Seismic Analysis and Performance of High Strength Composite Special Moment Frames (C-SMFs)

    Seismic Analysis and Behavior of High Strength Composite Special Moment Frames (C-SMFs) Zhichao Lai, Zhihui Huang, Amit H. Varma PII: DOI: Reference:

S2352-0124(16)30110-2 doi:10.1016/j.istruc.2016.12.004 ISTRUC 169

To appear in: Received date: Revised date: Accepted date:

15 May 2016 12 December 2016 13 December 2016

Please cite this article as: Lai Zhichao, Huang Zhihui, Varma Amit H., Seismic Analysis and Behavior of High Strength Composite Special Moment Frames (C-SMFs), (2016), doi:10.1016/j.istruc.2016.12.004

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ACCEPTED MANUSCRIPT Seismic Analysis and Behavior of High Strength Composite Special Moment Frames (CSMFs) Zhichao Lai1, Zhihui Huang2, and Amit H. Varma3

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Abstract

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Composite special moment frames (C-SMFs) usually consist of concrete-filled steel tube

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(CFT) columns, wide flange (WF) steel beams, and rigid beam-to-column connections. The current International Building Code (IBC 2015) prevents the use of high strength materials (steel

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yield stress Fy ≥ 450 MPa and concrete compressive strength f’c ≥ 70 MPa) for CFT columns in

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C-SMFs. This is due to the lack of knowledge of the overall seismic behavior of high strength CSMFs. Therefore, this paper evaluates the seismic behavior of high strength C-SMFs by

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conducting nonlinear static pushover (NSP) analyses and nonlinear time-history (NTH) using

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analytical models developed and benchmarked by the authors. The NSP analyses indicate that high strength C-SMFs had excellent lateral behavior. The effects of local degradation on the

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lateral load response are negligible when the roof drift is less than an upper bound limit. The NTH analyses indicate that the high strength C-SMFs satisfy the acceptance criteria (including the interstory drift ratios) specified in FEMA-350 and ASCE 7-10 for Immediate Occupancy, Life Safety, Collapse Prevention performance level when subjected to frequent occurrence earthquake (FOE), design basis earthquake (DBE), and maximum considered earthquake (MCE), respectively. Higher modes dominate the seismic performance of high strength C-SMFs, but dynamic instability is not an issue when the maximum roof drift is less than the plateau drift (∆p), which corresponds to the onset of negative stiffness in the lateral load-displacement response from the NSP analyses. 1

Ph.D., Postdoctoral Research Associate, Purdue University, Lyles School of Civil Engineering, West Lafayette, IN. [email protected] 2 Ph.D., PE, SE, Structus Inc., San Francisco, CA. [email protected] 3 Professor, Purdue University, Lyles School of Civil Engineering, West Lafayette, IN. [email protected]

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ACCEPTED MANUSCRIPT 1. Introduction

Composite special moment frames (C-SMFs) usually consist of concrete-filled steel tube

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(CFT) columns, wide flange (WF) steel beams, and rigid beam-to-column connections. As an

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innovative and efficient structural system, C-SMFs have been widely used around the world, for example, in (i) Wuhan International Financial Center in Wuhan, China, and (ii) Postal Office

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building in Quanzhou, China. In these high-rise buildings, the C-SMFs are used along with other

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systems (such as shear walls or core wall structures) to resist the lateral loads. Significant research has been conducted to investigate the behavior of the components

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(i.e., columns, beams, and connections) of C-SMFs. Experimental tests on CFT columns have been conducted by numerous researchers, including Janss and Anslijin [1], Lin [2], Fujimoto et

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al. [3], Song and Kwon [4], Schneider [5], Uy [6] [7], Kang et al. [8], Han et al. [9], and Tao [10] et al. among others. These research on CFT columns have been summarized independently by

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Nishiyama et al. [11], Kim [12], Gourley et al. [13], Hajjar [14], Lai et al. [15], and Lai and Varma [16] among others. Experimental tests on various types of connections for C-SMFs have also been conducted. These include: (i) connections with interior or exterior diaphragms tested by Yokoyama et al. [17], Morino et al. [18], Kawano and Matsui [19], Fujimoto et al. [20], and Fukumoto and Morita [21] among others; (ii) DST connections tested by Kanatani et al. [22], Koester [23], Peng [24] and Ricles et al. [25] among others; and (iii) through-beam connections tested by Alostaz [26] and Elremaily [27] among others. Significant research has also been conducted to investigate the behavior of C-SMFs. For example, Matsui [28] tested C-SMFs with varying steel tube slenderness (width-to-thickness) ratios, diaphragm types, and loading histories. The tests indicated that: (i) the C-SMFs had excellent seismic performance, and (ii) the steel tube slenderness limit of CFT columns could be

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ACCEPTED MANUSCRIPT established as 1.5 times that of hollow tubes. Kawaguchi et al. [29] tested four C-SMFs with rectangular CFT columns, WF steel beams, and connections with interior diaphragms. It was

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concluded that the C-SMFs had excellent earthquake resistance. Wang et al. [30] tested 12 C-

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SMFs with CFT columns, WF steel beams, and connections with exterior diaphragms. The parameters included in the tests were the cross-section shapes (rectangular or circular) of the

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CFT columns, steel ratios of the CFT column, and axial load ratios. The experimental results

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showed that: (i) C-SMFs had great seismic behavior, (ii) C-SMFs with circular CFT columns had better seismic behavior than the C-SMFs with rectangular CFT column, and (iii) the axial load

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ratios had significant effects on the seismic behavior of the C-SMFs. Herrera et al. [31] tested a four-story C-SMFs with rectangular CFT columns, WF steel beams, and double split tee (DST)

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connections. Results from the tests indicated that C-SMFs satisfy the desired requirements for Immediate Occupancy, Life Safety, and Collapse Prevention seismic performance levels.

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These prior research projects provide value insights into the behavior and design of CSMFs with conventional strength steel (Fy < 450 MPa) and concrete (f’c < 70 MPa) materials. However, there is limited research on C-SMFs with high strength CFT columns. Due to this lack of knowledge, the current International Building Code (IBC 2012 [32]) limits the use of high strength materials (Fy ≥ 450 MPa and f’c ≥ 70 MPa) in composite constructions. This paper summarizes the development and benchmarking of analytical models for investigating the seismic behavior of C-SMFs with CFT columns made from high strength materials (Fy ≥ 450 MPa and f’c ≥ 70 MPa). The analytical models were developed in DRAIN-2DX [33], and benchmarked with experimental results. The models accounted for various complexities of member and connection behavior, including local buckling of the steel tube and WF steel beam, degradation of the high strength concrete, and connection flexibility. The benchmarked models

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ACCEPTED MANUSCRIPT were used to conduct nonlinear static pushover (NSP) analyses and nonlinear time-history (NTH) analyses. The NSP analysis was conducted to investigate the lateral load behavior of high

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strength C-SMFs and evaluate the ASCE 7-10 [34] recommended seismic design parameters

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and the effects of local degradation. The local degradation includes steel tube local buckling, steel beam local buckling, and concrete softening (after the peak strength is reached). The NTH

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analyses were conducted to investigate the seismic behavior of high strength C-SMFs and

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evaluate the global and local performance using the acceptance criteria specified in FEMA-350 and ASCE 7-10 for Immediate Occupancy, Life Safety, Collapse Prevention performance level.

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The NTH analyses were also conducted to evaluate the higher mode effects and dynamic stability. Results from the NSP and NTH analyses are summarized in this paper and used to

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illustrate the seismic behavior of C-SMFs with high strength CFT columns. 2. Seismic design of high strength C-SMFs

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The prototype structure used in this research is an office building located in Los Angeles, California, USA. The site class is D, which represents a stiff soil profile. The risk category is II per with ASCE 7-10 [34]. The design loads were determined in accordance with ASCE 7-10 [34]. The design roof and floor dead load (including all attachments) was 4309 Pa. The design floor live load was 4788 Pa. The seismic loads were determined using the equivalent lateral force method per ASCE 7-10 [34]. The design spectral accelerations at the short period (SDS) and 1-s period (SD1) were 1.0 g and 0.6 g, respectively. The structure was designed using a response modification factor (R) of 8, an overstrength factor (0) of 3.0, a deflection amplification factor (Cd) of 5.5, and a story drift limit of 2.5%. These values are specified for steel special moment frames in ASCE 7-10 [34]. Two structure heights corresponding to low-rise (6-story, 22.9 m) and medium-rise (12-story, 45.3 m) construction were used for the prototype building. Fig. 1

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ACCEPTED MANUSCRIPT shows the elevation view. Distributed C-SMFs with orthogonal braced frames were used as the structure layout (see Fig. 2).

