Experimental Study of H-Shaped Honeycombed Stub Columns with Rectangular Concrete-Filled Steel Tube Flanges Subjected to Axial Load

Hindawi Advances in Civil Engineering Volume 2021, Article ID 6678623, 18 pages https://doi.org/10.1155/2021/6678623

Research Article Experimental Study of H-Shaped Honeycombed Stub Columns with Rectangular Concrete-Filled Steel Tube Flanges Subjected to Axial Load

Jing Ji,1,2 Maomao Yang ,2 Zhichao Xu,3 Liangqin Jiang ,2 and Huayu Song2

1Key Laboratory of Structural Disaster and Control of the Ministry of Education, Harbin Institute of Technology, No. 92 West Dazhi Street, Nangang District, Harbin 150040, China 2College of Civil and Architectural Engineering, Northeast Petroleum University, Heilongjiang Key Laboratory of Disaster Prevention, Mitigation and Protection Engineering, No. 99 Xuefu Road, Longfeng District, Daqing 163318, China 3College of Engineering and Technology, Northeast Forestry University, No. 26 Hexing Road, Xiangfang, District, Harbin 150040, China

Correspondence should be addressed to Liangqin Jiang; [email protected]

Received 29 November 2020; Revised 11 May 2021; Accepted 24 May 2021; Published 8 June 2021

Academic Editor: Su¨leyman ˙Ipek

Copyright © 2021 Jing Ji et al. 1is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1e behavior of H-shaped honeycombed stub columns with rectangular concrete-filled steel tube flanges (STHCCs) subjected to axial load was investigated experimentally. A total of 16 specimens were studied, and the main parameters varied in the tests included the confinement effect coefficient of the steel tube (ξ), the concrete cubic compressive strength (fcu), the steel web thickness (t2), and the slenderness ratio of specimens (λs). Failure modes, load-displacement curves, load-strain curves of the steel tube flanges and webs, and force mechanisms were obtained by means of axial compression tests. 1e parameter influences on the axial compression bearing capacity and ductility were then analyzed. 1e results showed that rudder slip diagonal lines occur on the steel tube outer surface and the concrete-filled steel tube flanges of all specimens exhibit shear failure. Specimen load- displacement curves can be broadly divided into elastic deformation, elastic-plastic deformation, and load descending and residual deformation stages. 1e specimen axial compression bearing capacity and ductility increase with increasing ξ, and the axial compression bearing capacity increases gradually with increasing fcu, whereas the ductility decreases. 1e ductility significantly improves with increasing t2, whereas the axial compression bearing capacity increases slightly. 1e axial compression bearing capacity decreases gradually with increasing λs, whereas the ductility increases. An analytical expression for the STHCC short column axial compression bearing capacity is established by introducing a correction function (w), which has good agreement with experimental results. Finally, several design guidelines are suggested, which can provide a foundation for the popularization and application of this kind of novel composite column in practical engineering projects.

1. Introduction construction, and stress concentration. Many studies [5–8] have been devoted to steel-concrete composite structures Conventional multistory light steel structures have been with short construction period and high bearing capacity. widely applied for construction and reconstruction projects 1e steel-concrete composite frames not only can take [1–4]. Current structural systems are moving toward advantage of steel structural properties but also enhance superhigh, long-span, and heavily loaded structures, and their stiffness and overall stability and overcome defects and conventional light steel structures meet many new chal- shortcomings of conventional steel frame structures. 1is lenges such as small achievable span, low component study proposes a novel assembled composite frame con- bearing capacity, overall or local instability, complex joint sisting of H-shaped honeycombed columns with rectangular 2 Advances in Civil Engineering concrete-filled steel tube (CFST) flanges (STHCCs) and established an analytical expression to predict the bearing I-shaped honeycombed beams with rectangular CFST capacity. 1e accuracy of the proposed expression was flanges [9–11]. 1e columns and beams are connected to- verified by comparison with predictions calculated by ACI gether through integral joints, as shown in Figure 1. To and EC4. Sweedan et al. [21] investigated overall buckling reduce the deflection of composite beams, prestressing of axially loaded I-shaped columns with circular web tendons are arranged in the steel tubes of lower composite perforations and provided a simplified procedure for beam flanges, whose tension and anchorage are realized at evaluating the buckling capacity of columns. Chen and Ou the ends of the integral joint. 1e CFST sectional form is [22] studied CFST latticed column ultimate bearing ca- adopted as frame column flanges, where the concrete pre- pacity using ANSYS and proposed an expression based on a vents local steel tube buckling, while the steel tube con- parametric analysis to predict ultimate bearing capacity for tinuously restrains the concrete; hence, the concrete four-legged CFST latticed columns. Ellobody and Ghazy experiences three-dimensional compression, and interaction [23] experimentally studied fiber reinforced concrete-filled between the steel tube and concrete can be fully utilized. stainless steel tube columns subjected to axial and eccentric Honeycombed webs between double-limbed CFST flanges load and indicated that the EC4 code could accurately not only effectively connect indenpendent double CFST predict axial compressive bearing capacity for stainless steel columns but also greatly reduce composite member weights. tube concrete columns. Bao [24] proposed a practical Beam-column members and integral joints can be pre- method to calculate equivalent slenderness ratios for CFST fabricated in the factory, connected in the field, and then latticed columns, and an analytical expression was derived filled with concrete [12, 13]; therefore, there is no need to to predict CFST latticed column bearing capacity with support the template. Pouring concrete of the lower floor K-shaped joints. In order to simulate latticed columns does not affect upper steel member connections; hence, reasonably, Fooladi and Banan [25] developed a practical concrete can be poured continuously from the bottom to the super element based on the concept of finite element. top, and concrete maintenance time is not required, which Ekmekyapar and Al-Eliwi [26] tested 18 short, medium, can significantly shorten the construction period. 1e and long circular CFST columns and indicated that EC4 proposed composite structure frames are suitable for many predictions exhibited significantly better agreement with new construction and renovation projects due to the large test results, whereas AISC360-10 predictions were con- stiffness, high stability, and high bearing capacity. servative for all specimens. Liu et al. [27] experimentally Many studies have considered I-shaped steel beams studied the effects of different parameters on column with different flanges. Hassanein and Silvestre [14] instability under axial compression for 6 L-shaped and 12 vestigated transverse distortion buckling of hollow steel T-shaped CFST stub columns, and corresponding analyt- tube flange beams (HTFPG) without stiffeners to obtain ical expressions were proposed for stability bearing ca- HTFPG buckling capacity, verified the corresponding pacity based on experimental and finite element (FE) analytical expression, and finally provided corresponding analysis results. Yang et al. [28] researched the seismic design recommendations for this kind of beams. Erdal and behavior of four-legged square CFST latticed members Saka [9] experimentally investigated the flexural properties under lateral cyclic loading and revealed that the four- of twelve full-scale noncomposite cellular beams subjected legged square CFST latticed specimens outperformed to a concentrated load and presented ultimate load carrying hollow steel ones in terms of hysteretic behavior. Wang capacities of optimally designed steel cellular beams. Zhang et al. [29] experimentally investigated the axial compressive et al. [15] derived a nondimensional critical moment ex- performance of novel L-shaped and T-shaped concrete- pression for lateral torsional buckling of cantilever beams filled square steel tube (L/T-CFSST) columns and estab- with tip lateral elastic braces based on stability theory. lished formulae to calculate the axial compressive strength Zhang [16] investigated symmetric and antisymmetric and stability bearing capacity of the L/T-CFSST columns lateral-torsional buckling (LTB) performance of pre- accordingly. Shariati et al. [30] presented a numerical in- stressed steel I-beams and obtained analytical solutions for vestigation into the behavior of built-up concrete-filled symmetric and antisymmetric LTB of prestressed I-beams. steel tube columns under axial compression and indicated Based on tests and numerical analysis, Grilo et al. [17] that the raise of concrete strength with greater cross section proposed a new formula to determine the shear resistance led to a higher load bearing capacity compared to the steel of cellular beams for web-post buckling. Liu et al. [18] tube thickness increment. However, most of the previous proposed an analytical solution for the lateral-torsional research studies were mainly concentrated on beams with buckling (LTB) of steel girders with the CFST flange different flanges and CFST columns with various sections, subjected to a concentrated load. Wang et al. [19] predicted and it seems that there is seldom research reported on the flexural and shear yielding strength of short-span com- performance of H-shaped honeycombed columns with posite I-girder with concrete-filled tubular flanges and rectangular concrete-filled steel tube flanges (STHCCs). corrugated web. Studies on CFST composite columns have 1e honeycombed steel webs connect the two independent mainly focused on conventional CFST columns, latticed rectangular CFSTcolumns as a whole two-legged column, they columns, and specially shaped columns with various sec- can prevent the flanges from bending to both sides effectively, tions. Lam and Gardner [20] investigated axial compres- and it is similar to effect of oblique spars in the truss system. To sion for 16 concrete-filled stainless steel tubes to identify explore mechanical behavior of STHCCs, our research group parameter influences on column bearing capacity and [12] has investigated the buckling behavior of STHCCs and Advances in Civil Engineering 3

