Experimental and Numerical Investigations of

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(a) Construction of steel structure. (b) Detail of transfer beam. (c) Assembling slab reinforcement. (d) Casting slab concrete. (e) Completion of construction.
This manuscript was published at: Nie J G, Pan W H, Tao M X*, Zhu Y Z. Experimental and numerical investigations of composite frames with innovative composite transfer beams. ASCE Journal of Structural Engineering, 2017, 143(7): 04017041. The final publication is available at the journal website. The researchers can also privately get the final publication version via sending Email or ResearchGate message to Prof. Mu-Xuan Tao ([email protected]).

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Experimental and Numerical Investigations of Composite

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Frames with Innovative Composite Transfer Beams

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Jian-Guo Nie 1, Wen-Hao Pan 2, Mu-Xuan Tao 3, Yu-Zhi Zhu 4

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Abstract: Experimental and numerical studies were conducted to investigate the vertical

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load-carrying behavior and seismic performance of a composite frame structure with an

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innovative composite transfer beam, which was proposed to overcome the disadvantages of

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the traditional reinforced concrete or steel reinforced concrete transfer beams. In the

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experimental study, a vertical monotonic loading test and a lateral cyclic loading test were

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conducted. The test observations, load–displacement curves, and strain measurements were

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discussed to investigate the structural performance and failure mechanism. The experimental

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results demonstrated the excellent vertical load-carrying behavior and seismic performance of

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the composite transfer frame. The characteristics of the plastic hinge distribution were

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investigated based on extensive data of the steel strains measured to reveal the typical failure

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mechanism of the composite transfer frame. In the numerical simulation analysis, a

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multi-scale modeling scheme was developed to make full use of the fiber beam–column

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elements and multi-layer shell elements. Comparisons with the experimental results showed

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that the developed model predicted the overall structural behavior, the individual story and

1 Professor, Beijing Engineering Research Center of Steel and Concrete Composite Structures, Dept. of Civil Engineering, Tsinghua University, Beijing, China 100084. E-mail: [email protected] 2 Ph.D. Student, Key Lab. of Civil Engineering Safety and Durability of China Education Ministry, Dept. of Civil Engineering, Tsinghua University, Beijing, China 100084. E-mail: [email protected] 3 Associate Professor, Key Lab. of Civil Engineering Safety and Durability of China Education Ministry, Dept. of Civil Engineering, Tsinghua University, Beijing, China 100084 (corresponding author). E-mail: [email protected] 4 Ph.D. Student, Key Lab. of Civil Engineering Safety and Durability of China Education Ministry, Dept. of Civil Engineering, Tsinghua University, Beijing, China 100084. E-mail: [email protected] 1

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component behavior, and the failure mechanism with a reasonable level of accuracy. In

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addition, both the experimental tests and numerical analyses indicated that the shear

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deformation mode and the energy dissipation in the composite joint core were also significant

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mechanical characteristics of the composite transfer frame.

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Author Keywords: Composite transfer beam; Composite transfer frame; Steel–concrete

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composite structure; Seismic performance; Failure mechanism; Experimental study;

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Multi-scale modeling; Fiber beam–column model

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INTRODUCTION

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In high-rise buildings, large openings at the ground floor level for shopping malls,

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public lobbies, and parking lots can be usually achieved using transfer beams, as shown in

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Fig. 1(a). A transfer beam is specifically defined as a beam that transmits loads from the

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upper closely spaced columns or walls acting on it to the widely spaced columns or walls

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supporting it. The discontinuity of the vertical structural members is the most significant

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characteristic of a structural system with transfer beams because it makes the mechanism of

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the system more complex than that of a regular structural system. As a result, numerous

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researchers have been studying this topic since Colaco and Lambajian (1971) first analyzed a

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transfer girder system considering the changes in the stiffness of the system with the

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construction of every story.

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Some early studies mainly dealt with the static elastic behavior of structures with

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transfer beams subjected to a vertical load. Several practical methods for the analysis of a

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transfer girder system supporting in-plane loaded shear walls were proposed by a long-term

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research program performed at Hong Kong University of Science and Technology (Kuang

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and Puvvala 1996; Kuang and Atanda 1998; Kuang and Li 2001; Kuang and Zhang 2003;

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Kuang and Li 2005). In the 2000s, the seismic performance of structures with transfer beams

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attracted a lot of attentions with the development of numerical approaches such as nonlinear

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finite element (FE) analysis and experimental techniques such as shake-table test. Seismic

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assessments of both low-rise (Li et al. 2003) and high-rise (Su et al. 2002) buildings with

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transfer beams were conducted to explore the effects of the abrupt change in lateral stiffness

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at the transfer soft story. Moreover, the seismic performance of tall buildings with a

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high-level transfer story was experimentally and analytically studied by Wu et al. (2007). In

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recent years, the collapse resistance of structures with transfer beams has become another

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significant topic. Starossek and Wolff (2005) and Byfield and Paramasivam (2012) discussed

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the progressive collapse of a typical building with transfer beams (the Alfred P. Murrah

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Federal Building) after a car bombing in detail. Up to now, different opinions on the

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progressive collapse of structures with transfer beams still exist in the research community.