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The C-SMFs were designed using high strength square CFT columns, WF steel beams,

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and DST connections. Fig. 3 shows the typical details of DST connections. As shown, the Tee flange was attached to the column flange using pretensioned high strength through bolts, and the

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Tee stem was fillet welded to the beam flange. Previous research [22] [23] [24] [25] [35]

and the story drift capacity to exceed 5%.

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indicated that the DST connections enabled the beam plastic moment capacity to be developed,

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The prototype structure was designed in accordance with IBC 2012 [32], AISC 341-10 [36], AISC 360-10 [37], and ASCE 7-10 [34]. The CFT columns were subjected to both axial

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force and bending moment. They were designed using the beam-column interaction equations

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developed and verified by the authors in [38]. High strength steel tubes (Fy= 551.6 MPa) and

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concrete infill (f’c = 110.3 MPa) were used. The selected steel tube slenderness (width-tothickness) ratios were less than 32 to satisfy the AISC 341-10 [36] slenderness requirement for highly ductile member. The WF steel beams were designed in accordance with AISC 341-10 [36] and AISC 360-10 [37]. A992 steel (yield stress Fy = 344.8 MPa) rolled sections were used. The DST connections were designed according to the recommendations proposed by Peng [24] and Ricles et al. [25] and the procedures outlined in Fischer and Varma [35]. 31.75 mm diameter fully-tensioned A490 bolts (Fy = 1034.3 MPa) and A992 steel Tee sections were used. ASCE 7-10 [34] limits the fundamental period (T1) of a structure to be less than or equal to Tmax. This maximum permitted fundamental period (Tmax) can be calculated using Eq. (1), where Ta is the approximate fundamental period, hn is the structural height, and the coefficients Cu, Ct, and x can be calculated using ASCE 7-10 [34]. The resulting Tmax is 1.0 and 1.6 s for the

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ACCEPTED MANUSCRIPT 6- and 12-story C-SMFs, respectively. (1-1)

Ta  Ct hnx

(1-2)

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Tmax  CuTa

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However, the use of high strength materials is more efficient when the structures are

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designed with smaller member cross-sections. This results in reduced lateral stiffness and increased fundamental period. To evaluate the effects of flexibility (lateral stiffness), three

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designs with different fundamental periods (T1) were used for both the 6-story and 12-story high

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strength C-SMFs. The first design achieved 0.9 ≤ T1/Tmax ≤ 1.0, and is referred as rigid design. The second design achieved 1.0 < T1/Tmax ≤ 1.15, and is referred as flexible design. The third

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design achieved T1/Tmax > 1.15, and is referred as highly flexible design. The fundamental period

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of the rigid design satisfied the ASCE 7-10 [34] requirement, while the fundamental period of the flexible and highly flexible design exceeded the ASCE 7-10 [34] requirement. The structural

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details of each design are summarized in Table 1. As shown, the CFT column sizes (i.e., the diameter and tube thickness) decrease as the design changes from rigid to highly flexible, while the beam sizes are the same.

3. Analytical models for high strength C-SMFs This section summarizes the development and benchmarking of analytical models for high strength C-SMFs. For additional details of the analytical models, please refer to Huang [39]. These models were developed using DRAIN-2DX [33], which is a general-purpose nonlinear structural analysis program. DRAIN-2DX uses event-to-event solution strategies for conducting static or dynamic structural analysis. The analytical models for high strength C-SMFs consisted of the models for the high strength CFT columns, WF steel beams, and the DST connections. The high strength CFT

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ACCEPTED MANUSCRIPT columns and the WF steel beams were modeled using fiber-based beam-column elements (fiber elements). The behavior of these fiber elements was defined by specifying the corresponding

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stress-strain (σ-ε) relationships, which included envelopes of the cyclic responses and the

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hysteresis rules. The DST connections were modeled using spring elements. The behavior of the spring elements was defined by specifying the force-displacement responses. In a previous

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research [39], the authors have developed the σ-ε relationships for the high strength CFT

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columns and WF steel beams, and the force-displacement responses for the DST connections. The σ-ε relationships for the high strength CFT columns accounted for the effects of concrete

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confinement, steel tube yielding and local buckling, and strength degradation. The σ-ε relationships for the WF steel beams accounted for the effects of steel hardening and the inelastic

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flange and web buckling. The force-displacement responses for the DST connections accounted

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for the effects of bolt pretension and contact interaction between components. Details of these σ-

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ε relationships and force-displacement responses can be found in [39]. The fiber element was developed by Prakash et al. [33], and modified by Kurama et al. [40] and Cordero et al. [41] to more accurately model the behavior of steel, reinforced concrete, and steel-concrete composite members. The fiber element is a distributed-plasticity based finite element with a flexibility-based formulation. The mathematical formulation has been discussed in detail in Kurama et al. [40]. Assumptions of the fiber element include: (i) plane sections remain plane, (ii) slip does not occur between the materials in the cross section, (iii) inelastic shear deformations are negligible, and (iv) the materials in the cross section are subjected to uniaxial stress-strain states. Fig. 4 shows the schematic description of a fiber element. As shown, the length of the fiber element is defined by two end nodes. The element length is divided into several segments,

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ACCEPTED MANUSCRIPT and the behavior of each segment is represented by a slice located at the mid-length of the segment. For each slice, the cross section is discretized into layers of fibers. Each fiber has an

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associated area, the distance from the centroid, and the uniaxial stress-strain relationship. The

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force-deformation behavior of a slice is obtained by integrating the fiber stress-strain behavior over the cross section. The force-deformation behavior of a fiber element is obtained by

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integrating the slice force-deformation response over the length.

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Fig. 5 shows the overall beam-column subassembly model, which consists of four element groups. The CFT column was modeled by Element Group 1 (i.e., fiber elements G1-1

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and G1-2). Nodes 8 and 11 represented the story mid-height of the frame. The panel zone was modeled by Element Group 2 (i.e., fiber elements G2-1 and G2-2). The WF steel beams were

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modeled by Element Group 3 (i.e., fiber elements G3-1, G3-2, G3-3, and G3-4). Nodes 3 and 5 were placed at the edges of the column to account for the column depth. The DST connection

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was modeled by Element Group 4 (i.e., fiber elements G4-1, G4-2, G4-3, and G4-4). The welding between the Tee stems and the beam flange was modeled by coupling slave nodes 12 and 14 to master node 2, and coupling slave nodes 13 and 15 to master node 6. The bolt connections between the Tee flanges and the column flanges were modeled by using shared nodes 9 and 10. It should be noted that the effect of slab on the behavior of the connection and the overall assembly is not considered in the current study, but is recommended for future research. The analytical models were benchmarked by using them to predict the lateral forcedisplacement behavior of C-SMFs sub-systems tested by Peng [24]. Fig. 6 shows representative comparisons. These comparisons indicate that the analytical models can reasonably predict the cyclic response of the C-SMF sub-system. The models underestimate pinching effects and

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ACCEPTED MANUSCRIPT slightly overestimate the stiffness during unloading and reloading due to the limitations associated with the cyclic stress-strain rules implemented in DRAIN-2DX [33] for the fiber

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element. The fiber element cannot accurately model the effects of cyclic local buckling, i.e.,

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strength and stiffness degradation due to local folding and straightening of the plates, on the response of structural members. As shown in Fig. 7, the cyclic stress-strain relationships do not

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account for: (i) strength degradation of the envelope due to cyclic local buckling, (ii) stiffness