3 3

5 8 6 7

7 Integral node Integral node Layout of prestressed tendon Layout of prestressed tendon 1 2

1 Cross-shaped composite column with rectangular CFST ﬂanges 5 Connecting plate

2 H-shaped honeycombed composite column with rectangular CFST ﬂanges 6 High strength bolt

3 I-shaped honeycombed composite beam with rectangular CFST ﬂanges 7 Prestressing tendons

4 Integral node 8 Vertical stiffening rib Figure 1: Diagram of novel assembled composite frames. proposed eigenvalue and nonlinear buckling load expressions concrete mixture to test compressive strength. After these for this kind of composite columns. Based on this, this paper blocks were demolded, they were maintained under the same experimentally investigated axial compression of 16 STHCC conditions as specimens in the laboratory. 1e images of the stub columns, and the influences of different parameters on final specimens are shown in Figure 4(c). axial compression performance of the stub columns were studied. An analytical expression was derived to calculate ultimate bearing capacity of the stub columns based on the 2.3. Material Mechanical Properties measured experimental statistics. 2.3.1. Steel. Specimens were reasonably designed in accor- dance with the relevant regulations [32]. 1e experiment 2. Test Overview included 6 kinds of steel thicknesses (1.7, 2.3, 3.8, 6, 8, and 12 mm), and three identical samples were tested for each 2.1. Specimen Design. To study STHCC axial compression, thickness, i.e., 18 samples. Table 1 lists the measured average 16 specimens were designed with different hoop coefficient yield strength of tensile samples (fyf and fyw). (ξ), concrete cubic compressive strength (fcu), web thickness (t2), and slenderness ratio (λs) parameter values (see Table 1), where the physical meaning of the variables is shown in 2.3.2. Concrete. Four types of concrete (A, B, C, and D) were Figure 2. Honeycomb webs were formed by opening holes prepared with different strengths [33]. Table 2 lists the mix on steel webs with a diameter-to-height ratio (d/hw) of 0.7, proportions between cement, fine, and coarse aggregate and a space-between-holes-to-height ratio (s/hw) of 0.3. Two (P. O. 42.5 Portland cement, river sand, and gravel, re- steel cover plates were welded at the end of each specimen, spectively) and the corresponding average cubic compres- and two rectangular pouring holes were arranged in the sive strength (fcu). upper cover plate. To prevent local buckling of steel tubes and webs at the ends, 10 stiffening ribs were set amongst the steel tubes, webs, and cover plates. Figure 3 shows design and 2.4. Loading Scheme and Measurement. Axial compression compositions of the specimens. tests for all specimens were performed using a four column pressure tester (see Figure 5) in the Key Laboratory of Disaster Prevention and Mitigation Engineering and Pro- 2.2. Specimen Production and Maintenance of Specimens. tection Engineering of Heilongjiang Province. Specimens Rectangular steel tubes, steel webs, cover plates, and stiffening were placed on the pressure tester and leveled by the ribs were cut according to the specimen design, and rectangular SHEFFIELD-S078009 level ruler. holes were cut in symmetrical locations in the upper cover Automatic double-controlled loading was adopted. plates. 1e rust was removed from rectangular steel pipes, steel Preloading and unloading were performed during the webs, and cover plates surfaces after cutting; then, these preloading stage. Normal loading began after preloading components were welded together (see Figures 4(a) and 4(b)). with a rate of 0.5 kN/s in the initial stage. When vertical 1e H-shaped steel columns with rectangular steel tube flanges load reached 50% of the predicted peak load, the loading were placed on the vibrating platform, and concrete was mode was changed to displacement loading with a loading poured through the rectangular holes. When the assembly was rate of 0.02 mm/s. Axial load and displacement were vibrated until flooding slurry appeared, it is proved that the automatically collected using computer software columns were completely filled and compacted. Finally, the throughout the loading process. Resistance strain gauges concrete surface was pressed and leveled. 1ree standard cubic (RSGs) were placed near the central section of the blocks (150 ×150 ×150 mm) were also poured for each specimen flanges and webs, and DH3818Y static resistance 4 Advances in Civil Engineering

Table 1: Main parameters of specimens. 5 Specimens Dimensions hw × h1 × b × t1 × t2 (mm ) l (mm) λs fyf (MPa) fyw (MPa) ξ fcu (MPa) STHCC-1 100 × 50 ×100 ×1.7 × 06 370 12.82 269 321 0.60 49.50 STHCC-2 100 × 50 ×100 ×1.7 × 06 370 12.82 269 321 0.60 49.50 STHCC-3 100 × 50 ×100 × 2.3 × 06 370 12.82 282 321 0.88 49.50 STHCC-4 100 × 50 ×100 × 3.8 × 06 370 12.82 286 321 1.60 49.50 STHCC-5 100 × 50 ×100 × 3.8 × 06 370 12.82 286 321 1.60 49.50 STHCC-6 100 × 50 ×100 × 2.3 × 06 370 12.82 282 321 0.82 53.17 STHCC-7 100 × 50 ×100 × 2.3 × 06 370 12.82 282 321 0.66 65.60 STHCC-8 100 × 50 ×100 × 2.3 × 06 370 12.82 282 321 0.78 55.69 STHCC-9 100 × 50 ×100 ×1.7 × 08 370 12.82 269 325 0.60 49.50 STHCC-10 100 × 50 ×100 ×1.7 ×12 370 12.82 269 331 0.60 49.50 STHCC-11 100 × 50 ×100 × 2.3 × 06 270 12.82 282 321 0.88 49.50 STHCC-12 100 × 50 ×100 × 2.3 × 06 470 16.28 282 321 0.88 49.50 STHCC-13 100 × 50 ×100 ×1.7 × 06 270 9.35 269 321 0.60 49.50 STHCC-14 100 × 50 ×100 ×1.7 × 06 470 16.28 269 321 0.60 49.50 STHCC-15 100 × 50 ×100 × 3.8 × 06 270 9.35 286 321 1.60 49.50 STHCC-16 100 × 50 ×100 × 3.8 × 06 470 16.28 286 321 1.60 49.50

