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Strength gains of the axially and laterally loaded composite columns based on the concrete confinements provided by steel cores encased in structural concrete
Strength gains of the axially and laterally loaded composite columns based on the concrete...
Nguyen, Dinh Han; Hong, Won-Kee
JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 2021, VOL. 20, NO. 2, 193–209 https://doi.org/10.1080/13467581.2020.1782213 BUILDING STRUCTURES AND MATERIALS Strength gains of the axially and laterally loaded composite columns based on the concrete confinements provided by steel cores encased in structural concrete Dinh Han Nguyen and Won-Kee Hong Department of Architectural Engineering, Kyung Hee University, Yongin, Republic of Korea ABSTRACT ARTICLE HISTORY Received 14 December 2019 Most of the design codes for the composite columns including American Concrete Institute Accepted 29 May 2020 do not account for the concrete confinements offered by the steel cores encased in the concrete section. However, the flexural capacities of the axially and laterally loaded com- KEYWORDS posite columns were substantially underestimated as the axial load increases if the con- Double confining effects; crete confinement provided by a steel core is not considered. The aim of this study was to steel columns encased in identify the structural gains of the composite columns with the cross-, H- and T-shaped structural concrete; steel cores encased in the concrete when the concrete confinement provided by the steel confinement by steel sections; equivalent cores is taken into consideration. The formulation of the flexural strength considering the confinement factors; confining effects provided by the transverse reinforcements and cross-shaped steel cores cross-shaped steel section for the maximum load limit state was presented with a 50% axial load of the nominal column capacity. The formulation for an ultimate load limit state with a 40% axial load of the nominal column capacity is listed in the Appendix. The design charts were presented for the strain ranges between 0.001 and 0.01, leading to gaining the strengths of the composite columns that have been lost when the confining effects provided by the steel cores were ignored. 1. Introduction strength of the composite columns with the steel cores. According to Chen and Lin 2006; El-Tawil and 1.1. Previous research and objectives Deierlein 1999, the presence of the large steel cores A design strategy for the composite columns that encased in the concrete columns provides an reduces the likelihood of the collapse under the enhanced concrete confinement, leading to an severe seismic conditions must allow the concrete to increased strength and ductility. However, the study absorb as much energy as possible. A composite of the large steel cores and their contributions to the steel-concrete structure will help achieve the cost- composite columns was limited, and few research effective construction due to its high stiffness and results are available. The present study explored the ductility, strong earthquake resistance, and savings underestimated flexural strengths when the steel in terms of the construction time (Ricles and cores contributing to confining concrete were Paboojian 1994; Griffis and Lawrence 1986; Chen, neglected. For the composite columns, the nominal Astaneh-Asl, and Moehle 1992). Experimental investi- axial capacities were computed by summing all forces gations of the composite elements were performed in the structural components, including reinforcing by (Mirza and Skrabek 1992; Mirza, Hyttinen, and steel and steel cores encased in concrete. The nom- Hyttinen 1996; El-Tawil and Deierlein 1999; Dundar inal moment capacities were then calculated by sum- et al. 2008;; SSRC 1979). The analytical models of the ming the axial forces about the geometric centroid of concrete-encased steel composite elements have the composite column sections. The interactions been developed by (Munoz and Hsu 1997; Furlong between the axial forces and moments for the con- 1968; Kato 1996; Virdi and Dowling 1973; Roik and crete are based on a maximum compressive strain of Bergmann 1990; Chen and Lin 2006). A performance- 0.003, which corresponds to the compressive con- based design is receiving wide attention; however, crete failure. This study found the flexural strengths only a few studies of the axial force and moment of the composite columns are not significantly influ - interactions that consider the concrete confinements enced by the confining effect provided by the cross- provided by both the transverse reinforcements and shaped steel sections at a concrete strain of 0.003 or steel cores has been performed. The consequently lower. The present study explored the influence of the inaccurate results underestimated the flexural concrete confined by cross-shaped steel cores on the CONTACT Won-Kee Hong firstname.lastname@example.org Department of Architectural Engineering, Kyung Hee University, Yongin 17104, Republic of Korea This article has been republished with minor changes. These changes do not impact the academic content of the article. © 2020 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the Architectural Institute of Japan, Architectural Institute of Korea and Architectural Society of China. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 194 D. H. NGUYEN AND W.