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degradation when unloading from compression or from tension, or when reloading from compression to tension. The hysteresis rules only account for the stiffness degradation during

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reloading from tension to compression by using the factor α. 4. Nonlinear static pushover (NSP) behavior of high strength C-SMFs

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Local degradation, for example, steel tube local buckling, steel beam local buckling, and concrete softening, can potentially have unfavorable effects on the overall NSP behavior of high

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strength C-SMFs. In order to evaluate the relative influence of these local degradations, five NSP analyses were conducted for each of the three designs of the 6- and 12-story C-SMFs. The five analyses consisted of the following cases: (i) no degradation, (ii) concrete softening only, (iii) concrete softening and steel beam local buckling, (iv) concrete softening and steel tube local buckling, and (v) concrete softening, steel beam local buckling, and steel tube local buckling. The concrete softening, steel beam local buckling, and steel tube local buckling was specified by using the effective  relationships developed by the authors in [39]. These effective  relationships have negative post-peak slopes in compression. If no local degradation was required, then the post-peak responses of the effective  relationships were modified to remain constant (i.e., perfectly plastic). The NSP analyses were conducted in accordance with ASCE 41-13 [42] using the

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ACCEPTED MANUSCRIPT benchmarked analytical models. The second order (P-) effects were included. The applied lateral loads had vertical distributions (as shown in Fig. 8) proportional to the equivalent lateral

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forces (specified in ASCE 7-10 [34]). Figs. 9 and 10 show the results from the NSP analyses of

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the 6- and 12-story high strength C-SMFs. In these figures, Vs is the base shear, and W is the effective seismic weight. These results indicate that: The effect of concrete softening is negligible.

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When the roof drift angle is less than an upper bound limit, local degradation have negligible

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influence on the overall NSP pushover behavior. This upper bound limit is 1.5%, 1.5%, and

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1.0% for the rigid design, flexible design, and highly flexible design, respectively. When the roof drift angle is greater than the upper bound limit, local degradation result in the

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decrease of the peak strength and post-peak stiffness. Steel beam local buckling has the most significant influence on the overall NSP behavior, followed by the steel tube local buckling.

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Fig. 9 (a) and Fig. 10(a) compare the normalized base shear-roof drift angle responses of rigid, flexible, and highly flexible designs of the 6- and 12-story high strength C-SMFs. These responses were obtained from NSP analyses that included all local degradation effects. These figures indicate that all designs result in significant overstrength as compared to the design base shear (Vs). The rigid designs have the best normalized base shear-roof drift angle response, i.e., the highest strength and initial stiffness. As the design changes from rigid to highly flexible, the peak strength decreases, and the post-peak slope becomes more negative. For the 6-story CSMFs, the strength degradation is negligible (less than 5%) when the roof drift angle is less than 4.5%, 4.0%, and 1.5% for the rigid, flexible and highly flexible design, respectively. For the 12story C-SMFs, the strength degradation is negligible (less than 5%) when the roof drift angle is less than 6.0%, 5.5%, and 3.0% for the rigid, flexible and highly flexible design, respectively.

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ACCEPTED MANUSCRIPT Figs. 9 and 10 also indicate that the base shear-roof drift angle responses of the highly flexible designs have significant negative post-peak slopes. This is due to the second-order (P- effect.

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ASCE 7-10 [34] specifies the minimum requirements on design factors for C-SMFs.

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These include the deflection amplification factor (Cd≥5.5) and overstrength factor (0≥3). To

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evaluate the seismic design of the 6- and 12-story high strength C-SMFs, the specified minimum values of these factors were compared to the values obtained from the NSP analyses. Table 2

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summarizes the comparisons. In Table 2, the displacement ductility ratio () are also included. The ductility ratio was calculated as the ratio of the target displacement to yield displacement

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(roof displacement corresponds to ∆y, as explained later in Section 5.3). As shown, all designs (except the highly flexible 6-story C-SMFs) satisfy the ASCE 7-10 [34] requirements (0≥3 and

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Cd≥5.5) for C-SMFs. The rigid and flexible 6- and 12-story high strength C-SMFs have good

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ductility ( > 4), while the highly flexible designs have lower ductility ( < 3). The flexible

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designs of the 6- and 12-story high strength C-SMFs are acceptable despite their slightly negative post-peak slope. The highly flexible designs are not recommended due to their low ductility and significant negative post-peak slope. 5. Nonlinear time history (NTH) analyses of high strength C-SMFs The NSP analyses provide valuable insights into the lateral load behavior of high strength C-SMFs, and the effects of local degradation. However, the NSP analyses cannot account for higher mode effects and cyclic responses, which influence the seismic performance of high strength C-SMFs. In this section, NTH analyses were conducted on the flexible 6- and 12-story high strength C-SMFs using the benchmarked analytical models. In the NTH analyses, the SAC ground motion records (Somerville et al. [43]) for Los Angeles were used. Three sets of ground motions corresponding to three earthquake levels were

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ACCEPTED MANUSCRIPT selected from the SAC ground motion records: the maximum considered earthquake (MCE), the design basis earthquake (DBE), and the frequent occurrence earthquake (FOE). The MCE, DBE,

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and FOE have a probability of exceedance of 2%, 10%, and 50% in 50 years, respectively. Table

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3 summarizes the selected ground motions. Each ground motion record consists of two components: strike normal and strike parallel components. The strike normal component was

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used in the NTH analyses in this research because its spectral value is usually greater than that of

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the strike parallel component. For additional details of these ground motions, please refer to Somerville et al. [43].

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The original SAC ground motions, which match with a least-square error fit to the USGS mapped values at 0.3, 1.0, 2.0, and 4.0 s, are not suitable for the flexible 6- and 12-story high

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strength C-SMFs, which have a fundamental period of 1.02 s and 1.70 s, respectively. Therefore, the original SAC ground motions were rescaled so that their spectral values match with a least-

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square error fit to the response spectra at 0.3, 1.0, 1.5 and 2.0 s. The scaling procedure followed Somerville et al. [43]. The scale factor SF is given by Eq. (2). In this equation, Starget,T and SGM, T are the spectral values of the target spectrum and the ground motion spectrum being scaled, respectively, for a period equal to T in seconds.

SF  (

St arget, 0.3 SGM , 0.3

) 0.1 (

St arget,1.0 SGM ,1.0



St arget,1.5 SGM ,1.5



St arget, 2.0 SGM , 2.0

) 0.3

(2)

5.1 Performance evaluation Three performance levels were evaluated in accordance with ASCE 41-13 [42]. These include the Immediate Occupancy performance level, Life Safety performance level, and Collapse Prevention performance level. The Immediate Occupancy performance level, defined as the post-earthquake damage state in which only very limited structural damage has occurred, should be achieved for C-SMFs subjected to FOE ground motions. The Life Safety performance 12

ACCEPTED MANUSCRIPT level, defined as the post-earthquake damage state in which a structure has damaged components but retains a margin against the onset of partial or total collapse, should be achieved for C-SMFs

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subjected to DBE ground motions. The Collapse Prevention performance level, defined as the

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post-earthquake damage state in which a structure has damaged components and continues to support gravity loads but retains no margin against total collapse, should be achieved for C-

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SMFs subjected to MCE ground motions.