Note. hw, h1, b, t1, and t2 are√ the� web width, flange steel tubes’ height, width, and thickness, and web thickness, respectively. l is specimen length. λs is the slenderness ratio, i.e., λs � 2 3l/b. fyf and fyw are the measured average yield strength for flange and web steel, respectively. fcu is the measured average cubic compressive strength for concrete. ξ is the hoop coefficient, i.e., ξ � Asfyf/Acfck. 1e physical meaning of these variables is explained in the study by Yang and Han [31].

h w b 3. Test Results and Analysis

h1 t1 3.1. Test Phenomena and Failure Modes. Figure 7 shows the d t2 specific failure modes for the 16 short columns subjected to axial compression. 1e failure development process is ba- s hw H sically similar in the range of test parameters. l (i) During the initial loading, vertical load was small h1 and there was no significant surface change for all specimens. Steel strain increased linearly, and load- displacement (L-D) and load-strain (L-S) curves increased linearly. (ii) With increasing vertical load, the attachment to the (a) (b) steel tube surface gradually fell off, and a rudder slip diagonal line formed on the outer surface of the steel Figure 2: Physical meaning of all variables. tubes. Slight outward bulging appeared at the W and E sides (see Figure 5) of both ends of some specimens. Specimens began to show nonlinear characteristics, with L-D curves gradually deviating from

Upper cover plate the original linear trajectory. When load reached 80% of peak load, slight bulges appeared in the

Concrete middle of some specimens. With further increasing of vertical displacement, swelling in the middle of Concrete pouring hole the specimens increased gradually, accompanied by

Steel web the sound of cracking concrete. (iii) When the specimens reached ultimate bearing ca- Stiffening rib pacity, vertical load reduced gradually and the Lower cover specimens showed good ductility. 1e N and W side plate bulges of some specimens increased gradually, and S and N sides’ multiple bulges occurred in the upper, middle, and lower sections as vertical load reduced. Figure 3: Design and compositions of specimens. 1e flanges of both sides of the specimens bent outward gradually, the webs shrunk, and honeycomb holes gradually evolved into ellipses. With strain devices were used to collect the steel strains. further increasing of vertical displacement, bulges Figure 6 displays the residual strain gauge (RSG) layout on the flanges gradually connected to form overall at different heights for the specimens. bulging for the section. Advances in Civil Engineering 5

(a) (b)

(c)

Figure 4: Specimen production and maintenance. (a) Welding in progress. (b) Welded specimens. (c) Specimens ﬁlled with concrete.

Table 2: Concrete compositions.

Mix proportion − Types Water ash ratio w/c Cement content (kg·m 3) f (MPa) Cement : sand : gravel : WRA : SF cu A 1 :1.111 : 2.062 : 0 : 0 0.380 487 49.50 B 1 :1.020 : 2.062 : 0.010 : 0 0.288 548 53.17 C 1 :1.469 : 2.869 : 0.0293 : 0.0995 0.272 437 65.60 D 1 :1.660 :1.871 : 0.0411 : 0.1371 0.295 474 55.69 Note. WRA � water reducing agent; SF � silica fume.

(iv) CFST flanges showed shear failure characteristics Stage 1: elastic deformation (OA). 1e L-D curves for all specimens. increase linearly with basically constant slope. For (v) Comparing web failure modes of the specimens, 370 specimens STHCC-14–STHCC-16, nonlinearity ap- and 470 mm specimens showed web deformation pears in the initial stage of L-D curves, which is mainly developed along the same plane as the sides of the due to poor compaction between the loading device honeycombs, and the honeycombs gradually be- and specimens. 1is error has no effect on the overall came elliptical without local buckling. However, for process analysis for the specimens. 270 mm length specimens, web deformations not Stage 2: elastic-plastic deformation (AB). 1e steel only developed along the same plane to the two tubes enter the elastic-plastic state, and the restrained sides of the honeycombs but also appeared to buckle concrete shows significant nonlinearity. L-D curves outward slightly. significantly deviate from linearity with increasing slopes. Finally, the specimens reach ultimate load, i.e., peak bearing capacity (point B). 3.2. Load-Displacement Curves. Figure 8 shows the L-D Stage 3: load reduction (BC). After peak load, the load curves for the 16 specimens. It is seen that the curves can be in the L-D curves reduces and the reduction rate is very broadly divided into four stages. slow. All specimens show good plasticity and good 6 Advances in Civil Engineering

Load loading rate: 0.5 kN/s Displacement loading Pressure tester rate: 0.02 mm/s

N E Axial pressure W S control system

Upper loading plate Loading frame

Specimen

Lower loading plate Hydraulic cylinder

Strain measuring device Pressure tester

Figure 5: Loading device and measurement system for testing.

1 3 7 9 1 5 11 15 5 9 6 8 10 2 6 10 12 16 2 4 3 7 13 17 1 5 11 15 4 8 14 18 2 6 12 16 3 7 17 9 13 10 4 8 14 1 8

(a) (b) (c) (d)

Figure 6: Residual strain gauge (RSG) layout at diﬀerent heights for the specimens. (a) RSG appearance. (b) 270 mm. (c) 370 mm. (d) 470 mm.

displacement ductility. After passing the inflection around the steel tubes is connected together in many places. point (point C), the L-D curves change from convex to 1e L-S curves of the steel tubes become close to horizontal, concave. and the steel tubes have entered the complete plastic state. Stage 4: residual deformation (CD). Specimen deformation increases, and bulging around the steel tubes connects together, while the core concrete is still re- 3.4. Steel Web Load-Strain Curves. Figure 10 shows longi- strained by the steel tubes, and the specimens retain tudinal and transverse L-S curves for the steel webs. 1e web significant bearing capacity. Finally, the specimen is strain is relatively complex and smaller compared with destroyed. flange strain, i.e., web deformation is smaller than that of flanges under load; hence, local buckling does not occur for the webs during loading, maintaining stable vertical com- 3.3. Steel Tube Flange Load-Strain Curves. Due to the pression deformation. 1e rectangular CFST flanges mainly symmetrical cross section of the STHCC specimens, the bear load for STHCCs, whereas the honeycombed webs deformation trends are basically consistent for left and right mainly connect the two limbs of the flanges. 1e web itself flanges. Figure 9 shows only the longitudinal and transverse has little effect on improving bearing capacity for this kind of load-strain ((L-S) curves for the right flanges (see Figures 9 composite short column. (a1–p1) and (a2–p2)), respectively. Initial loading L-S curves are linear for all specimens. With increasing load, the slope gradually decreases and the 3.5. Specimen Force Mechanism. When the specimens are steel tube enters the elastic-plastic stage. After peak load, the subjected to longitudinal axial pressure, P, longitudinal steel tube strain rate gradually accelerates, and bulging strain, ε3, will be generated in the steel tubes and concrete. Advances in Civil Engineering 7

