a stable hysteretic behavior as shown in Fig. 6(g). Additionally, it has a balanced behavior; as the panel zone and beam share the inelastic deformation. For assemblies with strong panel zones the beam undergoes minor local buckling, resulting in a reduction in energy dissipation. For Assembly H, Assembly H-2, having a panel zone strength 0.96 according to AISC 341-16[22], dissipates the
most energy as shown in Fig. 5(h), it undergoes a stable behavior as shown in Fig. 6(h), it has a balanced behavior; as the panel zone and beam share the inelastic deformation. Therefore, the AISC panel zone strength is valid in this case. For assemblies with strong panel zone the beam undergoes minor local buckling, resulting in a reduction in energy dissipation. 5.2. Local behavior A summary of the maximum values of RI measured at 6% story drift at the critical locations in the sub-models is shown in Fig. 7. It was found that the beam flange complete joint penetration CJP groove weld is the most critical location; at which the largest plastic strain and triaxial stress occurs. In all beam to column configurations weak panel zones had the largest RI, due to the large plastic strain and high triaxiality ratio at the flange CJP groove weld resulting from the large panel zone distortion, thus more potential for fracture. It was found that assemblies with balanced panel zones, designed according to specifications AISC 341-16 [22], had 1.8–3.2 times less RI than that of assemblies with weak panel zones. For assemblies with strong panel zones, most of the inelastic deformation occurs in the beam, thus the panel zone endures small inelastic distortions, therefore, less plastic strain and less triaxiality at the beam flange CJP groove weld. Thus, the assemblies with strong panel zones had 5–13 times less RI compared to the weak panel zone assemblies. 5.3. Results discussion From the parametric study results, it is found that in weak panel zone RBS beam to column connections, the panel zone sustains most of the inelastic deformation, thus it dissipates most of the energy, resulting in a stable hysteretic behavior. However, weak panel zone connections have less lateral load capacity, and have significantly higher potential for fracture.
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Effect of panel zone strength ratio
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Fig. 7
Parametric Study Rupture Index (RI).
On the other hand, in strong panel zone connections the beam endures large inelastic rotations causing local buckling, which results in strength degradation. Additionally, strong panel zone connections have less potential for fracture. The panel zone design strength according to AISC 341-16 [22] for each beam to column configuration at which the maximum energy dissipation is achieved as shown in Table 3. It is found that the panel zone design strength from AISC 360-16 [25] overestimates the panel zone strength in the cases
Table 3
of thick column flanges (larger than 34 mm). Therefore, in assemblies designed as balanced the panel zone undergoes large inelastic deformation and dissipates most of the energy, while beams remain almost elastic. While assemblies designed as strong panel zones have a balanced behavior; as the beams and the panel zone participate together in the energy dissipation. Consequently, a larger panel zone strength is required for thick column flange connections. As shown in Fig. 8 the balanced panel zone design with panel zone strength ranging
Summary of assemblies that achieved the maximum energy dissipation.
Assembly No
Column flange thickness (tcf)
Aspect ratio (db/dc)
SCWB ratio (Mc/Mb)
PZ design ratio Rv/Vpz
Assembly Assembly Assembly Assembly Assembly Assembly Assembly Assembly
27.9 20.1 43.7 52.6 24.4 22.2 38.1 34
0.94 0.62 1.87 1.32 1.22 1.00 0.98 0.86
1.32 2.02 1.50 1.93 1.27 1.41 1.63 2.49
1.05 1.15 1.44 1.49 0.88 0.99 1.1 0.96
A B C D E F G H
Fig. 8
(AISC)
Effect of Column Flange Thickness on the PZ Design Strength.
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Fig. 9
Fig. 10
Effect of SCWB Ratio on the PZ Design Strength.