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In order to determine whether the C-SMFs satisfy the desired performance level, both the global and local performance were evaluated. The global performance is limited by the interstory

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drift. The local performance includes the connection and column performance. The global and local performance of C-SMFs for the Immediate Occupancy and Collapse Prevention

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performance level were evaluated using the confidence level, as recommended in FEMA-350 [44]. The confidence level was calculated per Table 4-6 in FEMA-350 [44] using the uncertainty

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parameter (βUT) and the factored demand-to-capacity ratio (λ). The uncertainty parameter (βUT) is related to the building’s configuration, the structural framing system (Ordinary Moment Frame or Special Moment Frame), the type of analytical procedure employed, and the performance level being evaluated. The factored demand-to-capacity ratio (λ) is defined as:



 a D C

(3)

In Eq. (3), C is the capacity of the structure, D is the demand for the structure calculated from structural analysis, γ is the demand variability factor that accounts for the variability inherent in the prediction of demand related to assumptions made in structural modeling and prediction of the character of ground shaking, γa is the analysis uncertainty factor that accounts for

the bias and uncertainty inherent in the analytical technique, and ϕ is the resistance factor that accounts for the uncertainty and variability in the prediction of structural capacity. Table 4 13

ACCEPTED MANUSCRIPT summarizes the minimum confidence levels recommended in FEMA-350 [44]. Due to the fact that FEMA-350 [44] does not recommend the confidence level for the

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Life Safety performance level, ASCE 7-10 [34] was used instead to evaluate the Life Safety

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performance level. ASCE 7-10 [34] recommends the interstory drift limits to evaluate the global performance. However, it does not provide any recommendation to evaluate the local

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evaluated for the Life Safety performance level.

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performance. Therefore, only the global performance limited by the interstory drift was

5.1.1 Global performance

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Tables 5 and 6 summarize the global performance evaluation for the Immediate Occupancy and Collapse Prevention performance level, respectively. In these two tables, the

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capacities are given by FEMA-350 [44], and the demands are the median values obtained from the NTH analyses. According to ASCE 7-10 [34], the median values computed from the NTH

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analyses may be used as the demand if at least seven ground motions are analyzed. In this research, 10 ground motions were used for all three earthquake levels (i.e., FOE, DBE, and MCE). Therefore, the median values were used as demands. As shown in Tables 5 and 6, the confidence levels for both the flexible 6-story and 12-story high strength C-SMFs satisfy the FEMA-350 [44] requirements.

For the flexible 6-story and 12-story C-SMFs subjected to DBE ground motions, the maximum of the median values of the interstory drift was 1.09% and 0.85%, respectively. These values were less than the drift limit (2%) for the Life Safety performance level, as specified in ASCE 7-10 [34]. These evaluations showed that the global performance of the flexible 6-story and 12-story high strength C-SMFs satisfied: (i) the FEMA-350 [44] acceptance criteria for the Immediate

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ACCEPTED MANUSCRIPT Occupancy performance level when subjected to FOE ground motions, (ii) the FEMA-350 [44] acceptance criteria for the Collapse Prevention performance level when subjected to MCE

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ground motions, and (iii) the ASCE 7-10 [34] acceptance criteria for the Life Safety performance

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level when subjected to DBE ground motions. 5.1.2 Local performance

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The local performance of the flexible 6- and 12-story high strength C-SMFs subjected to

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FOE and MCE ground motions was evaluated using the confidence level per FEMA-350 [44]. The local performance includes the connection performance and the column compression

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performance. Similar to the global performance evaluation, the local connection performance was limited by the interstory drift. Tables 7 and 8 summarize the local connection performance

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evaluation for the 6- and 12-story C-SMFs, respectively. In these two tables, the capacities are given by FEMA-350 [44], and the demands are the median values obtained from the NTH

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analyses. The local interstory drift capacities given by FEMA 350 [44] were determined from cyclic tests of full-size connection assemblies. This is explained as follows. The local Immediate Occupancy level capacity is defined as the inter-story drift angle at which any one of the following behavior occurs: (i) onset of local flange buckling of beams, (ii) degradation of moment-resisting capacity of the assembly to a value below the nominal moment-resisting capacity, or (iii) initiation of fracture of bolts, welds, or base metal that results in significant strength degradation of the assembly. The local Collapse Prevention level capacity is defined as the interstory drift angle at which the connection completely fails, characterized by an inability of the connection to maintain the integrity of the beam-to-column connection under gravity loading. As shown in Tables 7 and 8, the confidence levels for both the 6- and 12-storty C-SMFs are greater than 50% for the Immediate Occupancy and Collapse Prevention performance level,

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ACCEPTED MANUSCRIPT as required by the FEMA-350 [44]. Tables 9 and 10 summarize the local column compression performance evaluation for the

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flexible 6- and 12-story high strength C-SMFs, respectively. In these two tables, the capacities

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were calculated using the beam-column interaction equations developed and verified by the authors in [38], and the demands are the median values obtained from the NTH analyses. As

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shown, the confidence levels for the 6-story C-SMFs are greater than 50% and 90%, for the

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Immediate Occupancy and Collapse Prevention performance level, respectively, as required by FEMA-350 [44]. The confidence levels for the 12-story C-SMFs are greater than 50% and 90%,

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for the Immediate Occupancy and Collapse Prevention performance level, respectively, as required by FEMA-350 [44].

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The local column compression performance was also compared with experimental results from CFT beam-columns tested by Varma [45]. Fig. 11 shows representative comparisons of the

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normalized moment-curvature responses for the left corner column of the 6- and 12-story CSMFs. In this figure, values of the yield moment (My) and yield curvature (ϕ y) were determined from experimental tests when the steel tube first yielded in tension. The analytical results were obtained from NTH analysis of C-SMFs subjected to MCE ground motion lpvst03 (see Table 3). The experimental results were obtained from the cyclic test of the CFT beam-column specimen CBC-32-80-20 conducted by Varma [45]. This specimen had similar properties to the high strength CFT columns used in this study: the axial load ratio was 0.2, the steel yield stress (Fy) was 551.6 MPa, the concrete compressive strength (f’c) was 110.3 MPa, and nominal steel tube slenderness (i.e., width-to-thickness) ratio was 32. The axial load ratio is the ratio of the applied axial load (P) to the nominal axial compressive strength of CFT column (Po). The experimental test of specimen CBC-32-80-20 showed that the following significant

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ACCEPTED MANUSCRIPT events occurred during the cyclic beam-column test: (A) concrete went into tension, (B) steel tube flange in compression yielded, (C) extreme concrete compression fiber reached cylinder

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failure strain, (D) steel tube flange in tension yielded, (E) concrete crushing initiated, (F) steel

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tube flange local buckling occurred, (G) steel tube web local buckling occurred, (H) steel tube corner yielded, and (I) steel tube corner cracked or fractured. Fig. 11 identifies events D-H. As

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shown, local buckling of the steel tube flange occurs (event F) in the left corner column of the 6-

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story C-SMFs subjected to MCE ground motion lpvst03. Concrete crushing initiates (event E) in the left corner column of the 12-story C-SMFs subjected to MCE ground motion lpvst03. In both

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cases, failure did not occur in the CFT column. This agrees with the performance evaluation using the confidence levels.

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Evaluations presented in this section showed that the local performance of the flexible 6and 12-story high strength C-SMFs satisfied the FEMA-350 [44] acceptance criteria for

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Immediate Occupancy (when subjected to FOE ground motions) and Collapse Prevention performance level (when subjected to MCE ground motions). The local performance of the 6and 12-story C-SMFs for the Life Safety performance level was not evaluated because no acceptance criteria are available. 5.2 Higher mode effects

Results from the NTH analyses of the flexible 6-story high strength C-SMFs are shown in Fig. 12, and discussed as follows. Fig. 12(a), (b), and (c) show the interstory drift envelopes of the flexible 6-story high strength C-SMFs subjected to MCE, DBE, and FOE ground motions, respectively. Each figure includes the interstory drift envelopes for ten ground motions of the same magnitude and highlights the minimum, median, and maximum responses. Fig. 12(d) summarizes the median interstory drift envelopes for all three sets of ground motions.

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ACCEPTED MANUSCRIPT Fig. 12(a) shows that the maximum interstory drift for most of the MCE ground motions occur at the 2nd story and the interstory drift reduces as the height increases. This indicates that

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the first mode dominates the performance of the 6-story C-SMFs subjected to MCE ground motions. Fig. 12(b) shows that the maximum interstory drifts for two DBE ground motions

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(llpgil3 and lpsdhsp) occur at the 5th story and the interstory drift reduces as the height decreases.

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This means that the first mode has less influence on the performance of the 6-story C-SMFs

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subjected to DBE ground motions. Fig. 12 (c) shows that the maximum interstory drift for most of the FOE ground motions occurs in the 4th or 5th story and the interstory drift reduces as the

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height decreases. This means that the higher modes have significant influences on the performance of the 6-story C-SMFs subjected to FOE ground motions.