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m) (n) (o) (p)

Figure 7: Specimen failure modes. (a) STHCC-1. (b) STHCC-2. (c) STHCC-3. (d) STHCC-4. (e) STHCC-5. (f) STHCC-6. (g) STHCC-7. (h) STHCC-8. (i) STHCC-9. (j) STHCC-10. (k) STHCC-11. (l) STHCC-12. (m) STHCC-13. (n) STHCC-14. (o) STHCC-15. (p) STHCC-16. 8 Advances in Civil Engineering

800 800 1000 1400 B (3.82, 741.21) B (4.18, 706.12) B (3.07, 864.59) B (5.62, 1170.37) 640 C 640 C C C A A 800 A 1050 D A 480 D 480 D 600 D 700 320 ξ = 0.60 320 ξ = 0.60 400 ξ = 0.88 ξ = 1.60 N (kN) N (kN) N (kN) N (kN) λ = 1.85 λs = 1.85 λs = 1.85 λs = 1.85 s t = 6 mm 350 t = 6 mm 160 t2 = 6 mm 160 2 200 t2 = 6 mm 2 f = 49.50 MPa fcu = 49.50 MPa fcu = 49.50 MPa fcu = 49.50 MPa cu 0 0 0 0 0246810 0246810 0246810 04812 16 µ (mm) µ (mm) µ (mm) µm (mm) m m m

(a) (b) (c) (d) 1400 1200 1200 1200 B (3.44, 1182.15) B (3.19, 1067.75) B (3.55, 1173.69) B (3.08, 1086.86) C C C C 1050 900 900 A 900 A A D A D D D 700 600 600 600 ξ = 1.60 ξ = 0.82 ξ = 0.66 ξ = 0.78 N (kN) N (kN) N (kN) N (kN) λ = 1.85 λ = 1.85 λ = 1.85 λs = 1.85 350 s 300 s 300 s 300 t2 = 6 mm t2 = 6 mm t2 = 6 mm t2 = 6 mm fcu = 49.50 MPa fcu = 53.17 MPa fcu = 65.60 MPa fcu = 55.69 MPa 0 0 0 0 0 5 10 15 0246810 0246810 0246810 µ (mm) µ (mm) µ (mm) µm (mm) m m m

(e) (f) (g) (h) 1000 1000 1000 1000 B (3.09, 948.52) C B (2.70, 841.31) B (3.30, 798.26) 800 A C 750 B (2.96, 763.17) 750 C 750 C D A D 600 A D D A 500 500 500 ξ = 0.60 400 ξ = 0.88 ξ = 0.88 N (kN) N (kN)

ξ = 0.60 N (kN) N (kN) λ = 1.35 λ = 2.35 λs = 1.85 λs = 1.85 s s 250 250 t = 6 mm 250 t = 6 mm t2 = 8 mm t2 = 12 mm 200 2 2 f = 49.50 MPa f = 49.50 MPa fcu = 49.50 MPa fcu = 49.50 MPa cu cu 0 0 0 0 03691215 0481216 0426810 0426810 µ (mm) µ (mm) µ (mm) µm (mm) m m m

(i) (j) (k) (l) 900 900 1400 1200 B (2.22, 781.37) B (4.18, 1261.72) B (3.91, 1076.86) B (3.36, 716.92) C C C 1050 D C A A D 600 600 800 A D A D 700 ξ = 0.60 ξ = 0.60 ξ = 1.60 ξ = 1.60 N (kN) N (kN) N (kN) N (kN) 300 λ = 1.35 400 300 λs = 1.35 λs = 2.35 s λs = 2.35 350 t = 6 mm t2 = 6 mm t2 = 6 mm 2 t2 = 6 mm f = 49.50 MPa fcu = 49.50 MPa fcu = 49.50 MPa cu fcu = 49.50 MPa 0 0 0 0 0246810 0246810 0246810 0246810 µ (mm) µm (mm) µ (mm) µm (mm) m m

(m) (n) (o) (p)

Figure 8: Specimen load-displacement (L-D) curves. (a) STHCC-1. (b) STHCC-2. (c) STHCC-3. (d) STHCC-4. (e) STHCC-5. (f) STHCC-6. (g) STHCC-7. (h) STHCC-8. (i) STHCC-9. (j) STHCC-10. (k) STHCC-11. (l) STHCC-12. (m) STHCC-13. (n) STHCC-14. (o) STHCC-15. (p) STHCC-16.

1e transverse strain that steel tubes and concrete (ε1s and steel tubes, and its lateral expansion is hindered. Figure 11(a) ε1c, respectively) generate can be expressed as shows the interaction force generated between the steel tube and concrete core. Both the steel tubes and concrete core are ε1s � μsε3, (1) under three-directional stress (see Figure 11(b)). Since the steel tubes bulge outwards under the concrete and steel interaction (see Figure 12(a)), the hoop force significantly ε1c � μcε3, (2) reduces in the middle of the edge of steel tubes (see where μs and μc are Poisson’s ratio for steel and concrete, Figure 13(a)). Circumferential shear stress (τ) and normal respectively. stress pointing to the web honeycomb are also produced Initially, μc is lower than μs for the CFST flanges. When when the steel webs are subjected to P, as shown in steel longitudinal compressive stress reaches its proportional Figure 13(b). Steel tube flanges’ stability is improved due to limit, i.e., δ3 ≈ fp, μc≈μs. As P increases, steel stress exceeds its the support provided by the concrete core, allowing the steel proportional limit, i.e., δ3 > fp, μc > μs. From (1) and (2), the yield strength to be fully utilized. corresponding concrete strain exceeds that of steel, i.e., After peak load, the specimens bulge in many places and ε1c > ε1s, and expansion of the concrete core exceeds that of the bulges are connected together when displacement in- the steel tubes; hence, the concrete core is restrained by the creases, as shown in Figure 12(b). 1e honeycombed steel Advances in Civil Engineering 9

800 800 750 750

600 600 600 600

450 450 400 400 N (kN) N (kN) N (kN) N (kN) 300 300

200 200 150 150

0 0 0 0 –6000 –4500 –3000 –1500 0 0 1500 3000 4500 6000 –6000 –4000 –2000 0 2000 4000 6000 021000 0003000 4000 με με με με

1–11 1–15 1–12 1–16 2–11 2–15 2–12 2–16 1–13 1–17 1–14 1–18 2–13 2–17 2–14 2–18 (a (b ) STHCC-2 ) STHCC-2 1) STHCC-1 (a2) STHCC-1 1 (b2

800 800 1200 1200

600 600 900 900

400 400 600 600 N (kN) N (kN) N (kN) N (kN)

200 200 300 300

0 0 0 0 –6000 –5000 –4000 –3000 –2000 –1000 0 0 1000 2000 3000 4000 5000 6000 –6000 –4500 –3000 –1500 0 031500 0004500 6000 με με με με

