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Analysis and design of axially loaded square CFST columns with diagonal ribs
Journal of Constructional Steel Research xxx (xxxx) xxx
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Analysis and design of axially loaded square CFST columns with diagonal ribs Xuhong Zhou a, Zheng Zhou a, Dan Gan a, b, * a b
School of Civil Engineering, Chongqing University, Chongqing, 400045, China College of Water Resources and Architectural Engineering, Shihezi University, Shihezi, 832000, Xinjiang, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 August 2019 Received in revised form 23 October 2019 Accepted 1 November 2019 Available online xxx
Diagonal binding ribs, made of thin-walled steel plates with circular openings and welded to the steel tube of a square concrete-filled steel tubular (CFST) column, can improve the composite effect effectively by co-carrying axial compressive forces and confining the steel tube and concrete. The column with diagonal ribs is referred to as diagonal ribs stiffened CFST column. This paper summarizes the test results of axially loaded diagonal ribs stiffened and longitudinal ribs stiffened CFST columns comprehensively, followed by further tests of stub columns with longitudinal reinforcing bars. A verified finite element analysis (FEA) model was presented to implement parametric studies. The studied parameters included diagonal rib detailing (i.e., opening diameter, opening spacing, and welding position) and material strengths. Finally, based on the test and analysis results, design considerations, involving width-tothickness ratio limits of tube plates, diagonal rib detailing, thickness matching relationship between diagonal ribs and the steel tube, detailing of composite column with diagonal ribs, and load-carrying capacity prediction, were proposed. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Diagonal binding rib Concrete-filled steel tube Composite effect Axial compression Finite element analysis Design considerations
1. Introduction Square concrete-filled steel tubular (CFST) columns are widely used because of convenient beam-to-column joint construction, high moment capacity and aesthetic consideration [1]. However, the largely reduced confinement to the infilled concrete is mainly from the corners of the square steel tube, and the thin-walled square steel tube is susceptible to local buckling, as shown in Fig. 1(a). To improve the composite effect between the infilled concrete and a square steel tube, several kinds of stiffening schemes were proposed [2e11]. Based on these stiffening methods, the authors proposed diagonal ribs stiffened square CFST columns [12,13] (Fig. 1(b)). Test results about 34 stub columns with extensive parameters had been reported in companion papers [12,13], which mainly focused on the axial behavior of diagonal ribs stiffened square CFST columns and the comparison of composite effect of different kinds of stiffening schemes and cross-sectional shapes. It was concluded that the positions where the diagonal ribs were welded to the steel tube can act as a fixed end, changing the tube local buckling mode (Fig. 1(b)); and the diagonal ribs can not only
* Corresponding author. School of Civil Engineering, Chongqing University, Chongqing, 400045, China. E-mail address: [email protected] (D. Gan).
confine the steel tube and concrete, but also co-carry the axial forces. Hence, the ductility and ultimate strength were significantly enhanced, and the diagonal ribs stiffened square CFST columns behaved better than octangular CFST columns and square CFST columns with longitudinal ribs when the steel ratios were the same. In high-rise buildings, mega-columns are needed due to huge vertical loads [14,15]. As shown in Fig. 2, various stiffeners, including longitudinal ribs, studs and internal diaphragms, are applied in mega-column, leading to complex fabrication. The diagonal ribs stiffened square CFST column showed superior axial behavior, so the diagonal ribs have the potential of replacing the various stiffeners in CFST columns and thus simplify the fabrication process. In mega-columns, longitudinal reinforcing bars are usually needed to increase the ultimate strength and fire resistance [16]. Thus, this paper summarizes the test results of axially loaded diagonal ribs stiffened and longitudinal ribs stiffened CFST columns comprehensively, followed by further tests of stub columns with longitudinal reinforcing bars. To facilitate the use of the proposed diagonal ribs stiffened square CFST columns and propose a rational design method, a finite element analysis (FEA) model which was verified by test results was presented, followed by extensive parametric analysis. The main parameters included diagonal ribs detailing (i.e., opening
https://doi.org/10.1016/j.jcsr.2019.105848 0143-974X/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: X. Zhou et al., Analysis and design of axially loaded square CFST columns with diagonal ribs, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105848
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Nomenclature Ab Ac As Asc At B b bs d Ec Es fc fck fr fr’ fscy fyb fys fyt Is ke L Nb NDBJ
cross-sectional area of reinforcing bars cross-sectional area of concrete cross-sectional area of diagonal rib sum of effective cross-sectional areas of the steel tube, the concrete core and the diagonal ribs cross-sectional area of steel tube column width width of sub-plate diagonal rib width opening diameter on one diagonal rib elastic modulus of concrete elastic modulus of steel prism compressive strength of concrete characteristic compression strength of concrete confining stress effective confining stress nominal average strength of a square or rectangular CFST column yield strength of reinforcing bar yield strength of diagonal rib yield strength of steel strength index confinement effectiveness coefficient column height buckling load ultimate strength obtained from code DBJ/T13-512010
NEC4 NFEA Np Nu n ne nd s ts tt ε85% εb εr εth εtv εy
m mc ms x r sc scc ssh ssv st sth stv
ultimate strength obtained from code Eurocode 4 ultimate load obtained from FEA predicted ultimate strength experimental ultimate load opening number on one diagonal rib experimental axial load level designing axial load level opening spacing on one diagonal rib thickness of stiffener thickness of tube wall the axial strain when the load falls to 85% of the ultimate load local buckling strain longitudinal strains of reinforcing bars horizontal strains of steel tube longitudinal strains of steel tube yield strain ductility coefficient Poisson ratio of concrete Poisson ratio of steel confinement coefficient total steel ratio compressive strength of concrete in FEA compressive strength of confined concrete horizontal stress of the diagonal rib vertical stresses of the diagonal rib tensile strength of concrete in FEA horizontal stress of the steel tube vertical stress of the steel tube
Fig. 1. Buckling modes.
diameter, opening spacing, and welding position) and material strengths. At last, design considerations, involving width-tothickness ratio limits of the steel tube plates, diagonal ribs detailing, thickness matching relationship between diagonal rib and the steel tube, detailing of columns with diagonal ribs, and loadcarrying capacity prediction, were proposed. 2. Brief review of the previous tests and further stub column tests 2.1. Specimens details A total of 38 stub composite columns, including the previous tests of 34 columns in Refs. [12,13] and further stub column tests of 4 columns with longitudinal reinforcing bars in this paper, were tested under axial compression, which can be identified as six
groups, namely Groups A, B, D, F, G and H. The width B and length L of all the specimens are 300 mm and 900 mm, respectively. The specimen details are listed in Table 1 and Fig. 3. Note that the 25 mm large-diameter reinforcing bars were only located in four strongly confining corners to get a relatively large moment capacity (Fig. 3 (a) and (b)); no stirrups were used to better compare and understand the effect of the reinforcing bars, while reinforcing bars were positioned by spot-welded bars (Fig. 3 (g)); square annular plate was spot welded to the tube end to keep the square shape of the unstiffened steel tube, because the unstiffened thin-walled steel tube would deform inward or outward during welding. The square annular plate would be removed during test (Fig. 3 (g)). Specimen designations starting with SS mean stiffened square CFST columns with diagonal ribs or longitudinal ribs, while SU and OU refer to unstiffened square CFST columns and unstiffened octangular CFST columns, respectively. Following the SS or SU, the
Please cite this article as: X. Zhou et al., Analysis and design of axially loaded square CFST columns with diagonal ribs, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105848
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Fig. 2. Mega-column with various stiffeners.
Table 1 Summary of specimen information. No.
Specimen
fc/MPa
fyt/MPa
fys/MPa
fyb/MPa
tt/mm
ts/mm
d/mm
s/mm
r/%
Nb/kN
Nu/kN
Is
m
Source
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
SU-2-A SU-3-A SU-6-A SS-2-2-B SS-2-2-B2 SS-2-2-B3 SS-2-2-B4 SS-2-2-B5 SS-2-3-B SS-2-6-B SS-3-2-B SS-3-3-B SS-3-6-B SS-6-2-B SS-6-3-B OU-2-G OU-3-G SS-3-2-F1 SS-3-3-F2 SU-3-A-c SS-2-2-B1 SS-3-2-B1 SS-2-2-B-c SS-3-2-B-c SS-3-3-B-c SS-2-2-D1 SS-2-2-D2 SS-2-2-D3 SS-3-2-D2 SS-3-2-D3 SS-2-2-H SS-2-3-H SS-3-2-H SS-3-3-H SU-2-A-r SU-3-A-r SS-2-2-B-r SS-3-2-B-r
48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 81.4 48.6 48.6 48.6 48.6 48.6 48.6 48.6 81.4 48.6 48.6 81.4 81.4 81.4 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6
176.7 356.1 317.5 176.7 176.7 176.7 176.7 176.7 176.7 176.7 356.1 356.1 356.1 317.5 317.5 356.1 356.1 356.1 356.1 176.3 176.7 356.1 176.7 356.1 176.3 189.0 176.7 176.7 356.1 356.1 176.7 176.7 356.1 356.1 176.7 356.1 176.7 356.1
/ / / 176.7 176.7 176.7 176.7 176.7 356.1 317.5 176.7 356.1 317.5 176.7 356.1 / / 176.7 356.1 / 176.7 176.7 176.7 176.7 176.3 189.0 176.7 176.7 176.7 176.7 176.7 356.1 176.7 356.1 / / 176.7 176.7
/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / 499.1 499.1 499.1 499.1
2.0 3.0 6.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 3.0 3.0 3.0 6.0 6.0 2.0 3.0 3.0 3.0 3.0 2.0 3.0 2.0 3.0 3.0 2.0 2.0 2.0 3.0 3.0 2.0 2.0 3.0 3.0 2.0 3.0 2.0 3.0
/ / / 2.0 2.0 2.0 2.0 2.0 3.0 6.0 2.0 3.0 6.0 2.0 3.0 / / 2.0 3.0 / 2.0 2.0 2.0 2.0 3.0 2.0 2.0 2.0 2.0 2.0 2.0 3.0 2 3.0 / / 2.0 2.0
/ / /
/ / / 150 225 150 225 150 150 150 150 150 150 150 150 / / / / / 150 150 150 150 150 / / / / / 150 150 150 150 / / 150 150
2.7 4.0 8.0 3.8 3.8 3.6 3.8 3.6 4.3 6.0 5.1 5.7 7.4 9.1 9.7 2.8 4.1 4.4 5.3 4.0 3.8 5.1 3.8 5.1 5.7 3.8 3.4 3.3 4.8 4.7 3.5 3.9 4.8 5.2 4.8 6.2 6.0 7.3
2350 2500 5880 5405a 4900 5030 5300a 4850 4640a 5864a 5960a 6284a 6540a 6600a 6200a 3960 4000 5670 5500a 3424 2900 5960a e e e 3066 1900 1620 2000 1860 3200 2610 4400 4660 2400 4016 6223a 6690a
5322 5664 6498 5501 5284 5188 5572 5482 5605 5871 6184 6677 6754 7374 7540 4074 4560 5671 6207 7945 5427 6184 7994 8707 8015 5416 5226 5347 6382 6064 5427 5843 6015 6468 5861 5835 6248 6864
1.14 1.03 1.03 1.16 1.11 1.10 1.17 1.16 1.13 1.14 1.12 1.16 1.14 1.16 1.15 1.09 1.03 1.02 1.07 1.04 1.14 1.12 1.05 1.04 1.04 1.15 1.12 1.14 1.16 1.11 1.15 1.20 1.09 1.14 1.04 0.90 1.09 1.05
1.51 1.77 1.86 2.18 2.75 2.07 2.00 1.97 1.99 2.21 3.07 2.95 3.78 2.73 3.33 1.35 3.57 1.61 2.30 1.26 2.13 3.07 1.67 1.95 1.78 2.19 1.80 1.99 2.13 2.09 1.53 1.73 2.77 2.41 2.19 2.22 2.54 2.34
[12]
460 460 490 w55 w80 460 460 460 460 460 460 460 / / / / / 460 460 460 460 460 460 460 460 460 460 460 460 460 460 / / 460 460
[13]
This paper
-No obvious tube buckling was observed. a Tube buckling occurred in post-peak stage.