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Therefore, it can be summarized from Fig. 12 that the effects of higher modes on the performance of the 6-story C-SMFs depend on the earthquake levels. The first mode dominates

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the performance when the C-SMFs are subjected to MCE ground motions. However, the effects of higher modes become more obvious when the C-SMFs are subjected to DBE and FOE ground motions.

Results from the NTH analyses of the flexible 12-story high strength C-SMFs are shown in Fig. 13, and discussed as follows. Fig. 13(a), (b), and (c) show the interstory drift envelopes of the flexible 12-story high strength C-SMFs subjected to MCE, DBE, and FOE ground motions, respectively. Fig. 13(d) summarizes the median interstory drift envelopes for all three sets of ground motions. Fig. 13 indicate that the higher modes dominate the performance of the 12-story C-SMFs subjected to all levels of ground motions. Similar to the 6-story C-SMFs, the effects of higher modes on the global performance of the 12-story C-SMFs depend on the earthquake levels. The

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ACCEPTED MANUSCRIPT higher modes result in the maximum interstory drifts to occur at the mid-height stories for the MCE ground motions, and at the top stories for the FOE and DBE ground motions.

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Fig. 12 along with Fig. 13 indicate that the higher modes have a greater influence on the

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12-story C-SMFs than the 6-story C-SMFs. These figures also indicate that the maximum interstory drifts for both the 6- and 12-story high strength C-SMFs are less than 1%, 1.5% and

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3% when subjected to FOE, DBE, and MCE ground motions.

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5.3 Dynamic stability evaluation

Previous NSP analyses presented in Section 4 indicated that the flexible 6- and 12-story

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high strength C-SMFs had base shear-roof drift angle responses with negative post-peak slopes. Therefore, dynamic instability of these structures may occur due to the second order (P-∆)

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D

effects. This section evaluates the dynamic stability of the flexible 6- and 12-story high strength C-SMFs by comparing the base shear-roof drift angle responses obtained from the NSP and NTH

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analyses.

Fig. 14 shows the normalized base shear-story drift angle responses for the 6-story CSMFs. As shown, the base shear-roof drift angle response exhibits a relatively short yield (constant strength) plateau until a roof drift angle of 0.025. After that, the top two stories experience unloading (see Fig. 14(b)), the story drifts in the bottom three stories increase (see Fig. 14(a)), and the lateral loads applied to the structure have to be reduced to accommodate the increasing P-∆ effects in the bottom three stories. Fig. 14 indicates that the dynamic instability of the flexible 6-story high strength C-SMFs may occur if the roof drift angle is greater than the plateau drift angle (∆p) of 0.025. Similarly, Fig. 15 shows the normalized base shear-story drift angle responses for the 12story C-SMFs. As shown, the base shear-roof drift angle response exhibits a relatively long yield

19

ACCEPTED MANUSCRIPT plateau until a roof drift angle of 0.042. After that, the top two stories experience unloading (see Fig. 15(d)), the story drifts in the 2nd to 9th story increase (see Fig. 15(a)-(c)), and the lateral

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loads applied to the structure have to be reduced to accommodate the increasing P-∆ effects in

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the bottom stories. Fig. 15 indicates that the dynamic instability of the flexible 12-story high strength C-SMFs may occur if the roof drift angle is greater than the plateau drift angle (∆p) of

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0.042 rad.

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The NSP base shear-roof drift angle responses of the flexible 6- and 12 story high strength C-SMFs were idealized into a bilinear curve, as shown in Fig.16. The bilinear

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idealization was developed using an iterative procedure that approximately balances the area above and below the curve. The idealized bilinear curve was defined by two anchor points (Vy,

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∆y and Vt, ∆t), where Vy is the base shear corresponding to the maximum yield strength of the

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drift angle.

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structure, ∆y is the yield drift angle, Vt is the base shear corresponding to ∆t, and ∆t is the target

The dynamic stability of the flexible 6- and 12 story high strength C-SMFs were evaluated by comparing the base shear-roof drift angle responses obtained from NSP analyses and NTH analyses, using the procedure as follows. If the maximum roof angle obtained from NTH analyses is less than the yield drift angle (∆y), then the P-∆ effects are negligible and dynamic instability is an unlikely event. If the maximum roof angle is greater than the yield drift angle (∆y) but less than or equal to the plateau drift angle (∆p, 0.025 for the 6-story C-SMFs, and 0.042 for the 12-story C-SMFs), then the P-∆ effects become significant. However, dynamic instability is unlikely to occur because the P-∆ effects have not fully offset the 1st order shear resistance, and the global base shear-drift angle response has not become negative. If the maximum roof angle is greater than the plateau drift angle (∆p), then the P-∆ effects dominate

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ACCEPTED MANUSCRIPT the global response of the structure, and dynamic instability may occur. It should be noted that if the base shear-roof drift angle response obtained from the NSP analyses does not have negative

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post-peak slopes, then dynamic instability will not occur. If the base shear-roof drift angle

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response obtained from the NSP analyses does not have any yield plateau, then dynamic instability may occur if the maximum roof drift angle is greater than the angle corresponds to the

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peak strength.

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Fig. 16 shows representative comparisons of the base shear-roof drift angle responses obtained from the NSP and NTH analyses for the flexible 6- and 12-story high strength C-SMFs

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subjected to MCE ground motion lpvst03. As shown, the maximum roof drift is greater than the

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instability is unlikely to occur.

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yield drift angle (∆y) but less than or equal to the plateau drift angle (∆p). Therefore, dynamic

Tables 11 and 12 summarize the evaluations of the flexible 6- and 12-story high strength

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C-SMFs subjected to all 30 ground motions. These evaluations show that: (i) dynamic instability is unlikely to occur for the 6- and 12-story C-SMFs subjected to any of the 30 ground motions; (ii) when subjected to the MCE ground motions, the 6- and 12-story C-SMFs had entered the yield plateau in most cases, i.e., maximum roof drift angles were greater than the yield drift angle (∆y) but less than or equal to the plateau drift angle (∆p); (iii) when subjected to the DBE or FOE ground motions, the 6- and 12-story C-SMFs had maximum roof angles that were less than the yield drift angle (∆y) in most cases. It is important to note that although the high strength CSMFs had entered the yield plateau when subjected to MCE ground motions, the desired global and local performance objectives could still be met (as discussed previously in Section 5.1).

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ACCEPTED MANUSCRIPT 6. Summary and Conclusions This paper investigated the seismic behavior of high strength C-SMFs by conducting

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NSP and NTH analyses. Both the NSP and NTH analyses were conducted using analytical

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models developed and benchmarked previously by the authors in [39]. The NSP analyses were conducted to investigate the lateral behavior and the effects of local degradation. Results from

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the NSP analyses indicated that the rigid and flexible 6- and 12-story high strength C-SMFs had

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excellent lateral behavior, while the highly flexible high strength C-SMFs had significant negative post-peak slopes and were therefore not recommended. The seismic design parameters

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(overstrength factor 0 and displacement amplification factor Cd) of the rigid and flexible 6- and 12-story high strength C-SMFs are conservative with respect to the ASCE 7-10 [34]

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recommendations (0≥3 and Cd≥5.5)

The NSP analyses also indicated that the effects of local degradation on the lateral

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behavior 6- and 12-story high strength C-SMFs were negligible when the roof drift was less than 1.5%, 1.5%, and 1.0% for the rigid design, flexible design, and highly flexible design, respectively. When the roof drift was greater than these drift limits, local degradation resulted in the decrease of the peak strength and post-peak stiffness. The steel beam local buckling had the most significant influence on the overall NSP behavior, followed by the steel tube local buckling. The influence of concrete softening was negligible. The NTH analyses were conducted to evaluate the seismic performance, higher mode effects, and dynamic stability of the flexible 6- and 12-story high strength C-SMFs. The seismic performance was evaluated according to FEMA-350 [44] for the Immediate Occupancy and Collapse Prevention performance level, and according to ASCE 7-10 [34] for the Life Safety performance level. The evaluations showed that the high strength C-SMFs satisfied the

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ACCEPTED MANUSCRIPT acceptance criteria for Immediate Occupancy, Life Safety, Collapse Prevention performance level when subjected to FOE, DBE, and MCE ground motions, respectively.