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In addition to structural systems with transfer beams, the mechanical behavior of

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transfer beams has also been investigated by the researchers. When a traditional reinforced

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concrete (RC) transfer beam is used, a large depth-to-span ratio is required to bear the heavy

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loads from the upper stories. Therefore, the RC transfer beam should be considered as a shear

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critical deep beam; its shear strength analysis and its evaluation and enhancement method

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were discussed by Londhe (2011) and Bouadi et al. (2005). To enhance the load capacity of

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the RC transfer beam, the steel reinforced concrete (SRC) transfer beam was recommended

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and investigated by Wu et al. (2011) and Wang et al. (2011). However, the SRC transfer beam

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still have some disadvantages such as large self-weight, and time-consuming construction

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process. Therefore, although they have been widely used in practical engineering projects, the

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traditional RC/SRC transfer beams (Fig. 1(b)) still cannot meet the requirements of

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high-performance design, construction, and operation of building structures. This paper

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proposes an innovative steel–concrete composite transfer beam to overcome the

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disadvantages of the traditional RC/SRC transfer beams. The mechanical behaviors of the

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composite transfer frame with the proposed composite transfer beam subjected to both

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vertical monotonic and lateral cyclic loads were investigated through model tests and

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numerical simulations. The excellent performances of the proposed innovative composite

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transfer beam and the composite transfer frame were clearly demonstrated.

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SCHEME FOR COMPOSITE TRANSFER BEAMS

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Fig. 2(a) shows a traditional transfer frame with an RC/SRC transfer beam, and Fig. 2(b)

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illustrates a composite transfer frame with the proposed composite transfer beam. The

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proposed composite transfer beam is composed of a steel beam with a U-shaped cross-section,

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an RC slab, and partially filled concrete.

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Compared with the traditional steel–concrete composite beam (with no filled concrete in

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the U-shaped steel beam), the advantages of the proposed composite transfer beam are as

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follows: (i) the concrete is completely filled in the steel box at the support region, which can

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prevent the steel beam from buckling, increase the structural stiffness, and enhance the

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beam-end flexural, shear and energy dissipation capacity under cyclic loads; (ii) the concrete

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is partially filled in the upper part of the steel box at the mid-span sagging moment region,

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which can compensate for the insufficient compressive concrete flange cross-sectional area

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when the beam is subjected to sagging moment.

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Compared with the traditional RC/SRC transfer beams, the advantages of the proposed

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composite transfer beam are as follows: (i) small depth-to-span ratio, light self-weight, and

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superior seismic performance; (ii) the U-shaped steel beam can serve as the platform and

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formwork for in situ concrete casting, which can simplify the construction process and

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enhance the construction quality; (iii) exposure of concrete cracks can be avoided, which can

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improve the durability of the structure; (iv) the composite transfer beam can be easily

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connected to different types of frame column (e.g. steel, RC, and composite columns) and can

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also be applied to mega-frame structures.

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Fig. 3 shows beam-end and mid-span cross-sections of the composite transfer beam

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(Sections B and C) adopted in an actual hotel building to bear loads from the upper ten stories

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(Nie and Ding 2012). The two cross-sections are complete-infill and partial-infill schemes of

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a traditional composite beam cross-section (Section A), respectively. To demonstrate the

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effectiveness of the filled concrete in the composite transfer beam, the cross-sectional

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behaviors of the beam-end and mid-span cross-sections are analyzed using the fiber section

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model (Figs. 3(a) and (b)). The applied constitutive laws for the fiber materials in this

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numerical example are provided by Tao and Nie (2015) with a concrete compressive strength

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of 30 N/mm2 and a steel/reinforcement yield strength of 300 N/mm2. For the beam-end

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cross-section, Fig. 3(a) clearly demonstrates that the filled concrete in the U-shaped steel

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beam at the support region can effectively improve the cross-sectional hysteretic behavior; in

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particular, the cross-sectional capacity subjected to negative moment is significantly

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increased. For the mid-span cross-section, Fig. 3(b) demonstrates the evident increase in the

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cross-sectional capacity subjected to sagging moment owing to the filled concrete. With the

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increase in the cross-sectional height hfill of the filled concrete, the ultimate moment capacity

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of the mid-span cross-section will further increase, while the self-weight of the transfer beam

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will also increase correspondingly. In addition, it should be noted that the horizontal inner

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diaphragm for a shuttering purpose may significantly influences the post-peak responses;

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section C with filled concrete height of hfill = 1/4hs shows a hardening cross-sectional

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behavior (Fig. 3(b)) because the inner diaphragm in the compression zone can compensate for

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the softening behavior of the concrete exceeding its peak compressive strain ε0. Therefore, in

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an actual design practice, a reasonable cross-sectional height of the filled concrete in the

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mid-span cross-section should be determined considering several important factors, including

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the influence of both filled concrete and shuttering diaphragm, and a balance between

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strength and self-weight.

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EXPERIMENTAL PROGRAM

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Specimen design

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A two-story composite plane frame with the proposed composite transfer beam was

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designed and tested, as shown in Fig. 4. The specimen was designed according to a prototype

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frame structure with SRC transfer beams (the Multi-functional Building of Zhejiang

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Electric

Power

Corporation) (Li 2005). A 1:5 reduced scale was adopted. Five

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concrete-filled steel tube (CFST) columns at the second story were transferred to four CFST

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columns at the ground floor level. The middle column at the second story was discontinued at

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the mid-span of the transfer beam to double the column spacing. The composite joint with

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interior steel diaphragm (Nie et al. 2008) was applied to connect the CFST column and the

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composite beam.

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Fig. 4 also shows the constructional details and dimensions of the frame specimen and

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the cross-section of each component. The shear stud was provided in two rows at a

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longitudinal spacing of 60 mm, and its diameter and height were 10 mm and 40 mm,

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respectively. The middle column was mainly subjected to the vertical load, therefore, a

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smaller size is designed in the prototype structure and in the test specimen. Because of the

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construction difficulty, the reduced scale model of the prototype structure with two layers of

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rebar was simplified to the experimental specimen with one layer of rebar in the middle of the

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slab, and an equivalent reinforcement ratio was provided. Considering the small slab

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thickness relative to the overall beam height, this simplified design can produce identical

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cross-sectional responses of the composite beams. In addition, because of the different

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requirements for the cross-sectional moment capacity, the beam height and the flange

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thickness were reduced for the side beams in the transfer story.