first number represents the thickness of tube tt; the second number is the thickness of diagonal ribs ts (only for SS specimens); and the following letter represents the group classification. For example, B means Group B shown in Fig. 3(b); similarly, A, D, F, G and H correspond to Group A shown in Fig. 3(a), Group D in Fig. 3(c), Group F in Fig. 3(d), Group G in Fig. 3(e) and Group H in Fig. 3(f), respectively. In addition, B1, D1, D2, D3, F1 and F2 are specified in the corresponding Fig. 3 (b), (c) and (d) to represent different arrangements of the weld types or the stiffeners; specimens SS-2-2B2, SS-2-2-B3, SS-2-2-B4 and SS-2-2-B5 had different opening spacing or diameter from specimen SS-2-2-B; and the last letter c or r (if existing) denotes specimens with high-strength concrete or
longitudinal reinforcing bars. The measured steel and concrete properties of these specimens are also listed in Table 1, where fyt, fys and fyb are the yield strength of the steel tube, diagonal ribs and reinforcing bars, respectively; and fc is the prism (150 mm 150 mm 300 mm) compressive strength. In Table 1, d is the diameter or width of openings in the diagonal ribs and s is the spacing between two adjacent openings; 460 represents that the diameter of circular openings is 60 mm and w55 means that the width of square openings is 55 mm; r is the total steel ratio, r¼ (total volume of steel)/(total volume of column); Nb is the load corresponding to the first tube buckling; Nu is the ultimate load; and Is and m are the strength index and ductility
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coefficient, respectively, defined as follows:
Is ¼ Nu =ðfc Ac þ fyt At þ fys As þ fyb Ab Þ
(1)
m ¼ ε85% =εy
(2)
where Ac, At, As and Ab are the total cross-sectional areas of the concrete, steel tube, diagonal ribs and reinforcing bars, respectively; ε85% is the axial strain when the load falls to 85% of the ultimate load; and εy is the yield axial strain corresponding to the yield load which can be obtained from the equivalent energy method [17]. It should be mentioned that the strength index Is corresponds to the weakest cross-section in the column. That is, areas of the openings in diagonal ribs are subtracted when calculating As of the specimens. A 10000 kN capacity testing machine was used for the axial compression tests. The detailed test setup and instrumentation were the same as those described in Refs. [12,13]. 2.2. Test results The effect of reinforcing bars is shown in Fig. 4, where the stars represent the approximate locations of observed tube buckling. Generally, reinforcing bars enhanced the load-carrying capacity and ductility of the specimen without reinforcing bars. For example, specimen SS-2-2-B-r showed about 13.6% higher loadcarrying capacity and 15.5% higher ductility capacity than those of specimen SS-2-2-B (Fig. 4(b)). However, reinforcing bars cannot confine the infilled concrete and steel tube, so the strength index Is of the specimen without reinforcing bars decreased slightly. Fig. 5 gives typical strain development of reinforcing bars and steel tube, where εth and εtv are the average horizontal strains and longitudinal strains of the four symmetric measuring points of the steel tube, respectively; εr is the average longitudinal strains of the two symmetric measuring points of the reinforcing bars. Tensile strain was assumed to be positive, while compressive strain was negative. Besides, the symbol “C” indicates the steel tubes or reinforcing bars yielding. Note that all the strain gauges were placed on the mid-height of tubes and reinforcing bars. In Fig. 5(a), for unstiffened specimen SU-2-A-r, as the test progressed, the steel tube buckled when the load was about 40.9% of the ultimate load in the pre-peak stage, and then the longitudinal strain decreased. However, the strain of reinforcing bars increased linearly, indicating the embedded reinforcing bars did not buckle. After the ultimate load, the axial load decreased rapidly while the strains of reinforcing bars kept increasing, indicating the ductile reinforcing bars delayed the crushing of the concrete and helped improve the ductility of the column. As for diagonal ribs stiffened CFST specimen SS-2-2-B-r shown in Fig. 5(b), the strain development of the steel tube and reinforcing bars was linear and almost the same before the ultimate load, which was consistent with the experimental observations that both the steel tube and reinforcing bars did not buckle. After the ultimate load was obtained, the strains of reinforcing bars and steel tube increased abruptly while the applied load was almost unchanged, indicating that diagonal stiffened steel tube confined the infilled concrete well, and the reinforcing bars could delay the crushing of the concrete. Therefore, the ductility of the column was improved. 3. Nonlinear analysis 3.1. Model description Fig. 3. Specimen details (mm).
A damaged plasticity model was used to simulate the concrete material. For concrete under compression, the equivalent
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Fig. 4. Effect of reinforcing bars.
Fig. 5. Typical strain development of reinforcing bars and steel tube.
stressestrain model proposed by Han et al. [18] was adopted. For concrete under tension, a kind of fracture energy model was used, by defining the tensile stress and tensile fracture energy presented in CEB-FIP MC90 [19]. The elastic-perfectly plastic stress-strain model was applied for steel. Shell element S4R and solid element C3D8R were used to simulate steel tubes and diagonal ribs, and concrete, respectively. Truss element T3D2 was applied for reinforcing bars. A surface-tosurface contact interaction was used at the interface of the steel tube and concrete column. Reinforcing bars and stiffeners were
embedded in the concrete. As for the material properties, the measured yield strengths of steel and concrete strengths were adopted. The elastic modulus of concrete Ec and steel Es were taken as 4730 f0.5 [20] and c 206000 MPa, respectively. The Poisson's ratios of concrete mc and steel ms were chosen as 0.3 and 0.2, respectively. As shown in Fig. 6, the rigid bodies were set at both top and bottom surfaces of the column to simulate the steel end plate on column ends. The end surface of the column was completely fixed, while the top surface of the column was fixed but displacement in
Please cite this article as: X. Zhou et al., Analysis and design of axially loaded square CFST columns with diagonal ribs, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105848
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Comparisons of axial load-strain curves from the numerical models and the experiments are shown in Fig. 8. Generally, the FEA model could simulate the axial performance well before the ultimate load, while the load-strain curves from FEA decreased faster than those of the tested results after the ultimate load, as shown in Fig. 8(aeb). A mean ratio (NFEA/Nu) of 0.977 is obtained with a standard deviation of 0.046 (Fig. 8 (c)). Therefore, the FEA model could predict the strength and strain development of the tested specimens with satisfactory accuracy. Hence, this model can be considered acceptable.
3.3. Parametric studies (1) Opening diameter
Fig. 6. Finite element model.
the z direction was allowed. Note that the residual stresses and initial imperfections of steel tubes were not taken into consideration, because the strength reduction is generally within 4% even if the aforementioned two unfavorable factors are considered and most strength of the column is contributed by its concrete core for a thin-walled composite column according to Ref. [21]. The corners of CFST columns were assumed to be exact 90 and corner radii was not considered.
Since specimens with circular openings behaved more ductile than those with square openings according to Ref. [12], this paper mainly focused to find out the appropriate diameter of circular opening. 18 specimens with opening diameter d varied from 0 to 0.9 times the diagonal rib width bs based on specimen SS-3-3-B were designed, and the FEA results are shown in Fig. 9. The ultimate load decreased with increasing opening diameter d. However, the strength differences of the specimens with d smaller than 0.5bs were within the range of 5.0%. A larger d would facilitate concreting, increase the anchorage and avoid the disengagement at the interface between the concrete and steel tubes. However, when d increased to some extent, the diagonal rib would be weakened much. Therefore, the circular opening diameter d is proposed to be within the ranges of 0.2e0.5bs (i.e., d ¼ 0.2e0.5bs). Smaller d can be adopted for wider diagonal ribs, and larger for narrower.
3.2. Model verification (2) Opening spacing To verify the feasibility of the finite element analysis (FEA) model, the test results in this paper and the companion papers [12,13] were adopted and compared. All detailed information of tested specimens is summarized in Table 1. (1) Failure modes It was found that, generally good agreement was achieved between the failure modes predicted by using the current FEA models and those observed in the tests. Some typical comparisons between the experimental and predicted failure modes are shown in Fig. 7. (2) Axial load-strain curves
Eight specimens, with opening spacing s varied from 0 to 5 times the opening diameter d, based on specimen SS-3-3-B were designed. As shown in Fig. 10, the effect of opening spacing s on the ultimate load was not significant. This is attributed to fact that the effective cross-sectional area of the diagonal ribs was the same for all the specimens. According to Ref. [22], the stress fields from the concrete dowels would be overlapped as the distance between the openings reduces, which would result in highly stressed regions and a decrease in strength. Thus, the opening spacing should be at least 2.25 times the diameter of the opening (i.e., s 2.25d). (3) Welding position
Fig. 7. Comparison of observed and predicted failure modes.