3–11 3–15 3–12 3–16 4–11 4–15 4–12 4–16 3–13 3–17 3–14 3–18 4–13 4–17 4–14 4–18 (c (d ) STHCC-4 ) STHCC-4 1) STHCC-3 (c2) STHCC-3 1 (d2

1200 1400 1200 1200

900 1050 900 900

600 700 600 600 N (kN) N (kN) N (kN) N (kN)

300 350 300 300

0 0 0 0 –8000 –6000 –4000 –2000 0 0 2000 4000 6000 8000 –15000–12000 –9000 –6000–3000 0 042000 0006000 με με με με

5–11 5–15 5–12 5–16 6–11 6–15 6–12 6–16 5–13 5–17 5–14 5–18 6–13 6–17 6–14 6–18 (f ) STHCC-6 ) STHCC-6 (e1) STHCC-5 (e2) STHCC-5 1 (f2

1200 1200 1200 1200

900 900 900 900

600 600 600 600 N (kN) N (kN) N (kN) N (kN)

300 300 300 300

0 0 0 0 –9000–7500 –6000 –4500 –3000–1500 0 0 2000 4000 6000 8000 –15000–12000 –9000 –6000 –3000 0 042000 0006000 8000 10000 με με με με

7–11 7–15 7–12 7–16 8–11 8–15 8–12 8–16 7–13 7–17 7–14 7–18 8–13 8–17 8–14 8–18

(g1) STHCC-7 (g2) STHCC-7 (h1) STHCC-8 (h2) STHCC-8

800 800 850 850

680 680 600 600 510 510 400 400

N (kN) N (kN) N (kN) 340 N (kN) 340 200 200 170 170

0 0 0 0 –4000 –3000 –2000 –1000 0 –1000 10000 20003000 4000 –12000 –9000 –6000 –3000 0 063000 0009000 12000 με με με με

9–11 9–15 9–12 9–16 10–11 10–15 10–12 10–16 9–13 9–17 9–14 9–18 10–13 10–17 10–14 10–18 (j ) STHCC-10 ) STHCC-10 (i1) STHCC-9 (i2) STHCC-9 1 (j2 (a) Figure 9: Continued. 10 Advances in Civil Engineering

1200 1200 900 900

720 900 900 600 540 600 600 N (kN) N (kN) N (kN) 360 N (kN) 300 300 300 180

0 0 0 0 –15000 –12000 –9000 –6000 –3000 0 0 3000 6000 9000 12000 15000 –15000 –12000 –9000 –6000 –3000 0 041500 3000 5006000 με με με με 11–7 11–8 12–11 12–15 12–12 12–16 11–9 11–10 12–13 12–17 12–14 12–18

(k1) STHCC-11 (k2) STHCC-11 (l1) STHCC-12 (l2) STHCC-12

800 800 800 800

600 600 600 600

400 400 400 400 N (kN) N (kN) N (kN) N (kN)

200 200 200 200

0 0 0 0 –10000 –8000 –6000 –4000 –2000 0 062000 4000 0008000 –6000 –5000 –4000 –3000 –2000 –1000 0 –2000 0 2000 4000 6000 8000 10000 με με με με

13–7 13–8 14–11 14–15 14–12 14–16 13–9 13–10 14–13 14–17 14–14 14–18

(m1) STHCC-13 (m2) STHCC-13 (n1) STHCC-14 (n2) STHCC-14

1400 1400 1200 1200

1000 1050 1050 900 800

700 700 600 600 N (kN) N (kN) N (kN) N (kN) 400 350 350 300 200

0 0 0 0 –15000 –12000 –9000 –6000 –3000 0 0 3000 6000 9000 12000 15000 –15000 –12000 –9000 –6000 –3000 0 0 3000 6000 9000 12000 15000 με με με με

15–7 15–8 16–11 16–15 16–12 16–16 15–9 15–10 16–13 16–17 16–14 16–18

(o1) STHCC-15 (o2) STHCC-15 (p1) STHCC-16 (p2) STHCC-16 (b)

Figure 9: Steel ﬂange load-strain (L-S) curves.

1200 1200 1200

900 900 900

600 600 600 N (kN) N (kN) N (kN) 300 300 300

0 0 0 0 600 1200 1800 30002400 –1200 –900 –600 –300 3000 –600 –400 –200 0 200 600400 με με με

STHCC-1 STHCC-4 STHCC-1 STHCC-4 STHCC-1 STHCC-2 STHCC-5 STHCC-2 STHCC-5 STHCC-2 STHCC-3 STHCC-3 STHCC-3

(a) (b) (c) Figure 10: Continued. Advances in Civil Engineering 11

1200 850 850

680 680 900 510 510 600 340 340 N (kN) N (kN) N (kN) 300 170 170

0 0 0 –4000 –2000 0 2000 4000 6000 0 100 200 300 400 500 –200 –150 –100 –50 0 με με με

STHCC-6 STHCC-9 STHCC-9 STHCC-7 STHCC-10 STHCC-10 STHCC-8

(d) (e) (f) 1500 1500

1200 1200

900 900

N (kN) 600

300 300

0 0 0 300600 900 1200 1500 –6000 –4500 –3000 –1500 0 με με

STHCC-11 STHCC-14 STHCC-11 STHCC-14 STHCC-12 STHCC-15 STHCC-12 STHCC-15 STHCC-13 STHCC-16 STHCC-13 STHCC-16

(g) (h)

Figure 10: Steel web load-strain (L-S) curves. (a) STHCC-1-5, web 9. (b) STHCC-1-5, web 10. (c) STHCC-6-8, web 9. (d) STHCC-6-8, web 10. (e) STHCC-9-10, web 9. (f) STHCC-9-10, web 10. (g) STHCC-11-16, web 5 or 9. (h) STHCC-11-16, web 6 or 10.

P δ δ 3 1

δ δ 2 2

δ Steel tube 1 δ 3 δ δ 3′ 1′

δ δ 2′ 2′

δ Concrete 1′ δ 3′ P

(a) (b) (a) (b)

Figure 11: 3D steel and concrete stress. (a) Steel tube. (b) Steel and Figure 12: Local bulging and connection. (a) Local bulging. concrete. (b) Bulging connection. 12 Advances in Civil Engineering