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Fabrication and material properties

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Fig. 5 shows the fabrication process of the specimen including the fabrication of the

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steel structure (Figs. 5(a) and (b)), assembling of the slab reinforcement (Fig. 5(c)), and

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pouring of concrete (Fig. 5(d)). Fig. 5(e) shows the completion of specimen fabrication, and

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Fig. 5(f) shows the specimen under testing.

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The mechanical properties of the steel and reinforcement materials including yield

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strengths, ultimate strengths, and elongation ratios obtained from the material property tests

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are given in Table 1. For the concrete in the CFST columns, the average cubic compressive

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strength (obtained on the same day of the model test using 150 × 150 × 150 mm specimens)

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was 21.3 N/mm2; for the concrete in the slabs and beams, the average cubic compressive

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strength was 27.7 N/mm2.

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Test setup and loading procedure

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The bottom ends of all four continued columns were embedded in a strong RC beam that

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was anchored to the laboratory base to provide a fixed boundary condition (Figs. 4(a) and

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5(f)). Axial compressive forces were applied on the tops of all five columns in a symmetric

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pattern with respect to the middle column, denoted as N1 for the side columns, N3 for the

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middle column, and N2 for the other two inner columns, as shown in Fig. 4(a). A horizontal

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lateral force, denoted as F, was imposed on the end of the top-floor beam as shown in Fig.

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4(a), resulting in identical horizontal shear forces carried by both stories.

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A vertical monotonic loading test and then a lateral cyclic loading test were conducted.

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The vertical monotonic loading test aimed to explore the elastic vertical load-carrying

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behavior of the composite transfer beam in a composite frame system, and the lateral cyclic

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loading test aimed to investigate the seismic performance of the composite frame with the

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composite transfer beam. The loading procedures for both load cases are illustrated in Fig. 6

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and described as follows:

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(i) In the vertical monotonic loading test, a loading procedure that can facilitate the

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observation of crack development under the compressive load N3 was designed. First, the

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axial compressive load N1 was applied to 600 kN (corresponding to an axial load ratio of 0.2

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for the side columns). Then, the axial compressive load N2 was applied to 80 kN. Next, the

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axial compressive load N3 was applied to 100 kN. N2 and N3 were then proportionally

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increased to 400 kN and 500 kN (corresponding to axial load ratios of 0.2 and 0.5 for

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corresponding columns), respectively. Finally, the applied loads were unloaded. In addition,

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the load N3 was increased at an increment of 100 kN and was kept constant at each step to

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observe the crack development in the concrete slab.

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(ii) In the lateral cyclic loading test, the axial compressive loads N1, N2, and N3 were

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proportionally applied to 600 kN, 400 kN, and 350 kN (corresponding to axial load ratios of

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0.2, 0.2, and 0.35), respectively. Then, the lateral load F was applied using the force-control

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scheme before yielding of the specimen and the displacement-control scheme after yielding.

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In the displacement-control scheme, the displacement cycle was applied twice at each control

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point and then increased to the next loading level by 0.5∆y (where ∆y is the yielding

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displacement of the frame determined in the experiment based on the load-displacement

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curve and the strain measurements).

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Measurement arrangements

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Fig. 7 shows the measurement arrangements in the experiment. Built-in load cells were

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used for measuring the vertical and horizontal loads. The displacement meter ∆1 was installed

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for obtaining the mid-span vertical deflection of the composite transfer beam. In addition,

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two displacement meters, ∆ and ∆2, were used for measuring the lateral displacements in the

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beam ends of the second story and the transfer story, respectively. A large number of strain

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gauges were carefully placed on the specimen to study the mechanism of the transfer beam

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and the composite transfer frame, and the main strain gauges shown in Fig. 7 were installed

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based on the following considerations: (i) To measure the strain distribution along the transfer

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beam, six longitudinal steel strain gauges were installed on the upper steel flange and the

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lower steel flange along the transfer beam, numbered from S1 to S6 and S7 to S12,

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respectively. (ii) Steel strain gauges S13 and S14 together with the measuring points S3 and

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S9 were used to obtain the strain distribution in the mid-span cross-section of the transfer

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beam. Steel strain gauges S15 and S16, reinforcement strain gauge R1, and concrete strain

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gauge C1, together with the measuring points S6 and S12, were used for studying the strain

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distribution in the support cross-section of the transfer beam. (iii) Sixteen steel strain gauges,

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numbered from S17 to S32, were placed at the beam/column ends to obtain evidence for the

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plastic hinge development and the failure mechanism of the composite transfer frame.

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MULTI-SCALE MODELING

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To efficiently simulate the potential nonlinear behavior of the beams, columns, and joint

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cores of the composite transfer frame, a multi-scale modeling scheme was developed as

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shown in Fig. 8. The CFST columns and the composite beams (including the composite

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transfer beam) were modeled using the fiber beam–column elements. The composite joint

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core including the outer steel plate and the filled concrete were modeled using the fiber

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beam–column elements and the multi-layer shell elements (as explained later). The adopted

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multi-scale constraint scheme connecting the joint core elements and the beam/column

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elements was well established in previous studies (Tao and Nie 2016; Li et al. 2007; Yu et al.

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2012; Nie et al. 2014). Moreover, this multi-scale modeling scheme was validated (Tao and

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Nie 2016) by ten floor plane joint substructures and five spatial joint substructures connecting

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rectangular CFST column and composite floor, which had similar composite joint details with

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this experiment.