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Fig. 8. Comparison of the FEA results and test results.
Seven specimens with the width of sub-plate b varied from 0 to 0.5 times the column width B based on specimen SS-3-3-H were designed, and openings were not considered in the FEA models to simplify the analysis. The FEA results are shown in Fig. 11. The ultimate load increased with increasing b because of the larger steel ratio. The strength index Is differed little with the range of 1.08e1.12 once the diagonal ribs existed (Fig. 11 (b)). According to the proposed calculation methods [12] (Fig. 12), the confinement effectiveness coefficient ke can be calculated by
ke ¼
B2 16 b2 8 16 ðB 2bÞ2 4 B2
To get the maximum value of ke, we have
(3)
dke 1 ¼ 00b ¼ B 3 db
(4)
Therefore, the value of ke is largest if the diagonal ribs were welded at a third of the tube width. Fig. 13 shows the effect of the welding position on the composite effect and ductility capacity of tested specimens. It was observed that the Is was almost not influenced by the welding position (Fig. 13(a)). However, the ductility of the specimens where the diagonal ribs were welded at a quarter of the tube width was reduced compared with their reference specimens (Fig. 13(b)). Therefore, it is suggested that b should be equaled to 1/3B (i.e., b ¼ 1/3B). (4) Concrete strength
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Fig. 9. Effect of opening diameters.
specimen SS-3-3-B were designed. As shown in Fig. 15, Is tended to increase with increasing strength of diagonal rib, but decrease with increasing the strength of steel tube. However, the difference of Is was within 2.5%. This was because both the steel tube and diagonal ribs yielded when approaching to the ultimate load. Therefore, this kind of column could facilitate the use of high-strength steel. 4. Design considerations 4.1. Width-to-thickness ratio limit of sub-plates
Fig. 10. Effect of opening spacing.
Specimens with different concrete strengths based on specimen SS-3-2-B-c were designed. It is obvious that the ultimate load increased with increasing concrete strength. Therefore, this paper mainly focused on the strength index Is. As depicted in Fig. 14 (a), Is decreased with increasing concrete strength, which is also proved by the test results [13], as shown in Fig. 14 (b). However, specimens with high-strength concrete confined by diagonal ribs stiffened CFST behaved more ductile than those confined by unstiffened steel tube. (5) Steel strength Eight specimens with different steel strengths based on
The width-to-thickness ratio of steel plates would affect the local buckling and structural behavior of the column. Once local buckling occurred, the ductility or ultimate strength of the column would be reduced. Additionally, the premature local buckling will be visually unacceptable. Premature local buckling can be avoided by setting a width-tothickness ratio limit although local buckling of the steel tube of a CFST column is inevitable in the post-peak stage. It can be concluded from the aforementioned test results that the welding position where the diagonal ribs were welded to the steel tube acted as a fixed end, and thus the width-to-thickness of a stiffened steel tube could be relaxed and the axial behavior was improved. Therefore, it is more reasonable to specify the width-to-thickness ratio limits of the sub-plates (Fig. 11). The width-to-thickness ratio limits were obtained by assuming that yielding would occur before the local buckling of steel plates, i.e., the yield strain εy of the steel plates should be smaller than the buckling strain εb. However, it is impossible to detect the exact time
Fig. 11. Effect of welding position.
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Fig. 12. Effectively confined regions for square CFST with diagonal ribs [12].
when steel tube first yielded only through the limited strain gauges placed on the steel tube, because maybe some parts of the steel tube yielded, and the tube where the strain gauges were attached yielded subsequently. Thus, proper definition of εy is the key issue of finding the relationship between εb/εy and the width-tothickness ratio, and then the width-to-thickness ratio limits can be specified. According to the unified theory of CFST structures proposed by Zhong et al. [23], the composite column can be seen as being composed of a kind of composite material. Therefore, for the stub composite column, the buckling should occur later than the column yielding. In this paper, the strain εb represents the axial shortening
9
at the occurrence of local buckling, while the strain εy is the axial shortening corresponding to specimen yielding strength which was obtained from the load-axial shortening curves according to the energy method [17]. To verify this method, the tested results of CFST columns in the companion papers [12,13] and other papers [7, 8, 20, 23 , 24 and 25] were used to evaluate the applicability of width-to-thickness ratio limits listed in Table 2. The detailed specimen information is summarized in Table 1 and Appendix. Note that the maximum width-to-thickness ratio of sub-plates, which dominates the local buckling, was used; specimens without any stiffener or with the longitudinal ribs satisfying the rigid requirement specified in Ref. [3] were chosen; and the test results, including both the buckling loads and relative smooth axial load versus axial shortening curves, were selected to get an accurate yield load. Fig. 16 (a) shows the effect of b/t ratio of sub-plates on εb/εy. As can be seen, the specimens seemed to yield before buckling when pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b/t ratios were smaller than 52 235=fyt , which agreed well with EC4. As can be seen from Fig. 16 (b), the b/t ratio had little influence on the values ofpIffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s, while Is was larger than unit if b/t ratio was smaller than 52 235=fyt . As for ductility coefficient m, Test results in Table 1 and Appendix show that the concrete strength would affect a lot on the ductility, so only the specimens with the same concrete strength in Refs. [12,13] were used to demonstrate the effect of b/tt ratio on m, as depicted in Fig. 16 (c). It can be observed that the specimens generallyp showed ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffibetter ductility capacity when b/t ratio was smaller than 52 235=fyt . This demonstrated that local buckling reduced the ductility obviously. Test results in Table 1 and Appendix also showed that local buckling reduced the ultimate load little, because the infilled concrete would carry most vertical
Fig. 13. Effect of welding position on composite effect and ductility capacity.
Fig. 14. Effect of concrete strength.
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Fig. 15. Effect of steel strength.
Table 2 Summary of width-to-thickness ratio limits.
b/tt limit
AISC [26], AS 5100 [27] sffiffiffiffiffiffiffiffiffi 235 67 fyt
EC4 [28] sffiffiffiffiffiffiffiffiffi 235 52 fyt
DBJ/T13-51-2010 [29] sffiffiffiffiffiffiffiffiffi 235 60 fyt
LRFD [30] sffiffiffiffiffiffiffiffiffi 235 51 fyt
AIJ [31] sffiffiffiffiffiffiffiffiffi 235 72 fyt
Fig. 16. Effect of b/tt ratio.
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buckling can be avoided by setting a width-to-thickness ratio limit of sub-plate), this paper proposed another way to avoid the premature local buckling by limiting the axial load levels applied on the column. Taking specimen SU-3-A (Nb ¼ 2500 kN, Nu ¼ 5664 kN, ne ¼ Nb/Nu ¼ 0.44) as an example, the actual axial force applied should be smaller than 2500 kN, that is, the actual axial load level ne should be smaller than 0.44. Fig. 17 shows the effect of b/tt ratio and ne on local buckling. The detailed information is given in Table 1 and Appendix, and the limits for experimental axial load level ne are summarized as follows:
Fig. 17. Effect of b/tt ratio and experimental axial load level on local buckling.
forces for the thin-walled CFST columns. Therefore, for sub-plates of stiffened pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiCFST columns, width-tothickness ratio limit of b=tt 52 235=fyt can be adopted. In this case, if the diagonal ribs were welded at a third of the tube, the width-to-thickness ratio limit of the specimen would be B=tt pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 156 235=fyt , which will facilitate the use of thin-walled steel tubes and high-strength steel. In addition to the aforementioned way (i.e., the premature local
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . ffi b=tt 60 235 fyt : ne 0:76
(5)
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . ffi . ffi 60 235 fyt < b=tt < 72 235 fyt : ne 0:44
(6)
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . ffi 72 235 fyt b=tt : ne 0:27
(7)
For a column mainly subjected to axial load in a high-rise building, premature local buckling is visually unacceptable, which does not satisfy the requirements specified in serviceability limit state. It should be mentioned that the designing axial load level nd was higher than the experimental axial load level ne because of safety reliability. Therefore, when designing a composite column where the axial load controls in serviceability limit state in practice, nd should be determined according to ne and the local requirements on the safety reliability.
Fig. 18. Matching relationship between diagonal ribs and steel tube.
Fig. 19. Detailing of mega-column with diagonal ribs.
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X. Zhou et al. / Journal of Constructional Steel Research xxx (xxxx) xxx Table 3 Summary of the bearing capacity formula. The proposed method [12,13] Np ¼ scc Ac þ stv At þ ssv As þ fyb Asb sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 0 f f 1 þ 7:94 r 2 r Þ fc fc scc ¼ f sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 0 f f fc ð0:413 þ 1:413 1 þ 11:4 r 2 r Þ fc fc fc ð1:254 þ 2:254
(8)
fc 50 MPa (9) fc > 50 MPa
fr 0 ¼ ke fr
ke ¼ f
(10)
0:78 for diagonal ribs stiffened square CFST column 0:33 for unstiffened square CFST column
2sth tt þ 2ssh cos 45 ts ð1
nd Þ ¼ fr ðB 2tt Þ L
(11)
(12)
stv ¼ 0:89fyt ; sth ¼ 0:19fyt
(13)
ssv ¼ 0:89fys ; ssh ¼ 0:19fys
(14)
NEC4 ¼ fyt At þ fys As þ fc Ac þ fyb Asb
(15)
EC4 [28]
DBJ/T13-51-2010 [29]
x¼
fyt At Ac fck
(16)
fscy ¼ ð1:18 þ 0:85xÞfck
(17)
NDBJ ¼ fscy Asc þ fys As þ fyb Asb
(18)
Notes: stv and ssv are the vertical stress of the steel tube and the diagonal rib, respectively; scc is the compressive strength of confined concrete; fr’ and fr the effective confining stress and confining stress, respectively; ke is the confinement effectiveness coefficient; sth and ssh are the horizontal stress of the steel tube and diagonal rib, respectively; n and d is the number and diameter or width of the openings on one diagonal rib, respectively; x is the confinement coefficient; fck is the characteristic compression strength of concrete (fck ¼ 0.88fc); fscy is the nominal average strength of a square or rectangular CFST column; Asc is the sum of effective cross-sectional areas of the steel tube, the concrete core and the diagonal ribs (Asc ¼ AtþAcþAs).
Fig. 20. Derivation of effectively confined regions for specimens in Group A.