P P 1300

1040

780 τ

N (kN) 520

260 Hoop coefficients ξ : 0.60, 0.88, 1.60 P 0 (a) (b) 0 3691215 μm (mm) Figure 13: Stress distribution. (a) Flange. (b) Web. STHCC-1-0.60 STHCC-4-1.60 STHCC-2-0.60 STHCC-5-1.60 webs connect two rectangular CFST columns as a whole; STHCC-3-0.88 hence, the webs prevent the flanges from bending to both Figure 14: Specimen load-displacement curves for different ξ. sides, which is similar to the effect of oblique spars in truss systems, thereby significantly improving ultimate bearing Table capacity of the composite short columns. 3: Specimen ultimate bearing capacity and ductility for different ξ. NT 4. Parameter Analysis Specimens t1 (mm) ξ u (kN) Δy (mm) Δu (mm) μ STHCC-1 1.70 0.60 706.12 2.23 5.51 2.47 4.1. Hoop Coefficient. Figure 14 shows L-D curves of spec- STHCC-2 1.70 0.60 741.21 2.06 5.13 2.49 imens for different ξ, and Table 3 lists the ultimate bearing STHCC-3 2.30 0.88 864.59 1.64 5.52 3.36 T STHCC-4 3.80 1.60 1170.37 2.81 14.46 5.15 capacity (Nu ) with different ξ. Stub column ductility is usually expressed using the ductility coefficient, where the STHCC-5 3.80 1.60 1182.15 1.83 10.36 5.66 larger coefficient implies improved ductility and vice versa. 1is paper analyzed STHCC specimen ductility using the displacement ductility coefficient: P Δu μ � , (3) BC Δy Pu P y AE where Δy and Δu are the yield and ultimate displacements obtained from the L-D curves for the specimens. 1e energy equivalent method [34] is used to determine the SOAO = SABCA equivalent yield point, as shown in Figure 15. We can obtain points A and B by making area (OAO) � area (ABCA), i.e., SOAO � SABCA. 1e projection of point B onto the x axis intersects with O Δ Δ the L-D curves at point E, which is the equivalent yield point. y 1e corresponding load and displacement are the yield load Figure 15: Yield point from equivalent energy. (Py) and yield displacement (Δy), respectively. 1e ultimate displacement (Δ ) is the displacement corresponding to the u 4.2. Concrete Cubic Compressive Strength. Figure 16 shows load falling to the nominal load limits, and we regarded 85% L-D curves for 4 specimens with different f , and Table 4 of the ultimate load as the nominal limit load. Table 3 lists μ cu lists corresponding NT and μ. Specimen NT increases by for specimens with different ξ. u u 23.5% as f increases from 49.50 to 53.17 MPa, and 9.9% as When ξ increases from 0.60 to 0.88, STHCC-3 NT in- cu u f increases from 53.17 to 65.60 MPa, whereas μ reduces creases by 22.4% and 16.6%, respectively (Figure 14 and cu from 3.36 to 1.90 as f increases from 49.50 to 65.60. 1us, Table 3), compared to STHCC-1 and STHCC-2. When ξ cu enhancing concrete strength can improve ultimate bearing increases from 0.88 to 1.60, STHCC-4 and STHCC-5 NT are u capacity of the composite stub columns, while reducing 35.4% and 36.7% higher than that of STHCC-3, respectively. ductility. When ξ increases from 0.60 to 1.60, specimen μ increases significantly from 2.47 to 5.66. To improve ultimate bearing capacity and ductility, ξ may be increased appropriately 4.3. Steel Web @ickness. Figure 17 shows L-D curves for under the condition that the steel ratio of the column meets specimens with different t2, and Table 5 lists corresponding T T the design requirements of STHCC columns. Nu and μ. Specimen Nu increases from 706.12 and 741.21 to Advances in Civil Engineering 13

1300 900

1040

600 780 Web thickness

N (kN) 520 N (kN) t2 (mm): 6, 8, 12 300 Concrete strength grade k 260 fcu (MPa): 49.50, 53.17, 55.69, 65.60

0 0 0 246810 0 246810

μm (mm) μm (mm) STHCC-3-49.50 MPa STHCC-1-6 mm STHCC-6-53.17 MPa STHCC-2-6 mm STHCC-7-65.60 MPa STHCC-9-8 mm STHCC-8-55.69 MPa STHCC-10-12 mm Figure Figure 16: Specimen load-displacement curves for diﬀerent fcu. 17: Specimen load-displacement curves for diﬀerent t2.

Table 5: Specimen ultimate bearing capacity and ductility for Table 4: Specimen ultimate bearing capacity and ductility for diﬀerent t2. diﬀerent fcu. T T Specimens t2 (mm) Nu (kN) Δy (mm) Δu (mm) μ Specimens fcu (MPa) Nu (kN) Δy (mm) Δu (mm) μ STHCC-1 6 706.12 2.23 5.51 2.47 STHCC-3 49.50 864.59 1.64 5.52 3.36 STHCC-2 6 741.21 2.06 5.13 2.49 STHCC-6 53.17 1067.75 1.93 5.78 2.99 STHCC-9 8 763.17 1.61 4.85 3.01 STHCC-7 65.60 1173.69 3.01 5.72 1.90 STHCC-10 12 798.26 1.39 8.11 5.84 STHCC-8 55.69 1086.86 1.82 3.71 2.04

superimposing bearing capacity of rectangular CFST col- 763.17 kN (8.1% and 3.0%, respectively) as t2 increases from umns and webs based on the expression for bearing capacity NT 6 to 8 mm. However, specimen u increases from 763.17 to of ordinary rectangular CFST columns: 798.26 kN (4.6%), and μ increases from 2.47 to 5.84 (136.4%) 2 as t2 increases from 6 to 12 mm. 1us, increasing web Nu1 � 2�aλs + bλs + c�Asc(1.18 + 0.85ξ)fck + kyfywhwt2, thickness can eﬀectively improve composite stub column (4) ductility, while the contribution to increasing bearing capacity is not signiﬁcant. 1erefore, appropriately increasing 1 +�35 + 2λp − λ0� · e web thickness will improve composite stub columns’ sta- a � , (5) bility and vertical seismic performance. 2 �λp − λ0 �

b � e − a , ( ) 4.4. Slenderness Ratio. Figure 18 shows L-D curves for 2 λp 6 specimens with different λs, and Table 6 lists corresponding T T 2 ( ) Nu and μ. Specimen Nu decreases by 11.3% as λs increases c � 1 − aλ0 − bλ0, 7 from 9.35 to 16.28 (Figure 18(a)), from 781.37 to 716.92 kN 0.3 (8.3%) as λs increases from 9.35 to 16.28 (Figure 18(b)), and 235 25 α 0.05 d � �13500 + 4810 ln� �� , decreases from 1261.72 to 1076.86 kN (14.6%) when λs in- f f + 5 0.1 creases from 9.35 to 16.28 (Figure 18(c)). 1us, specimen yf ck ultimate bearing capacity decreases with increasing slen- (8) derness ratio. Table 6 and Figure 19 also show that specimen −d μ increases correspondingly with increasing λs. e � , 3 (9) �λp + 35 � 5. STHCC Ultimate Bearing Capacity √� �� where �A��sc � h1b, α � As/Ac, λs � 2 3l/h1, λp � 1811/ fyf , T Nu for STHCC composite stub columns subjected to axial λ0 � π (220ξ + 450)/[(0.85ξ + 1.18)fck], λs is the slender- load can be obtained from test results of 16 STHCC spec- ness ratio of single CFST flange for specimens, Asc is the imens with different parameters. To consider influences of ξ, cross-sectional area, ξ is the hoop coefficient, fck is the fcu, t2, and λs on ultimate bearing capacity of composite stub standard concrete axial compressive strength, fyf is the steel columns, an analytical expression (Nu1) is constructed by flange yield strength, fyw is the steel web yield strength, α is 14 Advances in Civil Engineering

1000 900

750 600

Slenderness ratio 500 Slenderness ratio λs : 9.35, 12.82, 16.28 N (kN) N (kN) λs : 9.35, 12.82, 16.28 300 250