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Modeling beams and columns

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The fiber beam–column element developed by Tao and Nie (2015) for the nonlinear

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analysis of typical composite structural members including CFST columns and composite

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beams was applied in this simulation. This element was developed from a standard

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displacement-based beam–column element and was implemented into the general

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commercial FE package, MSC.MARC Version 2007r1.

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The element mesh scheme of the developed fiber element model is shown in Fig. 8(a).

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To accurately consider the deformation localization effect (Coleman and Spacone 2001;

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Belytschko et al. 1986) in displacement-based fiber models, the element size was selected as

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about half of the cross-sectional height, which approximately equals the length of the plastic

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hinge formed at the end of the structural component, as recommended by Tao and Nie (2015).

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The material constitutive laws used in the developed fiber element model (Tao and Nie

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2015) are briefly summarized here.

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For the CFST columns, the composite action between steel tube and concrete (including

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the effect of hoop stresses in increasing the compressive strength of concrete and reducing the

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yielding strength of steel) is reflected in the confinement factor ξ = Asfy/Acfck and considered

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in the uniaxial stress–strain relationship of concrete fiber (Han et al. 2001), where As and fy

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are the cross-sectional area and yielding strength of steel, respectively; Ac and fck are the

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cross-sectional area and characteristic compressive strength of concrete, respectively.

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Figs. 9(a) and (b) shows the uniaxial stress–strain skeleton curve of the concrete fiber in

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compression. Before the peak compressive strain ε0, the stress–strain (σ–ε) relationship

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assumes a parabolic form. When the peak compressive strain ε0 is exceeded, the stress–strain

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relationship is considered separately for the ordinary compressive concrete (Fig. 9(a), such as

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the concrete in the composite beams and slabs in this experiment) and the confined

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compressive concrete in CFST (Fig. 9(b)). In Fig. 9(b) for the confined compressive concrete,

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the strain hardening or softening behaviors may be selected based on the section shape and

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the confinement factor ξ (for the rectangular CFST columns in this experiment, the strain

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softening behavior (branch (2)) is selected). In addition, Fig. 9(c) shows the bilinear model

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for the concrete in tension.

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The hysteretic model of the concrete fiber shown in Fig. 10 (Mander et al. 1988; Sakai

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and Kawashima 2006) is used to capture the complex strength and stiffness degradation

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effects of concrete under cyclic loading.

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Fig. 11 shows the uniaxial stress–strain skeleton curve and hysteretic law of the steel and

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rebar fibers. For the skeleton curve, the model proposed by Esmaeily and Xiao (2005) is

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adopted as shown in Fig. 11(a). In the strain hardening stage, the stress–strain relationship is

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assumed to have a parabolic form. For the hysteretic law, as shown in Fig. 11(b), the classical

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elastic unloading rule is assumed, and the elaborate reloading law proposed by Légeron et al.

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(2005) with good accuracy in simulating nonlinear kinematic hardening is applied.

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Modeling composite joint cores

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Fig. 8(b) details the modeling scheme for the composite joint core. The column steel

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flanges and the interior steel diaphragms surrounding the joint core concrete were modeled

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using the same fiber beam–column element as that adopted for the columns and beams. The

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composite shear behaviors of the core concrete and steel web were modeled using the

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multi-layer shell elements provided by MSC.MARC Version 2007r1. The adopted modeling

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parameters were suggested and validated by extensive experimental data in the previous

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studies (Tao and Nie 2016; Nie et al. 2011a,b, 2014; Hu and Nie 2015).

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To avoid the overestimation of the shear strength and stiffness of core concrete owing to

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the shear-locking effect in the fixed crack concept, a reasonable value of the shear retention

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factor η should be employed. According to previous studies (Rots 1991; Walraven and

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Reinhardt 1981; Lu et al. 2005, 2006), with the increase of cracking strain εcr (i.e. the

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increase of crack opening), the interlock of aggregate particles diminishes and the shear

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transferring ability reduces. Therefore, the shear retention factor η (as a function of the

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cracking strain εcr) was selected to reflect this important phenomenon (Tao and Nie 2016; Lu

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et al. 2005, 2006):

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η = η0 ⋅ exp ( −m ⋅ ε cr )

(1)

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where η0 denotes the initial shear retention factor; m is used to control the descending rate of

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η with the increase of cracking strain εcr; and εcr denotes the total cracking strain calculated

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as (εcr12+εcr22)0.5, where εcr1 and εcr2 represent the cracking strains in the two orthogonal crack

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directions.

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The parameters η0 and m in Eq. (1) need further calibrations by experimental results

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because all available shear retention models in the literature are only suitable for RC

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structural members. Many studies on the shear behavior of RC structures (Dahmani et al.

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2010; Kachlakev and Miller 2001; Jiang et al. 2005) adopted shear retention factors ranging

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from 0.2 to 0.3. Therefore, an average value of 0.25 was selected for the initial shear retention

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factor η0. The other parameter m was calibrated by trial and error, as in many similar studies

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(Walraven and Reinhardt 1981; Lu et al. 2005, 2006; Dahmani et al. 2010; Kachlakev and

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Miller 2001; Jiang et al. 2005; Pang and Hsu 1996), to obtain the “best fit” to the test results.

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Tao and Nie (2016) calibrated the parameter m by two groups of cyclic loading tests of

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composite joint substructures and obtained a value of 800; this value was selected in the

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current computational model.

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RESULTS AND DISCUSSIONS

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Vertical monotonic loading test

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Test observations

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After the axial compressive force N1 was increased to 600 kN, no evident experimental

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phenomenon was observed. When the axial compressive forces N2 and N3 reached 160 kN

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and 200 kN, respectively, several transverse cracks were developed on the top surface of the

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RC slab adjacent to both ends of the composite transfer beam owing to the negative moment.