4.2. Diagonal rib detailing The diagonal ribs should be the same height as the column and fully welded to the column tube. The opening diameter d can be within the ranges of 0.2e0.5 times the width of the diagonal rib
(i.e., d ¼ 0.2e0.5bs), and smaller d can be adopted for wider diagonal ribs, and larger for narrower. The opening spacing s should be higher than 2.25 times the diameter of the opening (i.e., s 2.25d). The width of the sub-plates b should be equaled to 1/3B (i.e., b ¼ 1/ 3B).
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Fig. 21. Derivation of effectively confined regions for specimens in Group B.
strength was not considered. To facilitate fabrication, the ratio of tt/ ts within the range of 0.4e2.0 was recommended. 4.4. Detailing of mega-column with diagonal ribs Due to the limitation of the loading apparatus only with a capacity of 10000 kN, the specimens with four large-diameter reinforcing bars in the corners were tested and no stirrups were used. In practice, the following construction characteristics were proposed to meet the demand for resisting huge compressive forces, as depicted in Fig. 19. 4.5. Load-carrying capacity prediction
Fig. 22. Comparison of test and prediction in ultimate strength.
4.3. Matching relationship between diagonal rib and steel tube Both the diagonal ribs and steel tubes can confine the concrete and contribute to carry the axial load, and thus they played the similar role. Therefore, there is a need to study the thickness matching relationship between the diagonal ribs and steel tube to make full use of materials. For a given steel strength, concrete strength, and column section, the thickness matching relationship is a function of the steel ratio. The superimposed strength would be the same if the steel ratio was the same. And the larger Is was, the better the composite effect would be. Hence, the thickness matching relationship between the diagonal rib and steel tube should be studied under a certain steel ratio. Because of the limited test results, based on specimen SS-3-3-B, a series of specimens with various steel ratios were designed and analyzed through ABAQUS with the proposed models mentioned previously. Note that the sub-plates of all specimens pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi satisfied the width-to-thickness ratio limit of b=tt 52 235=fyt . As shown in Fig. 18(a), generally, lager Is can be obtained if the ratio of steel tube thickness to diagonal rib thickness tt/ts equaled to unit, which was also proved by the test results for specimens with normal-strength and high-strength concrete, as indicated in Fig. 18(b). Furthermore, the aforementioned FEA results indicated that the effect of steel strength on the Is was small (within 3%), so the effect of steel
Based on the stress-strain model of confined concrete proposed by Mander et al. [32] for normal-strength concrete and Li et al. [33] for high-strength concrete, calculation method for predicting the ultimate strength of diagonal ribs stiffened square CFST columns, summarized in Table 3, was proposed, and the effect of the steel tubes and diagonal ribs was addressed [12,13]. The FEA results based on ABAQUS are shown in Fig. 20(a), the dark blue shades are low stress regions and the light shades are high stress regions. It can be seen that the boundaries between effectively confined concrete regions and ineffectively ones can be simplified and described by second-degree parabolas with an initial tangent angle of 45 . Therefore, the effectively confined concrete zones in Fig. 20(a) can be conservatively simplified as that in Fig. 20(b), which also agrees well with the failure modes [12,13]. Similarly, the boundaries between effectively confined concrete regions and ineffectively ones can also be simplified and described by second-degree parabolas with an initial tangent angle of 45 (Fig. 21(a)). Therefore, the effectively confined concrete zones in Fig. 21(a) can be conservatively simplified as that in Fig. 21(b), which can be also proved by the failure modes [12,13]. Figs. 21 and 22 also demonstrate the rationality of the proposed model [12,13]. The methods in EC4 [28] and DBJ/T13-51-2010 [29], summarized in Table 3, were compared with the proposed method. For the reinforcing bars, the contribution was considered by adding a term of fybAsb, where fyb and Asb are the yield strength and total crosssection area of reinforcing bars, respectively. Although width-tothickness ratios of some columns did not meet the required limitations specified by codes, an estimate can still be obtained. The predicted results are shown in Fig. 22. For the proposed calculation method, a mean ratio (Np/Nu) of
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thickness to diagonal rib thickness tt/ts within the range of 0.4e2.0 was recommended to get better composite effect; (3) The following diagonal rib detailing can be adopted: the diagonal ribs should be the same height as the column and fully welded to the column tube; the opening diameter d can be within the ranges of 0.2e0.5 times the width of the diagonal rib (i.e., d ¼ 0.2e0.5bs), and smaller d can be adopted for wider diagonal ribs, and larger for narrower; the opening spacing s should be higher than 2.25 times the diameter of the opening (i.e., s 2.25d); and the width of the sub-plates b should be equaled to 1/3B (i.e., b ¼ 1/3B); (4) The premature local buckling of square CFST column can be avoided by either limiting width-to-thickness ratios of the sub-plates or axial load levels in serviceability limit state. Diagonal ribs stiffened square CFST columns with different construction characteristics were proposed to fulfill the demand of resisting the huge vertical forces; (5) The proposed calculation method in the companion papers can well predict the ultimate strength of specimens and can be used for accurate calculation, while the methods in DBJ and EC4 were a little conservative and can be adopted for simplified calculation.
0.977 is obtained with a standard deviation of 0.056. As for the method in EC4, a mean ratio (NEC4/Nu) of 0.915 is obtained with a standard deviation of 0.053. With regard to the method in DBJ, a mean ratio (NDBJ/Nu) of 0.920 is obtained with a standard deviation of 0.049. It can be concluded that the proposed calculation method can well predict the ultimate strength of specimens, while the methods in DBJ and EC4 are more conservative. Therefore, for simplified calculation, both the methods in DBJ and EC4 are applicable. However, for more accurate calculation, the proposed methods are recommended, because the proposed methods can reflect the effect of discontinuous ribs or welds between the rib and steel tube, different welding positions, and the opening diameter or spacing.
5. Concluding remarks This paper summarizes the test results of axially loaded diagonal ribs stiffened and longitudinal ribs stiffened CFST columns comprehensively, followed by further tests of stub columns with longitudinal reinforcing bars. A verified finite element analysis (FEA) model was presented to implement parametric studies, focusing on proposing design methods. Based on the test and analysis results, the following conclusions can be drawn: (1) Reinforcing bars in the strongly confining regions did not buckle when the applied load drop to 85% of the ultimate load, and thus delayed the crushing of the concrete and improved the ductility of the column; (2) The FEA model could predict failure modes, ultimate loads and strain development of the tested specimens with satisfactory accuracy. FEA results showed that the strength of steel tube or diagonal rib only had slight influence on strength index Is, while strength index Is decreased with increasing concrete strength; and the ratio of tube wall
Acknowledgement The authors greatly appreciate the financial support provided by the Fundamental Research Funds for the Central Universities (No. 2019CDXYTM0033) and the National Natural Science Foundation of China (Nos. 51878097 and 51890902). However, the opinions expressed in this paper are solely the authors' own. Appendix. Summary of specimen information in literature
No.
Specimen
fc/MPa
fyt/MPa
fys/MPa
B/mm
tt/mm
hs/mm
ts/mm
r/%
Nb/kN
Nu/kN
Is
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
F1 S1 S5 UNC-L UNC-H DSNC-L DSNC-H UNC25a UNC19a UNC25c UNC19c SSNC25-2a SSNC25-3a SSNC25-2b SSNC25-3b SSNC19-2a SSNC19-3a SSNC19-2b SSNC19-3b DSNC25-1 DSNC25-2 DSNC25-3 DSNC19-1 DSNC19-2 DSNC19-3 LB1 LB3 LB5 LB7 LB9
49.6 42.5 42.5 19.4 38.6 19.4 38.6 50.9 50.9 44.3 44.3 50.9 50.9 44.3 44.3 50.9 50.9 44.3 44.3 50.9 50.9 50.9 50.9 50.9 50.9 40 50 32 38 38
168.0 301.0 315.0 338.0 338.0 338.0 338.0 342.0 342.0 270.0 270.0 342.0 342.0 270.0 270.0 342.0 342.0 270.0 270.0 342.0 342.0 342.0 342.0 342.0 342.0 300 300 300 300 300
/ / / 338.0 338.0 338.0 338.0 342.0 342.0 270.0 270.0 342.0 342.0 270.0 270.0 342.0 342.0 270.0 270.0 342.0 342.0 342.0 342.0 342.0 342.0 / / / / /
150 200 200 250 250 250 250 250 190 250 190 250 250 250 250 190 190 190 190 250 250 250 190 190 190 120 150 180 240 300
1.5 2.0 3.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 3 3 3 3 3
/ / / / / 35 35 / / / / 45 60 45 60 35 45 35 45 35 45 60 25 35 45 / / / / /
/ / / 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 / / / / /
4.0 4.0 7.0 4.0 4.0 5.1 5.1 4.0 5.3 4.0 5.3 4.7 5.0 4.7 5.0 6.2 6.5 6.2 6.5 5.1 5.4 5.9 6.6 7.2 7.8 10.0 8.0 6.7 5.0 4.0
350 600 2500 902 902 2373 3767 1610 1000 1330 750 3600 4000 3205 3078 2250 2305 1805 1908 4404 4416 4583 2809 2800 2900 950 1300 1200 2200 2519
1153 2185 2630 1993 1993 2395 3865 4080 2480 3495 2140 4525 4732 3850 3740 2730 2860 2245 2280 4540 4630 4780 2900 2910 2940 1133 1700 1500 3095 4000
0.91 1.00 1.01 0.96 0.96 1.04 1.11 1.01 1.00 1.01 1.01 1.08 1.12 1.08 1.04 1.05 1.08 1.02 1.02 1.06 1.07 1.07 1.09 1.07 1.05 1.12 1.02 0.89 1.01 0.89
m 2.01 1.93 4.28 1.94 4.69 1.82 1.72 1.61 1.50 1.88 1.57 1.50 1.76 3.05 1.65 1.80 3.02 2.05 2.10 1.73 1.62 2.02 1.90 1.97 / / / / /
Source [7] [8] [20]
[23]
[24]
Notes: the ratio L/B of length L to width B all the specimens are 3; all the stiffeners (if existing) were fully welded to the steel tube; and all specimen details is shown in the following figure.