0 0 0 246810 0 246810

μm (mm) μm (mm) STHCC-11-9.35 STHCC-13-9.35 STHCC-2-12.82 STHCC-3-12.82 STHCC-1-12.82 STHCC-14-16.28 STHCC-12-16.28

(a) (b) 1400

1050

700 Slenderness ratio λs : 9.35, 12.82, 16.28 N (kN)

350

0 0 3691215

μm (mm) STHCC-15-9.35 STHCC-5-12.82 STHCC-4-12.82 STHCC-16-16.28

Table 6: Specimen ultimate bearing capacity and ductility for diﬀerent λs. 7 t l NT Δ Δ b Specimens 1 λ u y u μ s 6 h (mm) (mm) (kN) (mm) (mm) 1 t1 t STHCC-1 1.70 370 12.82 706.12 2.23 5.51 2.47 2 5 h H STHCC-2 1.70 370 12.82 741.21 2.06 5.13 2.49 w STHCC-3 2.30 370 12.82 864.59 1.64 5.52 3.36 μ 4 h STHCC-4 3.80 370 12.82 1170.37 2.81 14.46 5.15 1 STHCC-5 3.80 370 12.82 1182.15 1.83 10.36 5.66 3 STHCC- 2.30 270 9.35 948.52 1.69 5.49 3.25 11 STHCC- 2 2.30 470 16.28 841.31 1.31 6.82 5.21 12 STHCC- 1 1.70 270 9.35 781.37 1.29 3.12 2.42 8 12 16 20 24 28 13 λ STHCC- s 1.70 470 16.28 716.92 1.67 6.16 3.69 14 t1 = 3.80 mm STHCC- t = 2.30 mm 3.80 270 9.35 1261.72 2.26 11.07 4.90 1 15 t1 = 1.70 mm STHCC- 3.80 470 16.28 1076.86 2.02 12.44 6.16 Figure 16 19: Specimen μ for diﬀerent λs. Advances in Civil Engineering 15

Table C T 7: Nu1 and Nu of 16 specimens. 5 T C C C T T C T T Specimens hw × h1 × b × t1 × t2 (mm ) ξ λs fcu (MPa) Nu (kN) Nu1 (kN) Nu (kN) |Nu1 − Nu |/Nu (%) |Nu − Nu |/Nu (%) STHCC-1 100 × 50 ×100 ×1.7 × 06 0.6 12.82 49.50 706.12 602.65 736.26 14.65 4.27 STHCC-2 100 × 50 ×100 ×1.7 × 06 0.6 12.82 49.50 741.21 602.65 736.26 18.69 0.67 STHCC-3 100 × 50 ×100 × 2.3 × 06 0.8 12.82 49.50 864.59 683.77 876.97 20.91 1.43 STHCC-4 100 × 50 ×100 × 3.8 × 06 1.6 12.82 49.50 1170.37 878.33 1188.7 24.95 1.57 STHCC-5 100 × 50 ×100 × 3.8 × 06 1.6 12.82 49.50 1182.15 878.33 1188.7 25.70 0.55 STHCC-6 100 × 50 ×100 × 2.3 × 06 0.8 12.82 53.17 1067.75 711.39 982.82 33.37 7.95 STHCC-7 100 × 50 ×100 × 2.3 × 06 0.6 12.82 65.60 1173.69 798.97 1164.5 31.93 0.78 STHCC-8 100 × 50 ×100 × 2.3 × 06 0.7 12.82 55.69 1086.86 729.67 1037.7 32.86 4.52 STHCC-9 100 × 50 ×100 ×1.7 × 08 0.6 12.82 49.50 763.17 633.04 766.65 17.05 0.46 STHCC-10 100 × 50 ×100 ×1.7 ×12 0.6 12.82 49.50 798.26 694.64 828.25 12.98 3.76 STHCC-11 100 × 50 ×100 × 2.3 × 06 0.8 9.35 49.50 948.52 702.32 955.11 25.96 0.69 STHCC-12 100 × 50 ×100 × 2.3 × 06 0.8 16.28 49.50 841.31 664.59 818.86 21.01 2.67 STHCC-13 100 × 50 ×100 ×1.7 × 06 0.6 9.35 49.50 781.37 623.45 805.09 20.21 3.04 STHCC-14 100 × 50 ×100 ×1.7 × 06 0.6 16.28 49.50 716.92 585.30 689.17 18.36 3.87 STHCC-15 100 × 50 ×100 × 3.8 × 06 1.6 9.35 49.50 1261.72 900.24 1268.3 28.65 0.52 STHCC-16 100 × 50 ×100 × 3.8 × 06 1.6 16.28 49.50 1076.86 855.59 1117.1 20.55 3.74

500 500

400 400

300 300

∗ y = Intercept + B1∗ × ^1 + y = Intercept + B1 × ^1 + Equation Equation ∗ ∗

ω (kN) B2 × ^2

ω (kN) B2 × ^2 200 200 Plot B Plot B Weight No weighting Weight No weighting Intercept –28.58294 ?120.18652 Intercept –71.71186 ?97.6333 B1 98.27278 ?56.52853 B1 2.279 ?0.91465 100 B2 –6.59816 ?5.68338 100 B2 –0.00312 ?0.00187 Residual sum of squa 79650.47235 Residual sum of sq 57376.62477 R-square (COD) 0.45237 R-square (COD) 0.60551 Adj. R-square 0.36812 Adj. R-square 0.54482 0 0 2 2 2 2 0.0 4.0 × 100 8.0 × 100 1.2 × 101 1.6 × 101 0.0 2.0 × 10 4.0 × 10 6.0 × 10 8.0 × 10 η η Test scatter Test scatter Fitting curve Fitting curve (a) (b) 500 500

400 400

300 300

∗ y = Intercept + B1∗ × ^1 + y = Intercept + B1 × ^1 + Equation Equation ∗ ∗ ω (kN) B2 × ^2 ω (kN) B2 × ^2 200 200 Plot B Plot B Weight No weighting Weight No weighting Intercept –65.67001 ?81.47276 Intercept –44.82875 ?70.85435 B1 0.04266 ?0.01551 B1 7.5052E-4 ?2.69904E 100 B2 –1.08602E-6 ?6.4848 100 B2 –3.43808E-10 ?2.2089 Residual sum of sq 41483.09157 Residual sum of sq 31513.22674 R-square (COD) 0.71479 R-square (COD) 0.78333 Adj. R-square 0.67091 Adj. R-square 0.75 0 0 0.0 8.0 × 103 1.6 × 104 2.4 × 104 3.2 × 104 4.0 × 104 0.0 4.0 × 105 8.0 × 105 1.2 × 106 1.6 × 106 η η Test scatter Test scatter Fitting curve Fitting curve

500 500

400 400

300 300

y = Intercept + B1∗ × ^1 + ∗ Equation Equation y = Intercept + B1 × ^1 + B2∗ × ^2 ∗ ω (kN) ω (kN) B2 × ^2 200 Plot B 200 Plot B Weight No weighting Weight No weighting Intercept –34.76061 ?49.7793 Intercept –20.46542 ?34.81186 B1 1.40167E-5 ?3.3967 B1 2.53327E-7 ?4.04657E 100 B2 –1.20277E-13 ?4.838 100 B2 –3.83363E-17 ?9.0561 Residual sum of s 24901.93595 Residual sum of squ 19719.61134 R-square (COD) 0.82879 R-square (COD) 0.86442 Adj. R-square 0.80245 Adj. R-square 0.84356 0 0 0.0 2.0 × 107 4.0 × 107 6.0 × 107 8.0 × 107 1.0 × 108 0.0 2.0 × 109 4.0 × 109 6.0 × 109 8.0 × 109 η η Test scatter Test scatter Fitting curve Fitting curve