-K. HONG flexural strength of the composite columns at the area of the highly confined concrete, influencing strains between 0.001 and 0.01, which led to identify- the strength and ductility of the columns. The ing the strength gains of the composite columns measured material properties used to obtain the when the steel cores were considered. (Chen and Lin fracture surfaces of the concrete-encased steel 2006) presented an analytical model for predicting composite columns with the cross-, H- and the axial capacity and the behavior of the concrete T-shaped flange sections are presented in Table 1. encasing H/cross-shaped steel cores. They performed The confinement effects of the steel cores loaded the structural tests to validate their study but did not axially and laterally on the strength and ductility of test the performance of the test specimens by the the composite columns were evaluated up to flexural loadings. The present study included the lat- a concrete strain of 0.01. The selected results eral loads to extend a study proposed by (Chen and were verified through the comparison with the Lin 2006). Valuable test data were also obtained by test data of the prior researchers. The readers are (El-Tawil and Deierlein 1999), who applied both the referred to the authors’ previous studies (Nguyen axial and lateral loads to the composite columns with and Hong 2020a) of the structural concrete con- the H-shaped steel cores. The present study included finements offered by the encased cross-shaped the cross-, H- and T-shaped steel cores with those steel cores, in which the area inside the confined proposed by (El-Tawil and Deierlein 1999). In this cores was idealized as equivalent to the confined study, the strain distributions between 0.001 and region representing highly confined and partially 0.01, and the corresponding neutral axes, were used confined regions proposed by (Chen and Lin 2006). to analytically calculate the compression block and The performance-based flexural strength ignoring the stress of the structural components. The strength the steel cores was underestimated. The spacing of gains contributed by the confining effects of both the hoops was also correlated with the confining transverse reinforcements and steel cores at their effects. ultimate limit state were discovered based on the axial force and moment interaction. 2. Modeling of the concrete confinement offered by the steel cores 1.2. Significance for the prediction of the 2.1. Material properties and boundary condition nonlinear structural behavior of the steel-concrete composite columns The material properties of concrete, steel and rebar including hoops are shown in Figure 1(a). The At a maximum load limit state, the strength gains boundary conditions and loads of the FEM model of the axially and laterally loaded composite col- are indicated in Figure 1(b) which shows the combi- umns based on the concrete confinements pro- nation between axial load with two cases (30% and vided by the steel cores encased in the structural 60% axial load column capacity) and the lateral load concrete were explored. The cores formed by the that applied on the column. However, the lateral cross-shaped steel sections resulted in the largest Table 1. Geometrical properties of the composite columns and material properties (SRC5 and CL-TO). SRC5 (Cross-shaped steel core, 29.8 MPa with a hoop of 75 mm) Composite columns section (mm x mm) D × B 280 × 280 Height of concrete column (mm) D 280 Width of concrete column (mm) B 280 Vertical part Horizontal part Depth of H-steel section (mm) h 175 175 Width of H-steel section (mm) b 90 90 Web thickness of H-steel section (mm) t 5 5 Flange thickness of H-steel section (mm) t 8 8 Rebar diameter (mm) Ø 15.96 Concrete compressive strength (MPa) f’ 29.8 Yield strength of rebar (MPa) f 350 yR Yield strength of steel (MPa) f 345 yS CL-TO (T-shaped steel core) Composite columns section (mm x mm) D × B 300 × 300 Height of concrete column (mm) D 300 Width of concrete column (mm) B 300 Vertical part Horizontal part Depth of H-steel section (mm) h 100 125 Width of H-steel section (mm) b 50 60 Web thickness of H-steel section (mm) t 5 6 Flange thickness of H-steel section (mm) t 7 8 Rebar diameter (mm) Ø 19.05 Concrete compressive strength (MPa) f’ 22.9 Yield strength of rebar (MPa) f 388 yR Yield strength of steel (MPa) f 333 yS JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 195 load was controlled by the lateral displacement cores with different shapes. However, the authors’ pre- using loading protocol (Nzabonimpa and Hong vious study divided the confined regions into the two 2019). regions including an equivalent confining region inside the transverse stirrups and an unconfined region out- side the transverse stirrups. The columns with the hoop 2.2. Idealization of the concrete confinement spacings of 75 mm were used with the application of the 50% of the nominal axial strength to determine an In (Chen and Lin 2006), the confined regions were equivalent confinement effect representing the con- divided into (1) a highly confined region inside the fined and unconfined regions provided by the cross- arches formed by the steel section, (2) a partially con- shaped steel cores. The confined equation proposed fined region outside the highly confined concrete by Mander, Priestley, and Park 1988 for the concrete region and inside parabolic arches formed by the long- sections was obtained from the equivalent confining itudinal bars, and (3) an unconfined region outside the factors. Equation 1 is used to calculate the concrete parabolic arches formed by the longitudinal bars. (El- strengths, for which the equivalent confinement factor Tawil and Deierlein 1999) proposed parabolic arches (K based on the highly confined and partially confined formed by the longitudinal bars and structural steel e, Figure 1. Strain compatibility based on equivalent confining factors. 