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Standards Australia, Sydney, Australia, 2017. [28] Eurocode 4, Design of Composite Steel and Concrete Structures Part 1-1: General Rules and Rules for Building, the European Committee for Standardization, Brussels, Belgium, 2004. [29] DBJ/T13-51-2010, Technical Specification for Concrete-filled Steel Tubular Structures, Department of Housing and Urban-Rural Development, Fujian, China, 2010 (in Chinese). [30] AISC-LRFD-1999, Load and Resistance Factor Design Specification for Structural Steel Buildings, American Institute of Steel Construction, Chicago, 1999. [31] AIJ, Recommendations for Design and Construction of Concrete Filled Steel Tubular Structures, Architectural Institute of Japan, Japan, 1997 (in Japanese). [32] J.B. Mander, M.J.N. Priestley, R. Park, Theoretical stress-strain model for confined concrete, J. Struct. Eng. 114 (8) (1988) 1804e1826. [33] B. Li, R. Park, H. Tanaka, Stress-strain behaviour of high strength concrete confined by ultra high and normal strength transverse reinforcements, ACI Struct. J. 98 (3) (2001) 395e406.
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Analysis and design of axially loaded square CFST columns with diagonal ribs Xuhong Zhou a, Zheng Zhou a, Dan Gan a, b, * a b
School of Civil Engineering, Chongqing University, Chongqing, 400045, China College of Water Resources and Architectural Engineering, Shihezi University, Shihezi, 832000, Xinjiang, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 August 2019 Received in revised form 23 October 2019 Accepted 1 November 2019 Available online xxx
Diagonal binding ribs, made of thin-walled steel plates with circular openings and welded to the steel tube of a square concrete-filled steel tubular (CFST) column, can improve the composite effect effectively by co-carrying axial compressive forces and confining the steel tube and concrete. The column with diagonal ribs is referred to as diagonal ribs stiffened CFST column. This paper summarizes the test results of axially loaded diagonal ribs stiffened and longitudinal ribs stiffened CFST columns comprehensively, followed by further tests of stub columns with longitudinal reinforcing bars. A verified finite element analysis (FEA) model was presented to implement parametric studies. The studied parameters included diagonal rib detailing (i.e., opening diameter, opening spacing, and welding position) and material strengths. Finally, based on the test and analysis results, design considerations, involving width-tothickness ratio limits of tube plates, diagonal rib detailing, thickness matching relationship between diagonal ribs and the steel tube, detailing of composite column with diagonal ribs, and load-carrying capacity prediction, were proposed. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Diagonal binding rib Concrete-filled steel tube Composite effect Axial compression Finite element analysis Design considerations
1. Introduction Square concrete-filled steel tubular (CFST) columns are widely used because of convenient beam-to-column joint construction, high moment capacity and aesthetic consideration [1]. However, the largely reduced confinement to the infilled concrete is mainly from the corners of the square steel tube, and the thin-walled square steel tube is susceptible to local buckling, as shown in Fig. 1(a). To improve the composite effect between the infilled concrete and a square steel tube, several kinds of stiffening schemes were proposed [2e11]. Based on these stiffening methods, the authors proposed diagonal ribs stiffened square CFST columns [12,13] (Fig. 1(b)). Test results about 34 stub columns with extensive parameters had been reported in companion papers [12,13], which mainly focused on the axial behavior of diagonal ribs stiffened square CFST columns and the comparison of composite effect of different kinds of stiffening schemes and cross-sectional shapes. It was concluded that the positions where the diagonal ribs were welded to the steel tube can act as a fixed end, changing the tube local buckling mode (Fig. 1(b)); and the diagonal ribs can not only
* Corresponding author. School of Civil Engineering, Chongqing University, Chongqing, 400045, China. E-mail address: [email protected] (D. Gan).
confine the steel tube and concrete, but also co-carry the axial forces. Hence, the ductility and ultimate strength were significantly enhanced, and the diagonal ribs stiffened square CFST columns behaved better than octangular CFST columns and square CFST columns with longitudinal ribs when the steel ratios were the same. In high-rise buildings, mega-columns are needed due to huge vertical loads [14,15]. As shown in Fig. 2, various stiffeners, including longitudinal ribs, studs and internal diaphragms, are applied in mega-column, leading to complex fabrication. The diagonal ribs stiffened square CFST column showed superior axial behavior, so the diagonal ribs have the potential of replacing the various stiffeners in CFST columns and thus simplify the fabrication process. In mega-columns, longitudinal reinforcing bars are usually needed to increase the ultimate strength and fire resistance [16]. Thus, this paper summarizes the test results of axially loaded diagonal ribs stiffened and longitudinal ribs stiffened CFST columns comprehensively, followed by further tests of stub columns with longitudinal reinforcing bars. To facilitate the use of the proposed diagonal ribs stiffened square CFST columns and propose a rational design method, a finite element analysis (FEA) model which was verified by test results was presented, followed by extensive parametric analysis. The main parameters included diagonal ribs detailing (i.e., opening
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Nomenclature Ab Ac As Asc At B b bs d Ec Es fc fck fr fr’ fscy fyb fys fyt Is ke L Nb NDBJ
cross-sectional area of reinforcing bars cross-sectional area of concrete cross-sectional area of diagonal rib sum of effective cross-sectional areas of the steel tube, the concrete core and the diagonal ribs cross-sectional area of steel tube column width width of sub-plate diagonal rib width opening diameter on one diagonal rib elastic modulus of concrete elastic modulus of steel prism compressive strength of concrete characteristic compression strength of concrete confining stress effective confining stress nominal average strength of a square or rectangular CFST column yield strength of reinforcing bar yield strength of diagonal rib yield strength of steel strength index confinement effectiveness coefficient column height buckling load ultimate strength obtained from code DBJ/T13-512010
NEC4 NFEA Np Nu n ne nd s ts tt ε85% εb εr εth εtv εy
m mc ms x r sc scc ssh ssv st sth stv
ultimate strength obtained from code Eurocode 4 ultimate load obtained from FEA predicted ultimate strength experimental ultimate load opening number on one diagonal rib experimental axial load level designing axial load level opening spacing on one diagonal rib thickness of stiffener thickness of tube wall the axial strain when the load falls to 85% of the ultimate load local buckling strain longitudinal strains of reinforcing bars horizontal strains of steel tube longitudinal strains of steel tube yield strain ductility coefficient Poisson ratio of concrete Poisson ratio of steel confinement coefficient total steel ratio compressive strength of concrete in FEA compressive strength of confined concrete horizontal stress of the diagonal rib vertical stresses of the diagonal rib tensile strength of concrete in FEA horizontal stress of the steel tube vertical stress of the steel tube
Fig. 1. Buckling modes.
diameter, opening spacing, and welding position) and material strengths. At last, design considerations, involving width-tothickness ratio limits of the steel tube plates, diagonal ribs detailing, thickness matching relationship between diagonal rib and the steel tube, detailing of columns with diagonal ribs, and loadcarrying capacity prediction, were proposed. 2. Brief review of the previous tests and further stub column tests 2.1. Specimens details A total of 38 stub composite columns, including the previous tests of 34 columns in Refs. [12,13] and further stub column tests of 4 columns with longitudinal reinforcing bars in this paper, were tested under axial compression, which can be identified as six
groups, namely Groups A, B, D, F, G and H. The width B and length L of all the specimens are 300 mm and 900 mm, respectively. The specimen details are listed in Table 1 and Fig. 3. Note that the 25 mm large-diameter reinforcing bars were only located in four strongly confining corners to get a relatively large moment capacity (Fig. 3 (a) and (b)); no stirrups were used to better compare and understand the effect of the reinforcing bars, while reinforcing bars were positioned by spot-welded bars (Fig. 3 (g)); square annular plate was spot welded to the tube end to keep the square shape of the unstiffened steel tube, because the unstiffened thin-walled steel tube would deform inward or outward during welding. The square annular plate would be removed during test (Fig. 3 (g)). Specimen designations starting with SS mean stiffened square CFST columns with diagonal ribs or longitudinal ribs, while SU and OU refer to unstiffened square CFST columns and unstiffened octangular CFST columns, respectively. Following the SS or SU, the
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Fig. 2. Mega-column with various stiffeners.
Table 1 Summary of specimen information. No.
Specimen
fc/MPa
fyt/MPa
fys/MPa
fyb/MPa
tt/mm
ts/mm
d/mm
s/mm
r/%
Nb/kN
Nu/kN
Is
m
Source
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
SU-2-A SU-3-A SU-6-A SS-2-2-B SS-2-2-B2 SS-2-2-B3 SS-2-2-B4 SS-2-2-B5 SS-2-3-B SS-2-6-B SS-3-2-B SS-3-3-B SS-3-6-B SS-6-2-B SS-6-3-B OU-2-G OU-3-G SS-3-2-F1 SS-3-3-F2 SU-3-A-c SS-2-2-B1 SS-3-2-B1 SS-2-2-B-c SS-3-2-B-c SS-3-3-B-c SS-2-2-D1 SS-2-2-D2 SS-2-2-D3 SS-3-2-D2 SS-3-2-D3 SS-2-2-H SS-2-3-H SS-3-2-H SS-3-3-H SU-2-A-r SU-3-A-r SS-2-2-B-r SS-3-2-B-r
48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 81.4 48.6 48.6 48.6 48.6 48.6 48.6 48.6 81.4 48.6 48.6 81.4 81.4 81.4 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6 48.6
176.7 356.1 317.5 176.7 176.7 176.7 176.7 176.7 176.7 176.7 356.1 356.1 356.1 317.5 317.5 356.1 356.1 356.1 356.1 176.3 176.7 356.1 176.7 356.1 176.3 189.0 176.7 176.7 356.1 356.1 176.7 176.7 356.1 356.1 176.7 356.1 176.7 356.1
/ / / 176.7 176.7 176.7 176.7 176.7 356.1 317.5 176.7 356.1 317.5 176.7 356.1 / / 176.7 356.1 / 176.7 176.7 176.7 176.7 176.3 189.0 176.7 176.7 176.7 176.7 176.7 356.1 176.7 356.1 / / 176.7 176.7
/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / 499.1 499.1 499.1 499.1
2.0 3.0 6.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 3.0 3.0 3.0 6.0 6.0 2.0 3.0 3.0 3.0 3.0 2.0 3.0 2.0 3.0 3.0 2.0 2.0 2.0 3.0 3.0 2.0 2.0 3.0 3.0 2.0 3.0 2.0 3.0
/ / / 2.0 2.0 2.0 2.0 2.0 3.0 6.0 2.0 3.0 6.0 2.0 3.0 / / 2.0 3.0 / 2.0 2.0 2.0 2.0 3.0 2.0 2.0 2.0 2.0 2.0 2.0 3.0 2 3.0 / / 2.0 2.0
/ / /
/ / / 150 225 150 225 150 150 150 150 150 150 150 150 / / / / / 150 150 150 150 150 / / / / / 150 150 150 150 / / 150 150
2.7 4.0 8.0 3.8 3.8 3.6 3.8 3.6 4.3 6.0 5.1 5.7 7.4 9.1 9.7 2.8 4.1 4.4 5.3 4.0 3.8 5.1 3.8 5.1 5.7 3.8 3.4 3.3 4.8 4.7 3.5 3.9 4.8 5.2 4.8 6.2 6.0 7.3
2350 2500 5880 5405a 4900 5030 5300a 4850 4640a 5864a 5960a 6284a 6540a 6600a 6200a 3960 4000 5670 5500a 3424 2900 5960a e e e 3066 1900 1620 2000 1860 3200 2610 4400 4660 2400 4016 6223a 6690a
5322 5664 6498 5501 5284 5188 5572 5482 5605 5871 6184 6677 6754 7374 7540 4074 4560 5671 6207 7945 5427 6184 7994 8707 8015 5416 5226 5347 6382 6064 5427 5843 6015 6468 5861 5835 6248 6864
1.14 1.03 1.03 1.16 1.11 1.10 1.17 1.16 1.13 1.14 1.12 1.16 1.14 1.16 1.15 1.09 1.03 1.02 1.07 1.04 1.14 1.12 1.05 1.04 1.04 1.15 1.12 1.14 1.16 1.11 1.15 1.20 1.09 1.14 1.04 0.90 1.09 1.05
1.51 1.77 1.86 2.18 2.75 2.07 2.00 1.97 1.99 2.21 3.07 2.95 3.78 2.73 3.33 1.35 3.57 1.61 2.30 1.26 2.13 3.07 1.67 1.95 1.78 2.19 1.80 1.99 2.13 2.09 1.53 1.73 2.77 2.41 2.19 2.22 2.54 2.34
[12]
460 460 490 w55 w80 460 460 460 460 460 460 460 / / / / / 460 460 460 460 460 460 460 460 460 460 460 460 460 460 / / 460 460
[13]
This paper
-No obvious tube buckling was observed. a Tube buckling occurred in post-peak stage.
