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
266
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
273
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.
275
2010; Kachlakev and Miller 2001; Jiang et al. 2005) adopted shear retention factors ranging
276
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
278
(Walraven and Reinhardt 1981; Lu et al. 2005, 2006; Dahmani et al. 2010; Kachlakev and
279
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
282
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
295
mm.
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Load–displacement curve
297
Fig. 13 illustrates the measured frame response with respect to the mid-span vertical
298
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
307
composite transfer beam were measured and predicted as shown in Figs. 14(a) and (b),
308
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
315
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
321
was observed. When the load reached 400 kN, new transverse cracks formed on the top
322
surface of the RC slab at the composite transfer beam end adjacent to the loading side owing
323
to the negative moment. When the lateral load reversed, the initial transverse cracks adjacent
324
to the loading side closed and new transverse cracks were developed at the other end of the
325
transfer beam. With further increase in the lateral load, the widths of the existing cracks
326
gradually increased and new cracks were further developed. At the lateral displacement level
327
of 55 mm (corresponding to a drift angle of 0.020), large sound continuously occurred. A
328
tensile fracture in the steel bottom flange occurred at the end of the composite transfer beam
329
(Fig. 15(a)), and local buckling of steel was observed adjacent to the base of the left inner
330
column (Fig. 15(b)). Moreover, evident shear deformation of the composite joint core
331
connecting the composite transfer beam and the inner CFST column (Fig. 15(c)) was
332
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
334
end (Fig. 15(d)), and the slab concrete crushed adjacent to the top of the side column (Fig.
335
15(e)). In the second load cycle of the lateral displacement level of 75 mm (corresponding to
336
a drift angle of 0.027), the lateral load F was decreased to less than 85% of the ultimate
337
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
339
test. A large number of cracks were observed in the slab concrete adjacent to the
340
beam–column joints of both stories. Most cracks even penetrated to the bottom surface of the
341
concrete slab. Moreover, the slab concrete near the side column of the second story was
342
crushed. Despite such a failure crack pattern, no significant degradation in the structural
343
response occurred (Fig. 17), indicating the good seismic performance of the composite
344
transfer frame.
345
Load–displacement curves
346
Fig. 17 shows the measured lateral load–displacement hysteretic curves in the test. Fig.
347
17(a) reflects the lateral behavior of the whole composite transfer frame, while Figs. 17(b)
348
and (c) reflect the lateral behaviors of the transfer story and the second story, respectively. In
349
general, the hysteretic curves took on a plump form, and no typical pinching effect was
350
observed. The load–displacement hysteretic curves also showed that no significant stiffness
351
or strength degradation occurred during the lateral cyclic loading test even when the drift
352
angle was as large as 1/40. Therefore, it can be concluded that the proposed composite
353
transfer frame has excellent seismic performance and energy dissipation capacity.
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354
Comparisons between Figs. 17(b) and (c) show that the behaviors of the transfer story
355
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