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The NTH analyses indicated that the higher modes dominated the performance of (i) the

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6-story C-SMFs subjected to FOE and DBE ground motions, and (ii) the 12-story C-SMFs subjected to FOE, DBE, and MCE ground motions. The NTH analyses also indicated that the

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higher modes had greater influence on the 12-story C-SMFs than the 6-story C-SMFs, and that

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the maximum interstory drifts for both the 6- and 12-story high strength C-SMFs were less than 1%, 1.5% and 3% when subjected to FOE, DBE, and MCE ground motions, respectively.

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Finally, comparisons of the base shear-roof drift angle responses obtained from the NSP and NTH analyses indicated that dynamic instability of the high strength C-SMFs may occur if

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the maximum roof drift was greater than the plateau drift (∆p). For the flexible 6- and 12-story

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high strength C-SMFs investigated in this research, the plateau drift (∆p) was 0.025 and 0.042,

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respectively. The maximum roof drifts for the 6- and 12-story high strength C-SMFs subjected to MCE, DBE or FOE ground motions were all less than the corresponding plateau drift. Therefore, dynamic instability was unlikely to occur. Nomenclature C

Capacity of the structure

Cd

Deflection amplification factor

D

Demand of the structure calculated from structural analysis

Fy

Steel yield stress

P

Axial force

SGM,T

Spectral values of the ground motion spectrum

Starget, T

Spectral values of the target spectrum

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Scale factor

T1

Fundamental period

Ta

Approximate fundamental period

Tmax

Maximum permitted fundamental period

Vs

Base shear

W

Effective seismic weight

f'c

Concrete uniaxial compressive strength

hn

Structure height

α

Stiffness degradation parameter

γ

Demand variability factor

γa

Analysis uncertainty factor

μ

Ductility

ϕ

Resistance factor

Ω0

System overstrength factor

∆

Displacement

SC

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MA

D

TE

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Washington, DC., USA: 2000.

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W27x84

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Fig. 1. Structural elevation of the flexible design of the 12-story high strength C-SMFs (unit: m)

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X X X X X X

X X X X X X

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9.1

Pin connection

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Moment connection

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XXX XXX

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Brace

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Fig. 2. Typical structural layout of high strength C-SMFs structures (unit: m)

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RI 47.6 mm.

95.25 mm.

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381 mm.

584.2 mm.

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44.5 mm.

44.5 mm.

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Fig. 3. Typical details of DST connections

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47.6 mm.

333.4 mm.

88.9 mm.

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88.9 mm.

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31.75 mm dia. A490 tension bolt (typ.)

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End node j

End node i

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X

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Segment Slice (Represented by the (Discretized into fibers) slice in the center)

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Fig. 4. Schematic description of the fiber element

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Slave node

Slaved DOF

2

12, 14

x, y, θ

6

13, 15

x, y, θ

Description

G1

CFT column

G2

Panel zone

G3

Beam

4

G4

DST

G1-2

Y

θ

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G4-2 13

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Fig. 5. Beam-column subassembly model in DRAIN-2DX

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x, y

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2 G3-2 3

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800 600

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0

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Lateral load, kN

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-100.0 0.0 100.0 Lateral displacement, mm

Fiber 200.0

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Fiber -100.0 0.0 100.0 Lateral displacement, mm

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(b) Fig. 6. Representative comparisons of lateral load-displacement response from experimental test and fiber analysis for specimens from Peng [19]: (a) Specimen 5 and (b) Specimen 6.

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α =0.9

Unloading: no stiffness degradation

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Compression

Unloading: no stiffness degradation

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Reloading: no stiffness degradation

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Fig. 7. Hysteresis rules in Drain-2Dx

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MA

NU

Fig. 8. Applied lateral force for the 6-story high strength C-SMFs

37

Highly flexible

Design base shear, Vs /W

0.02 0.04 Roof drift angle

0.06

Concrete softening

0.5

Beam and tube Beam local Tube local buckling local buckling buckling

0.4 0.3

Design base shear, Vs /W

0.2

0.1 0.0 0.00

0.02

Beam and tube Beam local Tube local buckling local buckling buckling

Design base shear, Vs /W

0.02

0.04

0.06

0.04

0.06

D

Roof drift angle

(b)

No degradation Concrete softening

0.5

NU

0.6

Normalized base shear, V/W

0.7

0.6

MA

Normalized base shear, V/W

No degradation

Concrete softening

Roof drift angle

(a) 0.8

No degradation

PT

Flexible

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.00

RI

Rigid

SC

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.00

Normalized base shear, V/W

Normalized base shear, V/W

ACCEPTED MANUSCRIPT

0.4 0.3

Beam and tube local buckling

Beam local buckling Tube local Design base shear, Vs /W buckling

0.2 0.1

0.0 0.00

0.02

0.04

0.06

Roof drift angle

AC CE P

TE

(c) (d) Fig. 9: (a) NSP behavior of the 6-story high strength C-SMFs, and effects of local degradation on the NSP behavior of the 6-story high strength C-SMFs with: (b) rigid, (c) flexible, and (d) highly flexible design

38

ACCEPTED MANUSCRIPT

0.4

Highly flexible

0.3 0.3 0.2 0.2

Design base shear, Vs /W

0.1 0.1 0.0 0.00

0.02

0.04

0.06

0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.00

Roof drift angle

0.3

Beam local Tube local buckling buckling

Design base shear, Vs /W

0.1 0.1 0.0 0.00

0.02

0.04 Roof drift angle

MA

0.2

0.2

0.02

0.04

0.06

0.06

(b)

No degradation

Concrete softening

0.4 0.3

NU

0.4 Beam and tube local buckling

Design base shear, Vs /W

SC

Normalized base shear, V/W

0.4

D

Normalized base shear, V/W

Concrete softening

No degradation

0.4

0.3

Beam and tube Beam local Tube local buckling local buckling buckling

Roof drift angle

(a) 0.5

Concrete softening

No degradation

PT

Flexible

RI

Rigid

0.4

Normalized base shear, V/W

Normalized base shear, V/W

0.5

0.3 0.2

Beam and tube local buckling

Beam local buckling

0.2

Tube local buckling

Design base shear, Vs /W

0.1 0.1 0.0 0.00

0.02

0.04

0.06

Roof drift angle

AC CE P

TE

(c) (d) Fig. 10. (a) NSP behavior of 12-story high strength C-SMF, and effects of local degradation on the NSP behavior of the 12-story high strength C-SMFs with: (b) rigid, (c) flexible, and (d) highly flexible design

39

ACCEPTED MANUSCRIPT

1.5

NTH analysis: lpvs03 G Experiment

F

PT

D,E

1

H

RI SC

M/My

0.5

-0.5 H G -1.5

-5

D,E

0 F/Fy (a)

D: Flange tension yielding E: Concrete crushing F: Flange local buckling G: Web local buckling H: Corner local buckling

5

10

AC CE P

TE

D

-10

F

MA

-1

NU

0

1.5

F D,E

1

NTH analysis: lpvs03 G Experiment H

M/My

0.5

0

-0.5

-1

H G

-1.5 -10

-5

F

D,E 0 F/Fy

D: Flange tension yielding E: Concrete crushing F: Flange local buckling G: Web local buckling H: Corner local buckling

5

10

(b) Fig. 11. Comparisons of the normalized moment-curvature responses obtained from NTH analyses and experimental tests: (a) 6-story C-SMFs, and (b) 12-story C-SMFs.