first number represents the thickness of tube tt; the second number is the thickness of diagonal ribs ts (only for SS specimens); and the following letter represents the group classification. For example, B means Group B shown in Fig. 3(b); similarly, A, D, F, G and H correspond to Group A shown in Fig. 3(a), Group D in Fig. 3(c), Group F in Fig. 3(d), Group G in Fig. 3(e) and Group H in Fig. 3(f), respectively. In addition, B1, D1, D2, D3, F1 and F2 are specified in the corresponding Fig. 3 (b), (c) and (d) to represent different arrangements of the weld types or the stiffeners; specimens SS-2-2B2, SS-2-2-B3, SS-2-2-B4 and SS-2-2-B5 had different opening spacing or diameter from specimen SS-2-2-B; and the last letter c or r (if existing) denotes specimens with high-strength concrete or
longitudinal reinforcing bars. The measured steel and concrete properties of these specimens are also listed in Table 1, where fyt, fys and fyb are the yield strength of the steel tube, diagonal ribs and reinforcing bars, respectively; and fc is the prism (150 mm 150 mm 300 mm) compressive strength. In Table 1, d is the diameter or width of openings in the diagonal ribs and s is the spacing between two adjacent openings; 460 represents that the diameter of circular openings is 60 mm and w55 means that the width of square openings is 55 mm; r is the total steel ratio, r¼ (total volume of steel)/(total volume of column); Nb is the load corresponding to the first tube buckling; Nu is the ultimate load; and Is and m are the strength index and ductility
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coefficient, respectively, defined as follows:
Is ¼ Nu =ðfc Ac þ fyt At þ fys As þ fyb Ab Þ
(1)
m ¼ ε85% =εy
(2)
where Ac, At, As and Ab are the total cross-sectional areas of the concrete, steel tube, diagonal ribs and reinforcing bars, respectively; ε85% is the axial strain when the load falls to 85% of the ultimate load; and εy is the yield axial strain corresponding to the yield load which can be obtained from the equivalent energy method [17]. It should be mentioned that the strength index Is corresponds to the weakest cross-section in the column. That is, areas of the openings in diagonal ribs are subtracted when calculating As of the specimens. A 10000 kN capacity testing machine was used for the axial compression tests. The detailed test setup and instrumentation were the same as those described in Refs. [12,13]. 2.2. Test results The effect of reinforcing bars is shown in Fig. 4, where the stars represent the approximate locations of observed tube buckling. Generally, reinforcing bars enhanced the load-carrying capacity and ductility of the specimen without reinforcing bars. For example, specimen SS-2-2-B-r showed about 13.6% higher loadcarrying capacity and 15.5% higher ductility capacity than those of specimen SS-2-2-B (Fig. 4(b)). However, reinforcing bars cannot confine the infilled concrete and steel tube, so the strength index Is of the specimen without reinforcing bars decreased slightly. Fig. 5 gives typical strain development of reinforcing bars and steel tube, where εth and εtv are the average horizontal strains and longitudinal strains of the four symmetric measuring points of the steel tube, respectively; εr is the average longitudinal strains of the two symmetric measuring points of the reinforcing bars. Tensile strain was assumed to be positive, while compressive strain was negative. Besides, the symbol “C” indicates the steel tubes or reinforcing bars yielding. Note that all the strain gauges were placed on the mid-height of tubes and reinforcing bars. In Fig. 5(a), for unstiffened specimen SU-2-A-r, as the test progressed, the steel tube buckled when the load was about 40.9% of the ultimate load in the pre-peak stage, and then the longitudinal strain decreased. However, the strain of reinforcing bars increased linearly, indicating the embedded reinforcing bars did not buckle. After the ultimate load, the axial load decreased rapidly while the strains of reinforcing bars kept increasing, indicating the ductile reinforcing bars delayed the crushing of the concrete and helped improve the ductility of the column. As for diagonal ribs stiffened CFST specimen SS-2-2-B-r shown in Fig. 5(b), the strain development of the steel tube and reinforcing bars was linear and almost the same before the ultimate load, which was consistent with the experimental observations that both the steel tube and reinforcing bars did not buckle. After the ultimate load was obtained, the strains of reinforcing bars and steel tube increased abruptly while the applied load was almost unchanged, indicating that diagonal stiffened steel tube confined the infilled concrete well, and the reinforcing bars could delay the crushing of the concrete. Therefore, the ductility of the column was improved. 3. Nonlinear analysis 3.1. Model description Fig. 3. Specimen details (mm).
A damaged plasticity model was used to simulate the concrete material. For concrete under compression, the equivalent
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Fig. 4. Effect of reinforcing bars.
Fig. 5. Typical strain development of reinforcing bars and steel tube.
stressestrain model proposed by Han et al. [18] was adopted. For concrete under tension, a kind of fracture energy model was used, by defining the tensile stress and tensile fracture energy presented in CEB-FIP MC90 [19]. The elastic-perfectly plastic stress-strain model was applied for steel. Shell element S4R and solid element C3D8R were used to simulate steel tubes and diagonal ribs, and concrete, respectively. Truss element T3D2 was applied for reinforcing bars. A surface-tosurface contact interaction was used at the interface of the steel tube and concrete column. Reinforcing bars and stiffeners were
embedded in the concrete. As for the material properties, the measured yield strengths of steel and concrete strengths were adopted. The elastic modulus of concrete Ec and steel Es were taken as 4730 f0.5 [20] and c 206000 MPa, respectively. The Poisson's ratios of concrete mc and steel ms were chosen as 0.3 and 0.2, respectively. As shown in Fig. 6, the rigid bodies were set at both top and bottom surfaces of the column to simulate the steel end plate on column ends. The end surface of the column was completely fixed, while the top surface of the column was fixed but displacement in
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Comparisons of axial load-strain curves from the numerical models and the experiments are shown in Fig. 8. Generally, the FEA model could simulate the axial performance well before the ultimate load, while the load-strain curves from FEA decreased faster than those of the tested results after the ultimate load, as shown in Fig. 8(aeb). A mean ratio (NFEA/Nu) of 0.977 is obtained with a standard deviation of 0.046 (Fig. 8 (c)). Therefore, the FEA model could predict the strength and strain development of the tested specimens with satisfactory accuracy. Hence, this model can be considered acceptable.
3.3. Parametric studies (1) Opening diameter
Fig. 6. Finite element model.
the z direction was allowed. Note that the residual stresses and initial imperfections of steel tubes were not taken into consideration, because the strength reduction is generally within 4% even if the aforementioned two unfavorable factors are considered and most strength of the column is contributed by its concrete core for a thin-walled composite column according to Ref. [21]. The corners of CFST columns were assumed to be exact 90 and corner radii was not considered.
Since specimens with circular openings behaved more ductile than those with square openings according to Ref. [12], this paper mainly focused to find out the appropriate diameter of circular opening. 18 specimens with opening diameter d varied from 0 to 0.9 times the diagonal rib width bs based on specimen SS-3-3-B were designed, and the FEA results are shown in Fig. 9. The ultimate load decreased with increasing opening diameter d. However, the strength differences of the specimens with d smaller than 0.5bs were within the range of 5.0%. A larger d would facilitate concreting, increase the anchorage and avoid the disengagement at the interface between the concrete and steel tubes. However, when d increased to some extent, the diagonal rib would be weakened much. Therefore, the circular opening diameter d is proposed to be within the ranges of 0.2e0.5bs (i.e., d ¼ 0.2e0.5bs). Smaller d can be adopted for wider diagonal ribs, and larger for narrower.
3.2. Model verification (2) Opening spacing To verify the feasibility of the finite element analysis (FEA) model, the test results in this paper and the companion papers [12,13] were adopted and compared. All detailed information of tested specimens is summarized in Table 1. (1) Failure modes It was found that, generally good agreement was achieved between the failure modes predicted by using the current FEA models and those observed in the tests. Some typical comparisons between the experimental and predicted failure modes are shown in Fig. 7. (2) Axial load-strain curves
Eight specimens, with opening spacing s varied from 0 to 5 times the opening diameter d, based on specimen SS-3-3-B were designed. As shown in Fig. 10, the effect of opening spacing s on the ultimate load was not significant. This is attributed to fact that the effective cross-sectional area of the diagonal ribs was the same for all the specimens. According to Ref. [22], the stress fields from the concrete dowels would be overlapped as the distance between the openings reduces, which would result in highly stressed regions and a decrease in strength. Thus, the opening spacing should be at least 2.25 times the diameter of the opening (i.e., s 2.25d). (3) Welding position
Fig. 7. Comparison of observed and predicted failure modes.