Effect of aspect ratio on the PZ design strength.
from (0.9–1.05) according to AISC 341-16 [22] is proposed as it gives the best performance. While for assemblies with thick column flanges (larger than 34 mm), they contradict with this design, as the design specifications AISC 360-16 [25] overestimates the panel zone strength. Except for Assembly B, which doesn’t match this design concept, this is caused by the low slenderness ratios of the beam used (W21X132), therefore no local buckling occurred at the beam even for strong panel zone assemblies, resulting in a stable hysteretic behavior and larger energy dissipation. The SCWB ratio and the aspect ratio of the panel zone have no effect on the proposed panel zone design ratio, as shown in Figs. 9 and 10 respectively, as the large scatter in the results implies that the proposed panel zone design ratio is not affected by these configuration variables. 6. Conclusion and recommendations A parametric study is conducted in order to study the effect of panel zone strength on the performance of RBS steel MRF connection, and to evaluate the panel zone design concepts in design specifications and guidelines for different beam to column configurations in order to achieve the best performance; to increase the energy dissipated, to have a stable hysteretic behavior, and to reduce the potential for fracture. Furthermore, this study presents a range for the validity of the panel zone design strength formula suggested by the AISC 360-16 [25]. Moreover, the effect of other parameters such as
the column flange thickness, SCWB ratio, and aspect ratio on the assembly behavior is presented. From the analytical study results the following observations are concluded: It was found in most of the cases that panel zone design according to AISC 341-16 [22] is accurate, and results in the best performance regarding the stable behavior, large energy dissipation, and potential for fracture. In assemblies with weak panel zones, the panel zone undergoes large inelastic deformation, having a stable hysteretic behavior. The panel zone dissipates most of the inelastic energy while the beam remains almost elastic. The weak panel zone assemblies have less lateral load capacity, and a significantly higher potential for fracture. While assemblies with strong panel zones the beams endure large inelastic rotation, causing local buckling of the beam web at the RBS, resulting in strength degradation and having an unstable behavior. Furthermore assemblies with strong panel zones have less potential for fracture A proposed panel zone design strength validity range is suggested for AISC formula according to the thickness of the column flanges; in order to achieve the best performance and to avoid the problems of weak and strong panel zones. It was found that for thick column flanges (larger than 34 mm) the design specifications AISC [22,25] overestimate the panel zone strength. As such, AISC 360-16 [25] formula for panel zone strength is only valid for assemblies with column flange of thickness less than 34 mm. Therefore the
Please cite this article in press as: A.A. Soliman et al., Effect of panel zone strength ratio on reduced beam section steel moment frame connections, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.07.017
Effect of panel zone strength ratio panel zone design strength according to AISC 360-16 [25] requires further refinement in the cases of thick column flanges in order to achieve the best performance. All beam to column configurations agree with the proposed design concept except Assembly B, as in Assembly B when increasing the panel zone strength, the energy dissipation increases, and it has a stable behavior even for strong panel zone assemblies. This is caused by the low beam slenderness ratio; thus, the beam has a large inelastic rotation capacity without the occurrence of local buckling. Therefore, the beam slenderness ratio needs to be taken into consideration in order to determine the optimal panel zone design. It was found that the SCWB ratio and the aspect ratio have no effect on the behavior of the assembly, whereas the panel zone behavior is affected by other variables. Further studies are required to properly estimate the panel zone strength in the case of thick column flanges, besides the beam slenderness ratio should be taken into account while designing the RBS beam to column connection. Acknowledgement The authors gratefully acknowledge the support of Prof. Dimitrios Lignos, who provided advice and assistance on this research. References [1] AISC, Seismic Provisions for Structural Steel Buildings, Chicago, Illinois, ANSI/AISC 341, 2002. [2] H. Krawinkler, Shear in beam-column joints in seismic design of steel frames, Eng. J., AISC 15 (1978) 82–91. [3] C.-H. Lee, S.-W. Jeon, J.-H. Kim, C.-M. Uang, Effects of panel zone strength and beam web connection method on seismic performance of reduced beam section steel moment connections, J. Struct. Eng. 131 (2005) 1854–1865. [4] S. El-Tawil, E. Vidarsson, T. Mikesell, S.K. Kunnath, Inelastic behavior and design of steel panel zones, J. Struct. Eng. 125 (1999) 183–193. [5] E.P. Popov, Seismic Moment Connections for MomentResisting Steel Frames, Earthquake Engineering Research Center: University of California Berkeley, 1983. [6] V. Nikolaidou, C.A. Rogers, D.G. Lignos, Influence of welding of doubler plates to ASTM A913 450 MPa grade columns. Naples (Italy): Eurosteel, 2014. [7] X. Zhang, J.M. Ricles, L.-W. Lu, J.W. Fisher, Development of seismic guidelines for deep-column, Steel Moment Connect. (2004).
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Please cite this article in press as: A.A. Soliman et al., Effect of panel zone strength ratio on reduced beam section steel moment frame connections, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.07.017