(e) (f) 500 500

400 400

300 300

∗ y = Intercept + B1 × ^1 + y = Intercept + B1∗ × ^1 + Equation ∗ Equation B2 × ^2 B2∗ × ^2 ω (kN) 200 Plot B ω (kN) 200 Plot B Weight No weighting Weight No weighting Intercept –5.19843 ?26.7778 Intercept 9.26923 ?21.84227 B1 4.51825E-9 ?5.48589 B1 8.06838E-11 ?8.15177 100 B2 –1.15481E-20 ?1.8698 100 B2 –3.39833E-24 ?4.2402 Residual sum of sq 15558.48474 Residual sum of squ 12579.34761 R-square (COD) 0.89303 R-square (COD) 0.91351 Adj. R-square 0.87657 Adj. R-square 0.90021 0 0 0.0 1 × 1011 2 × 1011 3 × 1011 4 × 1011 5 × 1011 0.0 6.0 × 1012 1.2 × 1013 1.8 × 1013 2.4 × 1013 3.0 × 1013 η η Test scatter Test scatter Fitting curve Fitting curve

(g) (h)

Figure 20: Fitting curves between ω and η for n � 1, 2, ..., 8. (a) n � 1. (b) n � 2. (c) n � 3. (d) n � 4. (e) n � 5. (f) n � 6. (g) n � 7. (h) n � 8. the steel content, and ky is the reduction factor of the webs where n � 1, 2, 3, ..., 8. calculated according to Zhang [34]. Figure 20 shows fitting curves for ω and η when n is 1, 2, ..., C Table 7 lists calculated ultimate bearing capacity (Nu1) 8. 1e fitted curves are consistent with experimental points T and experimental value (Nu ) of composite short columns. when n is 6, 7, and 8. It is seen from Figure 20 that the error is C Nu1 calculated by the superposition method exhibits larger not significant for n > 6. 1erefore, n is determined to be 8: error compared with the experimental value; hence, bearing − 17 2 − 7 capacity obtained by simple superposition is lower and ω � −3.8 × 10 η + 2.5 × 10 η − 20.5. (12) conservative. Considering coupling effect of CFST flanges and By substituting equation (12) into equation (10), the STHCC honeycombed webs, this study proposes an analytical ex- ultimate bearing capacity (N ) is expressed as pression by means of introducing correction function (ω) and u 2 influence factor (η) and modifies (4) as follows: Nu � 2�aλ + bλ + c �Asc(1.18 + 0.85ξ)fck + kyfywhwt2 Nu � Nu1 + ω(η). (10) 8 2 8 − 17 ξ × f − 7 ξ × f 1e experimental data (listed in Table 7) indicate that η is − 3.8 × 10 �cu � + 2.5 × 10 �cu � − 20.5. th λs λs proportional to ξ and the n power of fcu, while inversely (13) proportional to λs, i.e., n ξ × fcu Table 7 lists the calculated STHCC short column ulti- η � , (11) C λs mate bearing capacity (Nu ) from equation (13). Figure 21 Advances in Civil Engineering 17

1500 1500

1250 1250

1000 1000 (kN) (kN) C u C u 1 N N 750 750

500 500 500 750 1000 1250 1500 500 750 1000 1250 1500

T T Nu (kN) Nu (kN)

(a) (b)

Figure T C T C 21: Experimental and calculated results before and after correction. (a) Nu and Nu1. (b) Nu and Nu .

compares the experimental and calculated results before and increasing of λs, the ultimate bearing capacity of the spec- after correction. 1ere is relatively small error between imens decreases gradually; conversely, the ductility increases calculated and experimental ultimate bearing capacity, accordingly. which is suﬃcient for practical engineering. 1erefore, the By means of introducing the correction function (ω) and improved expression (equation (13)) is more reasonable to the inﬂuence factor (η), an analytical expression calculating calculate STHCC short column ultimate bearing capacity STHCC short column ultimate bearing capacity is estab- than the classical superposition approach. lished, which has good agreement with experimental results.

6. Conclusion Data Availability Axial compression of 16 STHCC stub specimens are ex- 1e data used to support the findings of this study are in- perimentally investigated with regard to the hoop coefficient cluded within the article. (ξ), concrete cubic compressive strength (fcu), web thickness (t2), and slenderness ratio parameters (λs). 1e experimental Conflicts of Interest phenomena, failure modes, L-D curves, and flange and web L-S curves are obtained. 1e force mechanism is clearly 1e authors declare that they have no conflicts of interest. defined for the specimens. A rudder slip diagonal line forms on the outer surface of the specimens. CFST flanges show shear failure character- Acknowledgments istics for all specimens, and the flanges bend outward 1e authors are grateful for the financial support received gradually; meanwhile, the webs shrink, which lead to from the Opening Fund for Key Laboratory of the Ministry honeycomb circular holes gradually evolving into ellipses. of Education for Structural Disaster and Control of Harbin 1e L-D curves for 16 specimens can be broadly divided into Institute of Technology (Grant no. HITCE201908), Na- four stages: elastic deformation, elastic-plastic deformation, tional Natural Science Foundation of China (Grant no. load reduction, and residual deformation. 1e L-S curves 51178087), Natural Science Foundation of Heilongjiang show that the flanges mainly bear load for STHCCs, whereas Province (Grant no. LH2020E018), Scientific Research the honeycombed webs mainly connect the two limbs of the Fund of Institute of Engineering Mechanics, China flanges. When the transverse strain of the core concrete Earthquake Administration (Grant no. 2020D07), and exceeds that of the steel tubes, both the steel tubes and core Northeast Petroleum University Guided Innovation Fund concrete are under three-directional stress; hence, the in- (Grant no. 2020YDL-02). 1e authors thank International teraction force is generated between the steel tubes and core Science Editing (http://www.internationalscienceediting. concrete. com) for editing this manuscript. 1e influences of parameters on ultimate bearing capacity and ductility are systematically investigated. 1e results indicate that, with increasing ξ, the ultimate bearing References capacity and the ductility of the specimens improve cor- [1] A. Kaveh, M. Kalateh-Ahani, and M. Fahimi-Farzam, respondingly. With increasing fcu, the ultimate bearing ca- “Damage-based optimization of large-scale steel structures,” pacity of the specimens enhances accordingly; on the Earthquakes and Structures, vol. 7, no. 6, pp. 1119–1139, 2014. contrary, the ductility decreases gradually. With the in- [2] C. D. Eamon, A. W. Lamb, and K. Patki, “Effect of moment creasing of t2, the ductility improves significantly, whereas gradient and load height with respect to centroid on the the ultimate bearing capacity increases slightly. With the reliability of wide flange steel beams subject to elastic lateral 18 Advances in Civil Engineering

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