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Fig. 8. Comparison of the FEA results and test results.
Seven specimens with the width of sub-plate b varied from 0 to 0.5 times the column width B based on specimen SS-3-3-H were designed, and openings were not considered in the FEA models to simplify the analysis. The FEA results are shown in Fig. 11. The ultimate load increased with increasing b because of the larger steel ratio. The strength index Is differed little with the range of 1.08e1.12 once the diagonal ribs existed (Fig. 11 (b)). According to the proposed calculation methods [12] (Fig. 12), the confinement effectiveness coefficient ke can be calculated by
ke ¼
B2 16 b2 8 16 ðB 2bÞ2 4 B2
To get the maximum value of ke, we have
(3)
dke 1 ¼ 00b ¼ B 3 db
(4)
Therefore, the value of ke is largest if the diagonal ribs were welded at a third of the tube width. Fig. 13 shows the effect of the welding position on the composite effect and ductility capacity of tested specimens. It was observed that the Is was almost not influenced by the welding position (Fig. 13(a)). However, the ductility of the specimens where the diagonal ribs were welded at a quarter of the tube width was reduced compared with their reference specimens (Fig. 13(b)). Therefore, it is suggested that b should be equaled to 1/3B (i.e., b ¼ 1/3B). (4) Concrete strength
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Fig. 9. Effect of opening diameters.
specimen SS-3-3-B were designed. As shown in Fig. 15, Is tended to increase with increasing strength of diagonal rib, but decrease with increasing the strength of steel tube. However, the difference of Is was within 2.5%. This was because both the steel tube and diagonal ribs yielded when approaching to the ultimate load. Therefore, this kind of column could facilitate the use of high-strength steel. 4. Design considerations 4.1. Width-to-thickness ratio limit of sub-plates
Fig. 10. Effect of opening spacing.
Specimens with different concrete strengths based on specimen SS-3-2-B-c were designed. It is obvious that the ultimate load increased with increasing concrete strength. Therefore, this paper mainly focused on the strength index Is. As depicted in Fig. 14 (a), Is decreased with increasing concrete strength, which is also proved by the test results [13], as shown in Fig. 14 (b). However, specimens with high-strength concrete confined by diagonal ribs stiffened CFST behaved more ductile than those confined by unstiffened steel tube. (5) Steel strength Eight specimens with different steel strengths based on
The width-to-thickness ratio of steel plates would affect the local buckling and structural behavior of the column. Once local buckling occurred, the ductility or ultimate strength of the column would be reduced. Additionally, the premature local buckling will be visually unacceptable. Premature local buckling can be avoided by setting a width-tothickness ratio limit although local buckling of the steel tube of a CFST column is inevitable in the post-peak stage. It can be concluded from the aforementioned test results that the welding position where the diagonal ribs were welded to the steel tube acted as a fixed end, and thus the width-to-thickness of a stiffened steel tube could be relaxed and the axial behavior was improved. Therefore, it is more reasonable to specify the width-to-thickness ratio limits of the sub-plates (Fig. 11). The width-to-thickness ratio limits were obtained by assuming that yielding would occur before the local buckling of steel plates, i.e., the yield strain εy of the steel plates should be smaller than the buckling strain εb. However, it is impossible to detect the exact time
Fig. 11. Effect of welding position.
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Fig. 12. Effectively confined regions for square CFST with diagonal ribs [12].
when steel tube first yielded only through the limited strain gauges placed on the steel tube, because maybe some parts of the steel tube yielded, and the tube where the strain gauges were attached yielded subsequently. Thus, proper definition of εy is the key issue of finding the relationship between εb/εy and the width-tothickness ratio, and then the width-to-thickness ratio limits can be specified. According to the unified theory of CFST structures proposed by Zhong et al. [23], the composite column can be seen as being composed of a kind of composite material. Therefore, for the stub composite column, the buckling should occur later than the column yielding. In this paper, the strain εb represents the axial shortening
9
at the occurrence of local buckling, while the strain εy is the axial shortening corresponding to specimen yielding strength which was obtained from the load-axial shortening curves according to the energy method [17]. To verify this method, the tested results of CFST columns in the companion papers [12,13] and other papers [7, 8, 20, 23 , 24 and 25] were used to evaluate the applicability of width-to-thickness ratio limits listed in Table 2. The detailed specimen information is summarized in Table 1 and Appendix. Note that the maximum width-to-thickness ratio of sub-plates, which dominates the local buckling, was used; specimens without any stiffener or with the longitudinal ribs satisfying the rigid requirement specified in Ref. [3] were chosen; and the test results, including both the buckling loads and relative smooth axial load versus axial shortening curves, were selected to get an accurate yield load. Fig. 16 (a) shows the effect of b/t ratio of sub-plates on εb/εy. As can be seen, the specimens seemed to yield before buckling when pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b/t ratios were smaller than 52 235=fyt , which agreed well with EC4. As can be seen from Fig. 16 (b), the b/t ratio had little influence on the values ofpIffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s, while Is was larger than unit if b/t ratio was smaller than 52 235=fyt . As for ductility coefficient m, Test results in Table 1 and Appendix show that the concrete strength would affect a lot on the ductility, so only the specimens with the same concrete strength in Refs. [12,13] were used to demonstrate the effect of b/tt ratio on m, as depicted in Fig. 16 (c). It can be observed that the specimens generallyp showed ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffibetter ductility capacity when b/t ratio was smaller than 52 235=fyt . This demonstrated that local buckling reduced the ductility obviously. Test results in Table 1 and Appendix also showed that local buckling reduced the ultimate load little, because the infilled concrete would carry most vertical
Fig. 13. Effect of welding position on composite effect and ductility capacity.
Fig. 14. Effect of concrete strength.
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Fig. 15. Effect of steel strength.
Table 2 Summary of width-to-thickness ratio limits.
b/tt limit
AISC [26], AS 5100 [27] sffiffiffiffiffiffiffiffiffi 235 67 fyt
EC4 [28] sffiffiffiffiffiffiffiffiffi 235 52 fyt
DBJ/T13-51-2010 [29] sffiffiffiffiffiffiffiffiffi 235 60 fyt
LRFD [30] sffiffiffiffiffiffiffiffiffi 235 51 fyt
AIJ [31] sffiffiffiffiffiffiffiffiffi 235 72 fyt
Fig. 16. Effect of b/tt ratio.
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buckling can be avoided by setting a width-to-thickness ratio limit of sub-plate), this paper proposed another way to avoid the premature local buckling by limiting the axial load levels applied on the column. Taking specimen SU-3-A (Nb ¼ 2500 kN, Nu ¼ 5664 kN, ne ¼ Nb/Nu ¼ 0.44) as an example, the actual axial force applied should be smaller than 2500 kN, that is, the actual axial load level ne should be smaller than 0.44. Fig. 17 shows the effect of b/tt ratio and ne on local buckling. The detailed information is given in Table 1 and Appendix, and the limits for experimental axial load level ne are summarized as follows:
Fig. 17. Effect of b/tt ratio and experimental axial load level on local buckling.
forces for the thin-walled CFST columns. Therefore, for sub-plates of stiffened pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiCFST columns, width-tothickness ratio limit of b=tt 52 235=fyt can be adopted. In this case, if the diagonal ribs were welded at a third of the tube, the width-to-thickness ratio limit of the specimen would be B=tt pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 156 235=fyt , which will facilitate the use of thin-walled steel tubes and high-strength steel. In addition to the aforementioned way (i.e., the premature local
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . ffi b=tt 60 235 fyt : ne 0:76
(5)
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . ffi . ffi 60 235 fyt < b=tt < 72 235 fyt : ne 0:44
(6)
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . ffi 72 235 fyt b=tt : ne 0:27
(7)
For a column mainly subjected to axial load in a high-rise building, premature local buckling is visually unacceptable, which does not satisfy the requirements specified in serviceability limit state. It should be mentioned that the designing axial load level nd was higher than the experimental axial load level ne because of safety reliability. Therefore, when designing a composite column where the axial load controls in serviceability limit state in practice, nd should be determined according to ne and the local requirements on the safety reliability.
Fig. 18. Matching relationship between diagonal ribs and steel tube.
Fig. 19. Detailing of mega-column with diagonal ribs.
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X. Zhou et al. / Journal of Constructional Steel Research xxx (xxxx) xxx Table 3 Summary of the bearing capacity formula. The proposed method [12,13] Np ¼ scc Ac þ stv At þ ssv As þ fyb Asb sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 0 f f 1 þ 7:94 r 2 r Þ fc fc scc ¼ f sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 0 f f fc ð0:413 þ 1:413 1 þ 11:4 r 2 r Þ fc fc fc ð1:254 þ 2:254
(8)
fc 50 MPa (9) fc > 50 MPa
fr 0 ¼ ke fr
ke ¼ f
(10)
0:78 for diagonal ribs stiffened square CFST column 0:33 for unstiffened square CFST column
2sth tt þ 2ssh cos 45 ts ð1
nd Þ ¼ fr ðB 2tt Þ L
(11)
(12)
stv ¼ 0:89fyt ; sth ¼ 0:19fyt
(13)
ssv ¼ 0:89fys ; ssh ¼ 0:19fys
(14)
NEC4 ¼ fyt At þ fys As þ fc Ac þ fyb Asb
(15)
EC4 [28]
DBJ/T13-51-2010 [29]
x¼
fyt At Ac fck
(16)
fscy ¼ ð1:18 þ 0:85xÞfck
(17)
NDBJ ¼ fscy Asc þ fys As þ fyb Asb
(18)
Notes: stv and ssv are the vertical stress of the steel tube and the diagonal rib, respectively; scc is the compressive strength of confined concrete; fr’ and fr the effective confining stress and confining stress, respectively; ke is the confinement effectiveness coefficient; sth and ssh are the horizontal stress of the steel tube and diagonal rib, respectively; n and d is the number and diameter or width of the openings on one diagonal rib, respectively; x is the confinement coefficient; fck is the characteristic compression strength of concrete (fck ¼ 0.88fc); fscy is the nominal average strength of a square or rectangular CFST column; Asc is the sum of effective cross-sectional areas of the steel tube, the concrete core and the diagonal ribs (Asc ¼ AtþAcþAs).
Fig. 20. Derivation of effectively confined regions for specimens in Group A.