40

ACCEPTED MANUSCRIPT

6

lnrrrs

5

l40ivir

4

lkbjma

4

livar05

2

lepst10

llpgil3

lepst04

1.5

2

-1.5

lpvst03

lknhsbf

4

lclgil2 llnfrti

3

lnrsylm lpsdhsp 1.0

1.5

lnrrrs

(b) 6

DBE 5

DBE

4

FOE

3

MCE

lmhgil3

2

llnyerm

-0.5 0.0 0.5 Story drift (%)

MCE

MA

5

Story

lclgil2

-1.0

NU

(a) 6

llnbars

SC

1

2

0

lepst13

-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 Story drift (%)

lnrnewh

1

lpvst06

0

3

PT

lnrsylm

Story

Story

3

1

Story

livar06

5

ltbtab

FOE

6

DBE

llplgpc

RI

MCE

FOE

2

lpkcs05

1

1

0 -0.5

0.0 Story drift (%)

0.5

1.0

0

lsfhsbf

-1.5

TE

-1.0

D

lpkcs08 -1

-0.5

0

0.5

1

1.5

Story drift (%)

AC CE P

(c) (d) Fig. 12. Interstory drift envelops from NTH analyses of the 6-story high strength C-SMF subjected to different earthquake levels: (a) FOE, (b) DBE, and (c) MCE; and (d) summary of median values

41

2

ACCEPTED MANUSCRIPT

lnrrrs lkbjma

Story

ltbtab lepst10 lepst04 lpvst06 2

2.5

3

-1

lpvst03

Story

NU

lmhgil3

FOE

DBE

MA

-0.4

lpkcs05 lpkcs08

0 Story drift (%)

0.4

0.8

lsfhsbf

-1.2

llpgil3 lnrnewh

-0.8

-0.4

llnbars llnyerm lnrsylm lpsdhsp 0.5

1

lnrrrs

(b)

12 11 10 9 8 7 6 5 4 3 2 1 0

MCE

FOE DBE

0

0.4

0.8

1.2

1.6

Story drift (%)

(d)

TE

(c)

livar05

0 Story drift (%)

MCE

lknhsbf

D

Story

-0.8

lclgil2

llnfrti

-0.5

SC

(a)

lclgil2

l40ivir

RI

lepst13 1.5

livar06

PT

lnrsylm

12 11 10 9 8 7 6 5 4 3 2 1 0

FOE

12 11 10 9 8 7 6 5 4 3 2 1 0

DBE

llplgpc

Story

12 11 10 9 8 7 6 5 4 3 2 1 0 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 Story drift (%)

MCE

AC CE P

Fig. 13. Interstory drift envelops from NTH analyses of the 12-story high strength C-SMF subjected to different earthquake inputs: (a) FOE, (b) DBE, and (c) MCE; and (d) summary of median values

42

ACCEPTED MANUSCRIPT

2nd story

3rd story

roof drift

0.5

0.025

0.25

Vs 0 0

0.01

0.02

0.03

0.04

0.05

0.06

5th story

roof drift

4th story

0.5

0.025

PT

Normalized base shear (V/W)

1st story

6th story

0.25

Vs 0 0

0.01

SC

Story drift angle

RI

Normalized base shear (V/W)

0.75 0.75

(a)

0.02

0.03

0.04

0.05

0.06

Story drift angle

(b)

AC CE P

TE

D

MA

NU

Fig. 14. Normalized base shear-story drift angle responses for the 6-story C-SMFs: (a) Story 1-3 and (b) Story 4-6

43

ACCEPTED MANUSCRIPT

roof drift

0.2 0.042 0.1 Vs

0.2

0.1 Vs

0

0 0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0

Story drift angle

0.3

9th story

0.2 0.042

8th story

0 0

0.01

0.02

0.03

0.04

Story drift angle

0.05

0.06

0.07

0.04

0.05

0.06

0.07

0.08

Story drift angle

(b)

roof drift

0.3 12th story

10th story

11th story

0.2 0.042

0.1 Vs

0 0.08

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Story drift angle

(b)

AC CE P

(a)

TE

D

0.1 Vs

MA

roof drift

0.03

0.4

Normalized base shear (V/W)

7th story

0.02

5th story

0.042

NU

(a) 0.4

0.01

SC

0

Normalized base shear (V/W)

roof drift 4th story

0.3

PT

2nd story

RI

0.3

6th story

0.4 Normalized base shear (V/W)

Normalized base shear (V/W)

3rd story

1st story

0.4

Fig. 15. Normalized base shear-story drift angle responses for the 12-story C-SMFs: (a) Story 13, (b) Story 4-6, (c) Story 7-9, and (d) Story 10-12.

44

ACCEPTED MANUSCRIPT

NSP analysis

Vy

0.75

-0.05

y d -0.04

-0.03

-0.02

-0.01

Vs

p=0.025

y

-0.05

0

Vs

Vt

0.02

0.03

t 0.04

0.05

NU

Vy

0.01

RI

t

PT

NTH analysis: lpvst03

SC

Normalized base shear (V/W)

Vt

-0.85

Roof drift angle

MA

(a)

-0.05

-0.04

-0.03

-0.02

NSP analysis

Vt

D TE

t

AC CE P

Normalized base shear (V/W)

0.4 Vy

NTH analysis: lpvst03

p=0.042 y

y

Vs

-0.025 -0.01 0V s

0.01

t 0.02

0.03

0.04

0.05

Vy Vt -0.45 Roof drift angle

(b) Fig. 16. Representative comparisons of the base shear-roof drift angle responses obtained from NSP analyses and NTH analyses for: (a) 6-story C-SMFs and (b) 12-story C-SMFs.

45

ACCEPTED MANUSCRIPT Table 1. Design details of 6- and 12-story high strength C-SMFs

Structure Height

Structural Design

6-story

12-story

12-story

10.67 m span

Rigid (0.9≤T1 /Tmax ≤1.0)

Floors 1-3: 711.2x711.2x22.3

Floors 1-4: W30x108

Floors 1-4: W33x118

Floors 4-6: 508x508x15.9

Floors 5-6: W24x62

Floors 5-6: W24x76

Flexible (1.0
Floors 1-3: 555.8x555.8x17.5

Floors 1-4: W30x108

Highly flexible (T1 /Tmax >1.15)

Floors 1-3: 457.2x457.2x14.3

Flexible (1.0
Highly flexible (T1 /Tmax >1.15)

RI

Floors 5-6: W24x62

Floors 5-6: W24x76

Floors 1-4: W30x108

Floors 1-4: W33x118

NU

SC

Floors 1-4: W33x118

Floors 4-6: 406.4x406.4x12.7

Floors 5-6; W24x62

Floors 5-6; W24x76

Floors 1-4: 812.8x812.8x25.4

Floors 1-6: W33x 118

Floors 1-6: W36x 135

Floors 5-8: 711.2x711.2x22.3

Floors 7-9: W27x94

Floors 7-9: W33x118

Floors 9-12: 609.6x609.6x19.1

Floor 10-12: W27x84

Floors 10-12: W27x94

Floors 1-4: 711.2x711.2x22.3

Floors 1-6: W33x 118

Floors 1-6: W36x 135

Floors 7-9: W27x94

Floors 7-9: W33x118

Floors 9-12: 609.6x609.6x19.1

Floor 10-12: W27x84

Floors 10-12: W27x94

Floors 1-4: 609.6x609.6x19.1

Floors 1-6: W33x 118

Floors 1-6: W36x 135

Floor 5-8: 555.8x555.8x17.5

Floors 7-9: W27x94

Floors 7-9: W33x118

Floors 9-12: 508x508x15.9

Floor 10-12: W27x84

Floors 10-12: W27x94

MA

Rigid (0.9≤T1/Tmax≤1.0)

Floors 4-6: 457.2x457.2x14.3

PT

9.14 m span

D

12-story

f’ c =110.3 MPa

Floor 5-8: 660.4x660.4x20.6

TE

6-story

WF Beams A992 steel, F y =344.8 MPa

AC CE P

6-story

CFT Columns F y =551.6 MPa

46

ACCEPTED MANUSCRIPT Table 2. NSP analyses results Design factors and coefficients Cd 0 

Structural Design

6-story

Rigid (0.9≤T1/Tmax≤1.0)