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With the gradual increase in the axial compressive forces N2 and N3, the widths of the

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existing cracks gradually increased and new cracks were further developed on the slab

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concrete of both stories. Fig. 12 shows the typical crack pattern of the slab concrete after the

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maximum values of the axial compressive forces N1, N2, and N3 were applied, and the

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maximum crack width observed at the end of the composite transfer beam was about 0.05

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mm.

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Load–displacement curve

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Fig. 13 illustrates the measured frame response with respect to the mid-span vertical

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load N3 and the mid-span vertical displacement ∆1, which reflects the stiffness of the

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composite transfer beam subjected to a vertical load. The slight nonlinearity of the measured

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loading and unloading branches indicates the slight stiffness degradation of the composite

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transfer beam owing to the concrete cracking at the hogging moment regions. Because of this

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nonlinear behavior, the unloading branch was not well-predicted by the numerical model.

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However, in general, the vertical stiffness of the composite transfer beam was predicted by

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the developed multi-scale numerical model with reasonable accuracy.

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Strain distribution analysis

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The normal strain distributions in both mid-span and support cross-sections of the

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composite transfer beam were measured and predicted as shown in Figs. 14(a) and (b),

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respectively. The plane-section assumption was approximately satisfied despite an evident

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sudden jump at the steel–concrete interface possibly owing to the shear slip effect. Generally,

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the predictions by the developed multi-scale model were in good average agreement with the

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experimental values. In addition, the longitudinal strain distributions in the upper and lower

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steel flanges along the composite transfer beam were obtained in the test, as shown in Figs.

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14(c) and (d), respectively. The inflection points of the transfer beam determined from the

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predicted longitudinal strain distributions were in very close agreement with the

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measurements. Therefore, the static behavior of the proposed composite transfer beam

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subjected to a vertical load can be reasonably simulated using the traditional fiber

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beam–column elements.

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Lateral cyclic loading test

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Test observations

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Before the lateral load F was increased to 400 kN, no evident experimental phenomenon

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was observed. When the load reached 400 kN, new transverse cracks formed on the top

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surface of the RC slab at the composite transfer beam end adjacent to the loading side owing

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to the negative moment. When the lateral load reversed, the initial transverse cracks adjacent

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to the loading side closed and new transverse cracks were developed at the other end of the

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transfer beam. With further increase in the lateral load, the widths of the existing cracks

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gradually increased and new cracks were further developed. At the lateral displacement level

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of 55 mm (corresponding to a drift angle of 0.020), large sound continuously occurred. A

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tensile fracture in the steel bottom flange occurred at the end of the composite transfer beam

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(Fig. 15(a)), and local buckling of steel was observed adjacent to the base of the left inner

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column (Fig. 15(b)). Moreover, evident shear deformation of the composite joint core

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connecting the composite transfer beam and the inner CFST column (Fig. 15(c)) was

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observed. At the lateral displacement level of 65 mm (corresponding to a drift angle of 0.024),

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buckling of the beam bottom flange was observed in the second story adjacent to the beam

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end (Fig. 15(d)), and the slab concrete crushed adjacent to the top of the side column (Fig.

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15(e)). In the second load cycle of the lateral displacement level of 75 mm (corresponding to

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a drift angle of 0.027), the lateral load F was decreased to less than 85% of the ultimate

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lateral load. The test was ended after this cycle.

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Fig. 16 shows the failure crack pattern of the slab concrete in the lateral cyclic loading

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test. A large number of cracks were observed in the slab concrete adjacent to the

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beam–column joints of both stories. Most cracks even penetrated to the bottom surface of the

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concrete slab. Moreover, the slab concrete near the side column of the second story was

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crushed. Despite such a failure crack pattern, no significant degradation in the structural

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response occurred (Fig. 17), indicating the good seismic performance of the composite

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transfer frame.

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Load–displacement curves

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Fig. 17 shows the measured lateral load–displacement hysteretic curves in the test. Fig.

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17(a) reflects the lateral behavior of the whole composite transfer frame, while Figs. 17(b)

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and (c) reflect the lateral behaviors of the transfer story and the second story, respectively. In

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general, the hysteretic curves took on a plump form, and no typical pinching effect was

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observed. The load–displacement hysteretic curves also showed that no significant stiffness

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or strength degradation occurred during the lateral cyclic loading test even when the drift

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angle was as large as 1/40. Therefore, it can be concluded that the proposed composite

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transfer frame has excellent seismic performance and energy dissipation capacity.

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Comparisons between Figs. 17(b) and (c) show that the behaviors of the transfer story

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and the second story are similar. This indicates that the lateral load capacity and lateral

356

stiffness (i.e. the ratio of the story shear force to the story drift angle) of the two stories were

357

close. No weak story existed although the middle column at the second story was

358

discontinued. As a result, energy dissipation could be fully developed throughout all stories in

359

the proposed composite transfer frame, and localized damages could be effectively avoided

360

under seismic loading.

361

Fig. 17 also compares the measured frame responses with the numerical results obtained

362

by the developed multi-scale model. The numerical results slightly underestimated the lateral

363

load capacity. In addition, the unloading response and thereby the plumpness of the hysteretic

364

curves were overestimated, indicating that the developed model could not well capture the

365

stiffness degradation. Nevertheless, the lateral stiffness of the whole frame and the two stories

366

were accurately predicted by the developed model. In general, the developed model was able

367

to predict the overall behavior of the frame and the individual behavior of the two stories with

368

a reasonable level of accuracy.