196 D. H. NGUYEN AND W.-K. HONG Figure 1. Continued. regions) accounts for the confining effects offered by 2.3. Local buckling of the longitudinal bars and the steel cores. Figure 1(c) shows the confined stress– structural steel strain relationships modified based on the equivalent A constitutive model for the longitudinal reinforcing confining factors when the concrete was confined by rebars in the compression zone was proposed by the cross-shaped (refer to Legends 2 to 5) and T-shaped (Bayrak and Sheikh 2001), who observed the load- (Legend 5) steel cores. The unconfined stress–strain carrying capacity and inelastic buckling of the longitu- relationship proposed by the Mander is represented by dinal rebars under compression. The longitudinal rein- Legend 1. The stress–strain relationship of the T-shaped forcing steel and steel sections with an elasto-plastic steel core (Legend 5) with K = 1.26 is slightly greater constitutive relationship were used to model the com- than that of the cross-shaped steel core (refer to posite members subjected to a flexural bending Legend 2) with K = 1.2. The equivalent confining factor moment in the tension zone. The local buckling of the is defined in Equation 1. longitudinal rebars and steel cores was assumed to occur after the crushing of the partially confined con- f ¼ K f (1) cc e co crete. Figure 1(d) illustrates the axial-strain relationships JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 197 for the concrete (refer to columns tested by Chen et al. C ¼ C C þ C ¼ α � c c c1 c1 c2 1 1 0 0 (Chen et al. 1999; Chen and Lin 2006)) with a hoop � B � f α � c � B � f þ α 1 1 2 2 2 c c spacing of 100 mm (22.9 MPa) confined by the core ð cm1 steel with T-shaped steel sections (CL-TO) when the f dε c1 c equivalent confining factor (K ) is 1.26. � c � B � f ¼ � c � B � e 2 2 1 1 f ε cm1 cm2 (6) f dε c1 c 0 0 2.4. Formulation of the flexural strength (M ) nd f � c � B � f 2 2 c c f ε cm2 considering the confining effects provided by both cm2 transverse reinforcements and steel cores f dε c2 c þ � c � B � f The equilibrium and neutral axes of the composite sec- 2 2 0 c f ε cm2 cc tions based on the two simplified zones with the concrete stress-strain profiles at the maximum load and ultimate The calculations of mean stress factors (α) for the two load limit state were calculated based on Equations 7 and zones can be found in the previous paper of the 8. The entire composite section was explored to find the authors (Nguyen and Hong 2020a). neutral axes and strains of all structural components con- The neutral axis (c ) was calculated from the equili- sisting of the composite sections. The nominal flexural brium equations given in Equations 7 and 8. strength was defined as the maximum load limit state. The substantial concrete was lost at the ultimate load limit F þ C þ F þ F ¼ F þ F axial c R steel R steel compression compression tension tenstion state. (7) or 2.5. Maximum load limit F ¼ F þ F C F F axial R steel c R steel tension tenstion compression compression The formulation of the flexural strength (M ) con- nd (8) sidering the confining effects provided by the trans- verse reinforcements and cross-shaped steel cores Equations 9 to 12 were used to determine the inter- for the maximum load limit state with a 50% axial nal force capacity, including the c10ontribution from load of the nominal column capacity was presented. the steel cores at a maximum load limit state with The formulation for an ultimate load limit state with a 50% axial load of the nominal column capacity; a 40% axial load of the nominal column capacity is listed in the Appendix. The unconfined and equiva- F ¼ F þ F ¼ A � E � ε þ A � E � ε R r3 r4 r3 r r3 r4 r r4 tension lent confined concrete zones based on the constitu- d c r3 1 ¼ A � E � ε � þ A � E � ε tive equation developed by (Mander, Priestley, and r3 r cm1 r4 r cm1 Park 1988) were calculated using Equations 2, 3, and d c r4 1 4, where c is the neutral axis of the section at the maximum load limit state. The depth of the com- (9) pressive concrete block (c ) represents the equiva- lent zone confined by the steel section. The compressive forces C & C’ were determined for F ¼ F þ F ¼ 0:5� A � f þ A c1 c1 steel s8 s9 s8 s8 s9 tenstion the unconfined concrete, and the compressive force � f ¼ 0:5� A � E � ε þ A � E � ε ¼ 0:5 s9 s8 s s3 s9 s s4 C was calculated for the equivalent confined c2 � ½ðh þ d c t Þ� t � 1 s 1 w1 f 12 concrete. � � h þ d c t 1 s 1 f 12 � E � ε � s cm1 C ¼ α � c � B � f (2) c c1 1 1 1 � � h þ d c 0:5t 1 s 1 f 12 þ b � t � E � ε � f 1 f 12 s cm1 0 0 0 C ¼ α � c � B � f (3) 2 2 c1 1 c ðh þ d c t Þ 1 s 1 f 12 ¼ 0:5� � t � w1 0 c C ¼ α � c � B � f (4) c2 2 2 2 cc E � ε þ b � t � E s cm1 f 1 f 12 s � � Relationships between the compressive concrete h þ d c 0:5t 1 s 1 f 12 � ε � blocks and the neutral axes c and c are also estab- cm1 1 2 lished in Equation 5. (10) c ¼ c x (5) 2 1 1 The compressive concrete block is then calculated by F ¼ F þ F ¼ ðA þ A Þ� f (11) R r1 r2 r1 r2 yR compression Equation 6. 198 D. H. NGUYEN AND W.-K. HONG � � F ¼ F þ F þ F þ F þ F þ F steel s1 s2 s3 s4 s5 s6 compression � E � ε � � ðd þ h t þ 0:5c Þ