7.4

8.7

4.3

6-story

Flexible (1.0
6.2

6-story

Highly flexible (T1/Tmax>1.15)

4.7

12-story

Rigid (0.9≤T1/Tmax≤1.0)

12-story

12-story

Highly flexible (T1/Tmax>1.15)

RI

4.3

5.3

2.4

5.9

7.4

5.2

Flexible (1.0
5.7

7.2

5.2

D

PT

Structure height

5.1

6.2

2.8

SC

NU

MA

TE AC CE P

47

7.1

ACCEPTED MANUSCRIPT Table 3. Summary of the ground motion records File name

1995 Kobe 1989 Lorna Prieta 1994 Northridge 1994 Northridge 1974 Tabas Elysian Park 1 Elysian Park 2 Elysian Park 3 Palos Verdes 1 Palos Verdes 2 1940 Imperial Valley 1979 Imperial Valley 1979 Imperial Valley 1992 Landers 1992 Landers 1989 Lorna Prieta 1994 Northridge 1994 Northridge 1994 Northridge 1986 N.Palrn Springs 1979 Coyote Lake 1979 Imperial Valley 1952 Kern 1992 Landers 1984 Morgan Hill 1966 Parkfield 1966 Parkfield 1986 N.Palm Springs 1971 San Femando 1987 Whittier

6.9 7.0 6.7 6.7 7.4 7.1 7.1 7.1 7.1 7.1 6.9 6.5 6.5 7.3 7.3 7.0 6.7 6.7 6.7 6.0 5.7 6.5 7.7 7.3 6.2 6.1 6.1 6.0 6.5 6.0

lkbjma llplgpc lnrrs lnrsylm ltbtab lepst04 lepst10 lepst13 lpvst03 lpvst06 l40ivir lvar05 livar06 llnbars llnyerm llpgil3 lnrnewh lnrrrs lnrsylm lpsdhsp lclgil2 livar06 lknhsbf llnfrti lmhgil3 lpkcs05 lpkcs08 lpsplma lsfhsbf lwhdown

MA

D

TE

AC CE P

DBE

FOE

48

RI

PT

Magnitude (Mw)

NU

MCE

Earthquake

SC

Earthquake level

ACCEPTED MANUSCRIPT Table 4. Minimum confidence levels recommended in FEMA-350

Global behavior limited by inter-story drift

PT

Performance level Immediate Occupancy Collapse Prevention 50%

Local connection behavior limited by inter-story drift Column compression behavior

AC CE P

TE

D

MA

NU

50%

RI

50%

SC

Behavior

49

90% 50% 90%

ACCEPTED MANUSCRIPT Table 5. Global performance evaluation for the 6-story C-SMFs

D Demand γa γ Factored demandto-capacity ratio, λ

0.50

0.24 0.40

99%>50%, OK

99%>90%, OK

MA

0.20

AC CE P

TE

D

Confidence level

NU

Uncertainty parameter, βUT

PT

ϕ

RI

C

Capacity

Collapse Prevention 0.10 0.85 0.016 1.06 1.20

SC

Immediate Occupancy 0.020 1.0 0.0071 1.02 1.40

Performance level

50

ACCEPTED MANUSCRIPT

Table 6. Global performance evaluation for the 12-story C-SMFs

D Demand γa γ Factored demandto-capacity ratio, λ

NU 99%>50%, OK

AC CE P

TE

D

Confidence level

0.20

MA

Uncertainty parameter, βUT

0.30

51

PT

ϕ

RI

C

Capacity

Collapse Prevention 0.10 0.85 0.015 1.06 1.20

SC

Immediate Occupancy 0.020 1.0 0.0042 1.02 1.40

Performance level

0.23 0.40

99%>90%, OK

ACCEPTED MANUSCRIPT Table 7. Local connection performance evaluation for the 6-story C-SMFs

ϕ

D Demand γa γ Factored demandto-capacity ratio, λ

0.75

PT

C

RI

Capacity

Collapse Prevention 0.034 0.90 0.016 1.06 1.20

SC

Immediate Occupancy 0.015 0.90 0.0071 1.02 1.40

Performance level

0.66

0.25

0.30

Confidence level

93.8%>50%, OK

96.1%>50%, OK

AC CE P

TE

D

MA

NU

Uncertainty parameter, βUT

52

ACCEPTED MANUSCRIPT

Table 8. Local connection performance evaluation for the 12-story C-SMFs

ϕ

D Demand γa γ Factored demandto-capacity ratio, λ

NU

Uncertainty parameter, βUT

0.45

MA

0.25

99%>50%, OK

AC CE P

TE

D

Confidence level

53

PT

C

Collapse Prevention 0.034 0.90 0.015 1.06 1.20

RI

Capacity

SC

Immediate Occupancy 0.015 0.90 0.0042 1.02 1.40

Performance level

0.87 0.30

82.2%>50%, OK

ACCEPTED MANUSCRIPT Table 9. Local column performance evaluation for the 6-story C-SMFs

ϕ

D Demand γa γ Factored demandto-capacity ratio, λ

0.12

PT

C

RI

Capacity

Collapse Prevention 4213.5 0.95 754.0 1.06 1.05

SC

Immediate Occupancy 6787.0 0.95 703.6 1.01 1.05

Performance level

0.22

0.17

0.26

Confidence level

99%>50%, OK

99%>90%, OK

AC CE P

TE

D

MA

NU

Uncertainty parameter, βUT

54

ACCEPTED MANUSCRIPT

Table 10. Local column performance evaluation for the 12-story C-SMFs

ϕ

D Demand γa γ Factored demandto-capacity ratio, λ

NU

Uncertainty parameter, βUT

0.10

MA

0.15

99%>50%, OK

AC CE P

TE

D

Confidence level

55

PT

C

Collapse Prevention 15572.4 0.95 1530.0 1.07 1.05

RI

Capacity

SC

Immediate Occupancy 15572.4 0.95 1390.0 1.02 1.05

Performance level

0.12 0.26

99%>90%, OK

ACCEPTED MANUSCRIPT Table 11. Dynamic stability evaluation of the 6-story C-SMFs

AC CE P

DBE

FOE

∆p

0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012

0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025

NU

MA 56

RI

PT

∆y

SC

Maximum roof drift angle, rad 0.018 0.012 0.016 0.014 0.009 0.013 0.013 0.014 0.019 0.015 0.009 0.012 0.007 0.011 0.011 0.009 0.011 0.011 0.009 0.009 0.009 0.012 0.007 0.011 0.011 0.009 0.011 0.011 0.009 0.009

D

MCE

Ground motion name lkbjma llplgpc lnrrs lnrsylm ltbtab lepst04 lepst10 lepst13 lpvst03 lpvst06 l40ivir lvar05 livar06 llnbars llnyerm llpgil3 lnrnewh lnrrrs lnrsylm lpsdhsp lclgil2 livar06 lknhsbf llnfrti lmhgil3 lpkcs05 lpkcs08 lpsplma lsfhsbf lwhdown

TE

Earthquake level

Dynamic Instability No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No

ACCEPTED MANUSCRIPT Table 12. Dynamic stability evaluation of the 6-story C-SMFs

∆y

lkbjma llplgpc lnrrs lnrsylm ltbtab lepst04 lepst10 lepst13 lpvst03 lpvst06 l40ivir lvar05 livar06 llnbars llnyerm llpgil3 lnrnewh lnrrrs lnrsylm lpsdhsp lclgil2 livar06 lknhsbf llnfrti lmhgil3 lpkcs05 lpkcs08 lpsplma lsfhsbf lwhdown

0.008 0.010 0.011 0.012 0.008 0.010 0.011 0.019 0.016 0.017 0.005 0.007 0.008 0.006 0.007 0.006 0.006 0.007 0.008 0.005 0.004 0.008 0.002 0.004 0.003 0.002 0.002 0.003 0.005 0.003

0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012

AC CE P

DBE

Maximum roof drift angle, rad

FOE

57

PT

∆p 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025

RI

SC

NU

MA D

MCE

Ground motion name

TE

Earthquake level

Dynamic Instability No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No