369

Plastic hinge distributions

370

Fig. 18 shows the steel strain measurements at the beam/column ends. To demonstrate

371

the yielding of the steel plates more clearly, the shear force versus steel strain curves are

372

plotted together with the yield strain marked as red dotted lines. These strain measurements

373

were used to identify whether the plastic hinge was formed at a beam/column end in the test.

374

In particular, the plastic hinge was determined to be formed at the beam/column ends where

18

375

the steel flange had undergone large plastic strain after yielding. Following this plastic hinge

376

determination process, the developed plastic hinges in the composite transfer frame are

377

highlighted in Fig. 18. The plastic hinges were formed throughout the frame, including the

378

column ends in the transfer story, the middle column ends in the second story, and most beam

379

ends with a low beam depth. For the transfer beam, plastic hinge was not developed and an

380

elastic behavior was observed instead. Therefore, because of the high cross-sectional capacity

381

of the transfer beam, the weak-beam/strong-column design goal and thereby a fully

382

developed beam hinge mechanism could not be achieved. Instead, a complex mixed failure

383

mechanism with plastic hinges distributed in both beam and column ends was dominated. In

384

this mechanism, the composite transfer beam could still carry a large vertical load, while

385

energy dissipation in the other beam and column ends could be sufficiently developed under a

386

lateral cyclic load.

387

Fig. 19 shows the development of plastic hinges during the lateral cyclic loading test

388

predicted by the developed multi-scale model. At a drift angle of 0.004, the first plastic hinge

389

was formed adjacent to the base of the right inner column. At a drift angle of 0.007, the first

390

beam plastic hinge was formed in the second floor adjacent to the right inner column, while

391

the plastic hinges were also formed adjacent to the bases of all four columns in the transfer

392

story. With further increase in the lateral displacement, the plastic hinges were gradually

393

formed and developed at the beam/column ends. When the frame approached failure, the

394

plastic hinges were distributed throughout the frame, including both beam and column ends.

395

In addition, the predicted plastic hinge distribution at the maximum lateral displacement level

19

396

shown in Fig. 19 was nearly the same as the measured plastic hinge distribution highlighted

397

in Fig. 18, indicating that the developed model could successfully predict the plastic hinge

398

distribution and thereby the failure mechanism of the composite transfer frame.

399

Behavior of joint cores

400

Fig. 20 shows the predicted behavior of the composite joint core connecting the

401

composite transfer beam and the inner CFST column. At the maximum lateral displacement

402

level, nearly the whole steel web of the joint core yielded (refer to the equivalent von Mises

403

stress contour plotted in Fig. 20(a)), and the filled concrete went through a large cracking

404

strain (Fig. 20(b)). In general, the joint core took on a typical parallelogram shear

405

deformation mode. Fig. 20 also indicates that the shear deformation mechanism in the

406

composite joint core was sufficiently developed, which was consistent with the experimental

407

observation (Fig. 15(c)). Therefore, the composite joint core connecting the composite

408

transfer beam and the CFST column was also fully participating in energy dissipation and

409

thus aided in the improvement of seismic performance.

410

In the proposed composite transfer frame, the shear deformation mode and the energy

411

dissipation in the composite joint core are critical mechanical characteristics. Compared with

412

the traditional RC joint core in a traditional transfer frame, the composite joint core with the

413

core concrete confined by the outer steel plates has considerably better seismic performance.

414

Therefore, although the joint core undergoes significant shear deformation under seismic

415

loading, good ductility and sufficient energy dissipation can be ensured for the composite

416

transfer frame.

20

417 418 419

CONCLUSIONS This paper presents experimental and numerical investigations of a composite frame with an innovative composite transfer beam. The following conclusions can be drawn:

420

(i) The proposed composite transfer beam has numerous advantages over the traditional

421

RC/SRC transfer beams and the traditional steel–concrete composite beam. The infill of

422

concrete in the U-shaped steel beam can effectively improve the cross-sectional responses of

423

the beam-end cross-section under hogging moment and the mid-span cross-section under

424

sagging moment.

425

(ii) The composite transfer frame showed excellent load-carrying behavior in supporting

426

the in-plane load from the upper story and excellent seismic performance as well as energy

427

dissipation capacity in resisting the lateral cyclic load.

428

(iii) Regarding the failure mechanism of the composite transfer frame, no weak story

429

existed although the middle column at the second story was discontinued. A satisfying mixed

430

failure mechanism with plastic hinges distributed in both beam and column ends was

431

achieved to ensure excellent seismic performance. In addition, the sufficiently developed

432

shear deformation and energy dissipation of the composite transfer beam–CFST column joint

433

core were also significant mechanical characteristics of the composite transfer frame.

434

(iv) The composite frame with a composite transfer beam could be accurately simulated

435

through the multi-scale modeling scheme. For the vertical monotonic loading test, the vertical

436

stiffness and strain distributions of the composite transfer beam were well predicted. For the

437

lateral cyclic loading test, the developed multi-scale numerical model was able to capture the

21

438

overall behavior of the frame and the individual behavior of the two stories with a reasonable

439

level of accuracy. In addition, the multi-scale model could also accurately predict the

440

distribution of plastic hinges, the shear deformation of composite joint cores, and thereby, the

441

failure mechanism.

442

ACKNOWLEDGMENTS

443

The writers gratefully acknowledge the financial support provided by the Beijing Natural

444

Science Foundation (grand number 8162023) and the Tsinghua University Initiative

445

Scientific Research Program (grant number 20161080107). The writers also express their

446

sincere appreciation to the reviewers of this paper for their constructive comments and

447

suggestions.