4.2. Diagonal rib detailing The diagonal ribs should be the same height as the column and fully welded to the column tube. The opening diameter d can be within the ranges of 0.2e0.5 times the width of the diagonal rib
(i.e., d ¼ 0.2e0.5bs), and smaller d can be adopted for wider diagonal ribs, and larger for narrower. The opening spacing s should be higher than 2.25 times the diameter of the opening (i.e., s 2.25d). The width of the sub-plates b should be equaled to 1/3B (i.e., b ¼ 1/ 3B).
Please cite this article as: X. Zhou et al., Analysis and design of axially loaded square CFST columns with diagonal ribs, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105848
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Fig. 21. Derivation of effectively confined regions for specimens in Group B.
strength was not considered. To facilitate fabrication, the ratio of tt/ ts within the range of 0.4e2.0 was recommended. 4.4. Detailing of mega-column with diagonal ribs Due to the limitation of the loading apparatus only with a capacity of 10000 kN, the specimens with four large-diameter reinforcing bars in the corners were tested and no stirrups were used. In practice, the following construction characteristics were proposed to meet the demand for resisting huge compressive forces, as depicted in Fig. 19. 4.5. Load-carrying capacity prediction
Fig. 22. Comparison of test and prediction in ultimate strength.
4.3. Matching relationship between diagonal rib and steel tube Both the diagonal ribs and steel tubes can confine the concrete and contribute to carry the axial load, and thus they played the similar role. Therefore, there is a need to study the thickness matching relationship between the diagonal ribs and steel tube to make full use of materials. For a given steel strength, concrete strength, and column section, the thickness matching relationship is a function of the steel ratio. The superimposed strength would be the same if the steel ratio was the same. And the larger Is was, the better the composite effect would be. Hence, the thickness matching relationship between the diagonal rib and steel tube should be studied under a certain steel ratio. Because of the limited test results, based on specimen SS-3-3-B, a series of specimens with various steel ratios were designed and analyzed through ABAQUS with the proposed models mentioned previously. Note that the sub-plates of all specimens pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi satisfied the width-to-thickness ratio limit of b=tt 52 235=fyt . As shown in Fig. 18(a), generally, lager Is can be obtained if the ratio of steel tube thickness to diagonal rib thickness tt/ts equaled to unit, which was also proved by the test results for specimens with normal-strength and high-strength concrete, as indicated in Fig. 18(b). Furthermore, the aforementioned FEA results indicated that the effect of steel strength on the Is was small (within 3%), so the effect of steel
Based on the stress-strain model of confined concrete proposed by Mander et al. [32] for normal-strength concrete and Li et al. [33] for high-strength concrete, calculation method for predicting the ultimate strength of diagonal ribs stiffened square CFST columns, summarized in Table 3, was proposed, and the effect of the steel tubes and diagonal ribs was addressed [12,13]. The FEA results based on ABAQUS are shown in Fig. 20(a), the dark blue shades are low stress regions and the light shades are high stress regions. It can be seen that the boundaries between effectively confined concrete regions and ineffectively ones can be simplified and described by second-degree parabolas with an initial tangent angle of 45 . Therefore, the effectively confined concrete zones in Fig. 20(a) can be conservatively simplified as that in Fig. 20(b), which also agrees well with the failure modes [12,13]. Similarly, the boundaries between effectively confined concrete regions and ineffectively ones can also be simplified and described by second-degree parabolas with an initial tangent angle of 45 (Fig. 21(a)). Therefore, the effectively confined concrete zones in Fig. 21(a) can be conservatively simplified as that in Fig. 21(b), which can be also proved by the failure modes [12,13]. Figs. 21 and 22 also demonstrate the rationality of the proposed model [12,13]. The methods in EC4 [28] and DBJ/T13-51-2010 [29], summarized in Table 3, were compared with the proposed method. For the reinforcing bars, the contribution was considered by adding a term of fybAsb, where fyb and Asb are the yield strength and total crosssection area of reinforcing bars, respectively. Although width-tothickness ratios of some columns did not meet the required limitations specified by codes, an estimate can still be obtained. The predicted results are shown in Fig. 22. For the proposed calculation method, a mean ratio (Np/Nu) of
Please cite this article as: X. Zhou et al., Analysis and design of axially loaded square CFST columns with diagonal ribs, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105848
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thickness to diagonal rib thickness tt/ts within the range of 0.4e2.0 was recommended to get better composite effect; (3) The following diagonal rib detailing can be adopted: the diagonal ribs should be the same height as the column and fully welded to the column tube; the opening diameter d can be within the ranges of 0.2e0.5 times the width of the diagonal rib (i.e., d ¼ 0.2e0.5bs), and smaller d can be adopted for wider diagonal ribs, and larger for narrower; the opening spacing s should be higher than 2.25 times the diameter of the opening (i.e., s 2.25d); and the width of the sub-plates b should be equaled to 1/3B (i.e., b ¼ 1/3B); (4) The premature local buckling of square CFST column can be avoided by either limiting width-to-thickness ratios of the sub-plates or axial load levels in serviceability limit state. Diagonal ribs stiffened square CFST columns with different construction characteristics were proposed to fulfill the demand of resisting the huge vertical forces; (5) The proposed calculation method in the companion papers can well predict the ultimate strength of specimens and can be used for accurate calculation, while the methods in DBJ and EC4 were a little conservative and can be adopted for simplified calculation.
0.977 is obtained with a standard deviation of 0.056. As for the method in EC4, a mean ratio (NEC4/Nu) of 0.915 is obtained with a standard deviation of 0.053. With regard to the method in DBJ, a mean ratio (NDBJ/Nu) of 0.920 is obtained with a standard deviation of 0.049. It can be concluded that the proposed calculation method can well predict the ultimate strength of specimens, while the methods in DBJ and EC4 are more conservative. Therefore, for simplified calculation, both the methods in DBJ and EC4 are applicable. However, for more accurate calculation, the proposed methods are recommended, because the proposed methods can reflect the effect of discontinuous ribs or welds between the rib and steel tube, different welding positions, and the opening diameter or spacing.
5. Concluding remarks This paper summarizes the test results of axially loaded diagonal ribs stiffened and longitudinal ribs stiffened CFST columns comprehensively, followed by further tests of stub columns with longitudinal reinforcing bars. A verified finite element analysis (FEA) model was presented to implement parametric studies, focusing on proposing design methods. Based on the test and analysis results, the following conclusions can be drawn: (1) Reinforcing bars in the strongly confining regions did not buckle when the applied load drop to 85% of the ultimate load, and thus delayed the crushing of the concrete and improved the ductility of the column; (2) The FEA model could predict failure modes, ultimate loads and strain development of the tested specimens with satisfactory accuracy. FEA results showed that the strength of steel tube or diagonal rib only had slight influence on strength index Is, while strength index Is decreased with increasing concrete strength; and the ratio of tube wall
Acknowledgement The authors greatly appreciate the financial support provided by the Fundamental Research Funds for the Central Universities (No. 2019CDXYTM0033) and the National Natural Science Foundation of China (Nos. 51878097 and 51890902). However, the opinions expressed in this paper are solely the authors' own. Appendix. Summary of specimen information in literature
No.
Specimen
fc/MPa
fyt/MPa
fys/MPa
B/mm
tt/mm
hs/mm
ts/mm
r/%
Nb/kN
Nu/kN
Is
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
F1 S1 S5 UNC-L UNC-H DSNC-L DSNC-H UNC25a UNC19a UNC25c UNC19c SSNC25-2a SSNC25-3a SSNC25-2b SSNC25-3b SSNC19-2a SSNC19-3a SSNC19-2b SSNC19-3b DSNC25-1 DSNC25-2 DSNC25-3 DSNC19-1 DSNC19-2 DSNC19-3 LB1 LB3 LB5 LB7 LB9
49.6 42.5 42.5 19.4 38.6 19.4 38.6 50.9 50.9 44.3 44.3 50.9 50.9 44.3 44.3 50.9 50.9 44.3 44.3 50.9 50.9 50.9 50.9 50.9 50.9 40 50 32 38 38
168.0 301.0 315.0 338.0 338.0 338.0 338.0 342.0 342.0 270.0 270.0 342.0 342.0 270.0 270.0 342.0 342.0 270.0 270.0 342.0 342.0 342.0 342.0 342.0 342.0 300 300 300 300 300
/ / / 338.0 338.0 338.0 338.0 342.0 342.0 270.0 270.0 342.0 342.0 270.0 270.0 342.0 342.0 270.0 270.0 342.0 342.0 342.0 342.0 342.0 342.0 / / / / /
150 200 200 250 250 250 250 250 190 250 190 250 250 250 250 190 190 190 190 250 250 250 190 190 190 120 150 180 240 300
1.5 2.0 3.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 3 3 3 3 3
/ / / / / 35 35 / / / / 45 60 45 60 35 45 35 45 35 45 60 25 35 45 / / / / /
/ / / 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 / / / / /
4.0 4.0 7.0 4.0 4.0 5.1 5.1 4.0 5.3 4.0 5.3 4.7 5.0 4.7 5.0 6.2 6.5 6.2 6.5 5.1 5.4 5.9 6.6 7.2 7.8 10.0 8.0 6.7 5.0 4.0
350 600 2500 902 902 2373 3767 1610 1000 1330 750 3600 4000 3205 3078 2250 2305 1805 1908 4404 4416 4583 2809 2800 2900 950 1300 1200 2200 2519
1153 2185 2630 1993 1993 2395 3865 4080 2480 3495 2140 4525 4732 3850 3740 2730 2860 2245 2280 4540 4630 4780 2900 2910 2940 1133 1700 1500 3095 4000
0.91 1.00 1.01 0.96 0.96 1.04 1.11 1.01 1.00 1.01 1.01 1.08 1.12 1.08 1.04 1.05 1.08 1.02 1.02 1.06 1.07 1.07 1.09 1.07 1.05 1.12 1.02 0.89 1.01 0.89
m 2.01 1.93 4.28 1.94 4.69 1.82 1.72 1.61 1.50 1.88 1.57 1.50 1.76 3.05 1.65 1.80 3.02 2.05 2.10 1.73 1.62 2.02 1.90 1.97 / / / / /
Source [7] [8] [20]
[23]
[24]
Notes: the ratio L/B of length L to width B all the specimens are 3; all the stiffeners (if existing) were fully welded to the steel tube; and all specimen details is shown in the following figure.
Please cite this article as: X. Zhou et al., Analysis and design of axially loaded square CFST columns with diagonal ribs, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105848
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Please cite this article as: X. Zhou et al., Analysis and design of axially loaded square CFST columns with diagonal ribs, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105848