448

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449

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25

537 538

Table 1

Material properties of steel plates and reinforcement (average values) Yield strength (MPa)

Ultimate strength (MPa)

Elongation ratio (%)

6-mm-thick steel plate

308.4

442.9

25.4

8-mm-thick steel plate

290.7

402.2

28.2

10-mm-thick steel plate

360.0

499.7

31.1

φ8 reinforcement

363.8

462.3

32.6

539

26

High depth/span ratio

Upper frame

Bottom column Large space

Transfer beam

(a) Transfer beam in high-rise buildings

(b) Typical reinforced concrete transfer beam (photographed by the authors)

Fig. 1 Transfer beams in practical engineering projects

RC beam

RC column

RC supporting column

RC/SRC transfer beam

RC section

SRC section

(a) RC/SRC transfer frame structure

Composite beam

CFST column CFST supporting column

Composite transfer beam

Section at mid-span

Section at support

(b) Steel-concrete composite transfer frame structure

Fig. 2 Different schemes for transfer frame structures

1200

300

300

1200

300

300

850

Section A: Conventional

850

hfill 22

Section C: Propose d for sagging moment region

50000 Moment (kN.m)

Moment (kN.m)

850

60000 Section A Section B

20000 0 -20000

40000 30000 20000 10000

-40000 -60000 -50

22

22

Section B: Propose d for hogging moment region

60000 40000

35

hs = 2090

22

22

Inner diaphragm

50

50

50

hs = 2090

22

300

50

φ12@100 φ12@100

hs = 2090

φ12@100

1200

120 35

35

120

120

300

-25

0 25 Curvature (×10-6 )

50

(a) Different schemes for beam-end cross-section

0 0

Section A Section C (hfil l = 1/4 hs) Section C (hfil l = 1/2 hs) Section C (hfil l = 3/4 hs) 12

24 36 Curvature (×10-6 )

48

(b) Different schemes for mid-span cross-section

Fig. 3 Comparison of cross-sectional behavior among different schemes (unit: mm)

740 1

1

2

3

2

7 200 Concrete filled in composite transfer beam 2

2

1340

2

1

202

1

180

300

2

1

3040

1

1340

2-2

6 260

500

3-3

6

500

500

6 500

600

3

180

5

160

7

6

6 140 152 6

50

100

500 8φ8

22

22 168

φ8-75

50

5-5

22

(b) Sectional view of components

Fig. 4 Detailed parameters of specimen (unit: mm)

50 6 168

164 8 180

50

350

330

6

6

22

8

168

10 50

6 22

6-6

φ8@75 4-4

168

10

6

50

50

10

50

7-7

168

50

350

50

φ8@75

500

6φ8

500 8φ8 6 150 280 10

φ8@75

100

50

(a) Elevation of specimen 500 8φ8

100

2

6

2

5

6

1-1

4

6

1

4

6

1

4

N1

4

640

4

N2

4

230

160

N3

4

3346

N2

4

1774

N1

F,Δ

(a) Construction of steel structure

(b) Detail of transfer beam

(d) Casting slab concrete

(e) Completion of construction

Fig. 5 Fabrication of specimen

(c) Assembling slab reinforcement

(f) Specimen under testing

400

N2 (kN)

80

600 400 350

600 400 200 -200 -400 -600

Δ (mm)

500

Time

N3 (kN)

Axial force (kN)

Time

F (kN)

N1 (kN) 600

100

(a) Vertical monotonic loading procedure

Time

Δy

N1 N2 N3

0.5Δy

0.5Δy

Time

Time

0.5Δy

-Δy

Time

(b) Lateral cyclic loading procedure

Fig. 6 Loading procedures for two load cases

Failure

N1

N3

N2

N2

N1 Δ

F

S7

S8

250 250

S5 S11

S12

300 160

120 S27 S29

S23

50

120

S26

50

C1 S25 R1 S6 S15 S16

120

S20

120

Δ2

S28

120

50

S2

S3 S13 S4 S14 S9 S10

S22

50

S1

120

S19

50

S24

S18

50

50

160

S21

50

S17

S30

Δ1

Fig. 7 Arrangement of main measuring devices

S32

50

S31

50

Force sensor Displacement meter Strain gage

Multi-layer shell elements Column web + in-filled concrete

Beam elements Column flange

Fiber beamcolumn elements Fiber beamcolumn elements Beam elements Diaphragm

(a) General modeling scheme

Column web Column flange Diaphragm

(b) Modeling scheme of joint core

Fig. 8 Multi-scale modeling of composite transfer frame structures

σ εpl (εro,2,σro,2)

(εro,1,σro,1)

ft

εt0

εtu ε

(εro,3,σro,3) (εun,3,σun,3) (εre,3,σre,3) (εre,2,σre,2)

σnew,2, σnew,3 σnew,1 σnew,0

(εun,2,σun,2) (εre,1,σre,1)

(εun,σun) (εun,1,σun,1) (εre,0,σre,0)

(ε0,σ0)

Fig. 10 Uniaxial stress–strain hysteretic law of concrete

σ k3fy A fy

σ

Slope Eh C (1t)

B

εy k1εy

k2εy

ε

(εa1t,σa1t) (εa2c,σa2c) (εa3c,σa3c) (2c) (3c) (εb3c,σb3c) (εb2c,σb2c)

(a) Skeleton curve

Fig. 11

Slope Eh (εb1t,σb1t)

C

(εa1c,σa1c) (1c)

A (εb1c,σb1c)

Slope Eh

(b) Hysteretic law

Uniaxial stress–strain skeleton curve and hysteretic law of steel and rebar

ε

Vertically loading region Top surface Bottom surface

Steel beam (a) Slab crack pattern on the second story

CFST column

CFST column Top surface Bottom surface

Steel beam (b) Slab crack pattern on the transfer story

CFST column

Fig. 12 Crack patterns in the vertical monotonic loading test

Mid-span vertical Load N3 (kN)

600

400

200

EXP FEA

0 0 1 2 3 4 5 Mid-span vertical displacement Δ1 (mm)

Fig. 13 Mid-span vertical load–displacement curve

FEA EXP

300

200

0.2P 0.4P 0.6P 0.8P 1.0P

100

0 -800

-400

0 400 800 Longitudinal strain (με)

1200

Position along transfer beam height (mm)

Position along transfer beam height (mm)

400

(a) Strain distribution on mid-span section of transfer beam

400

300

200 FEA EXP 100

0 -400

-200

0 200 400 Longitudinal strain (με)

600

800

(b) Strain distribution on support section of transfer beam 600

400

FEA EXP 400

0 -400 -800

FEA EXP

-1200 0

1000 2000 Position along transfer beam (με)

0.2P 0.4P 0.6P 0.8P 1.0P 3000

(c) Strain distribution of lower steel flange along beam

Longitudinal strain (με)

Longitudinal strain (με)

0.2P 0.4P 0.6P 0.8P 1.0P

200

0.2P 0.4P 0.6P 0.8P 1.0P

0 -200 -400 -600

0

1000 2000 Position along transfer beam (με)

3000

(d) Strain distribution of top steel flange along beam

Fig. 14 Strain analysis of transfer beam

(e) (d)

(c)

(b)

(a)

Fig. 15 Typical failure modes in the lateral cyclic loading test: (a) fracture of steel bottom flange; (b) buckling of column steel; (c) shear deformation of composite joint core; (d) buckling of steel beam flange; (e) crush of slab concrete

Crushing

Top surface Bottom surface

Steel beam (a) Slab crack pattern on the second story

CFST column

CFST column Steel beam

Top surface Bottom surface

CFST column (b) Slab crack pattern on the transfer story

Fig. 16 Failure crack patterns in the lateral cyclic loading test

0 -500

-1000 -80 -40 0 40 80 Lateral displacement on 2nd story Δ (mm) (a) General behavior

1000

1000 500 0 -500

EXP FEA

Shear force of 2nd story (kN)

500

EXP FEA

Shear force of transfer story (kN)

Lateral load F (kN)

1000

-1000 -0.03 -0.015 0 0.015 0.03 Drift angle of transfer story (rad) (b) Behavior of transfer story

EXP FEA

500 0 -500

-1000 -0.03

Fig. 17 Load–displacement hysteretic curves

0 0.015 0.03 -0.015 Drift angle of second story (rad) (c) Behavior of second story

0

-1000

0 400 Strain (με)

-8000 -4000 Strain (με)

1000 0

-1000

0

0 -800 Strain (με)

Y

1000

S22

0

S19 -1000 -8000 -4000 Strain (με)

800

Y

1000 0

-1000

0

Y S20

-4000 -2000 0 Strain (με)

1000

Shear force (kN)

-1000 -400

Y

Shear force (kN)

0

Y S18

Shear force (kN)

S17

Shear force (kN)

1000

Shear force (kN)

Shear force (kN)

1000

Y

0

S23 -1000 -2000 -1000 0 Strain (με)

Y Y

S21

0

-1000

Shear force (kN)

Shear force (kN)

0 -20000 -10000 Strain (με) Y 1000 0

Plastic hinge

Shear force (kN)

1000

S24 -20000 -10000 Strain (με)

Y

0

Yield strain of steel

0

-1000

-400 0 400 Strain (με)

S12

0

-1000

-400 0 400 Strain (με)

1000 0

S31 -1000 -10000 0 10000 20000 Strain (με)

1000

0

-1000

0

S29 10000 20000 Strain (με)

Shear force (kN)

0

1000

1000 Y Y

Shear force (kN)

S25

YY

0

S27 -1000-1200 -800 -400 0 400 Strain (με)

Fig. 18 Observed plastic hinges from strain measurements

0 Y

2000 S30

0

-1000

400 800 1200 Strain (με)

Shear force (kN)

Shear force (kN)

1000

S10

Shear force (kN)

-10000

S26

0

-1000 0 -4000 -2000 Strain (με) 1000

Shear force (kN)

-1000

0

-1000 -800 -400 Strain (με) Y 1000 S28

1000

Shear force (kN)

Shear force (kN)

Shear force (kN)

1000

1000

-800 -400 0 400 Strain (με) Y Y

0

-1000

S32 -4000 0 4000 Strain (με)

θ1 = 0.004 θ2 = 0.004

θ1 = -0.003 θ2 = -0.003

θ1 = 0.007 θ2 = 0.007

θ1 = -0.006 θ2 = -0.005

θ1 = 0.011 θ2 = 0.010

θ1 = -0.009 θ2 = -0.007

θ1 = 0.019 θ2 = 0.017

θ1 = -0.019 θ2 = -0.014

θ1 = 0.026 θ2 = 0.024

θ1 = -0.022 θ2 = -0.017 The section on which steel plate yields

Fig. 19 Prediction of plastic hinge development

(Unit: N/mm 2 ) 308.4 (fy) 269.8 231.3

0.0150 Direction of maximum principle stress

0.0131 0.0113

192.7

0.0094

154.2

0.0075

115.6

0.0056

77.1

0.0038

38.5

0.0019

0.0

θ1 = 0.026 θ2 = 0.024

(a) Equivalent von Mises stress of steel plate web

0.0000

Direction of maximum principle stress

θ1 = 0.026 θ2 = 0.024

(b) Equivalent cracking strain of filled concrete

Fig. 20 Prediction of composite joint core behavior