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Seismic behavior and strength of tubed steel reinforced concrete (SRC) short columns
Journal of Constructional Steel Research 66 (2010) 885–896
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Journal of Constructional Steel Research journal homepage: www.elsevier.com/locate/jcsr
Seismic behavior and strength of tubed steel reinforced concrete (SRC) short columns Xuhong Zhou a , Jiepeng Liu b,∗ a
School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China
b
Architectural Design and Research Institute, Harbin Institute of Technology, Harbin, 150090, China
article
info
Article history: Received 19 October 2009 Accepted 28 January 2010 Keywords: Tubed SRC Short column Axial load ratio Plastic deformation capacity Nominal shear strength
abstract The seismic behavior of tubed SRC short columns has been investigated by testing eight specimens subjected to combined constant axial compression and lateral cyclic load. Three circular tubed SRC columns (CTSRC) and three square tubed SRC (STSRC) columns were tested in this research with two common SRC columns for comparison. Different axial load ratios (n0 = 0.3, 0.4 and 0.5) have been adopted for the constant axial load. The test results indicate that the shear strength, plastic deformation capacity, ductility index, and energy dissipating capacity of the tubed SRC short columns were much higher than those of the SRC columns with the same steel ratio and axial compressive load. The lateral load strength of CTSRC and STSRC short columns increased with an increment in axial load level, while the axial load ratio has no obvious effect on the plastic deformation capacity of CTSRC and STSRC short columns. The steel tubes prevented the shear failure of the concrete more effectively in the circular columns than in the square ones. Shear connector studs should be used in CTSRC and STSRC short columns to prevent bond failure between concrete and flanges of the steel section. A modified ACI design method was adopted to calculate the nominal shear strength of STSRC columns as well as CTSRC columns. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction A tubed steel reinforced concrete (SRC) column as depicted in Fig. 1 is a special SRC column where reinforcement cage is in the form of an outer thin steel tube. The outer circular or square tube does not pass through the beam-to-column connection, therefore no axial load is directly applied on the steel tube and the tube confines the core concrete more effectively. This leads to an efficient use of the steel tube in preventing the concrete cover from spalling off and the longitudinal steel from buckling. At the same time, the strength and ductility of the concrete core will increase owing to the confinement of the steel tube. This approach leads to a pronounced enhancement in both strength and ductility of the overall column behavior. SRC columns can provide considerable advantages compared to open steel columns. SRC columns do not require any check on the thickness of the walls of the steel section, and the complete encasement of a steel section usually provides enough fire protection to satisfy the most stringent practical requirements [1]. In virtue
∗ Corresponding address: PO Box 2551, 202 Haihe Road, Nan’gang District, Harbin Institute of Technology (2nd District), Harbin 150090, China. Tel.: +86 0 451 8628 2083; fax: +86 0 451 86282083. E-mail address: [email protected] (J. Liu). 0143-974X/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2010.01.020
of the advantages, SRC columns are widely used in the construction of high rise buildings. In a SRC column, longitudinal and transverse reinforcements should be used to provide good confinement to the concrete [1–3]. However, the reinforcement does not confine the concrete cover, which will spall off during the occurrence of an earthquake. When subjected to combined high axial load and cyclic lateral load, the concrete cover tends to spall off rapidly. In such a situation, the transverse ties are not able to effectively prevent the longitudinal bars and the flanges of the encased steel shape from buckling, leading to a rapid decrease of the axial load strength and flexural strength. The existence of reinforcement in the SRC columns also makes the concrete casting difficult in construction. In order to increase the confinement to concrete and improve the concrete casting quality, it is proposed to replace the longitudinal and transverse reinforcement by a thin steel tube outside the concrete core, and the outside tube is terminated near the beam (tubed SRC). In such a manner, the steel tube confines the entire concrete column and the concrete casting becomes easier. To the knowledge of the authors no work has been published on the behavior of tubed SRC columns. Only limited research has been carried out in this area. Tomii et al. [4] firstly investigated the seismic behavior of square tubed reinforced concrete (RC) short columns. The objective of the research was to prevent the RC short columns from shear failure. The tested columns were 175 × 175 mm with a 350 mm height and a shear span to depth
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Nomenclature Ac Ag As Aw Aa Aa,w Aσ h Aτ b D fa fa,w fco 10 fcu fy h I L Mu MEC N n0 P Pu Py R Ru S t tf tw ta,w Vn Vc Va,w Vt Vσ h Vτ
∆ ∆y ∆u ∆0.85
µ∆ σv σh σz τ σhp τp α λ
Area of the concrete of the cross section Gross area of the cross section of SRC column Area of the steel tube of the cross section Total cross-section area of the two sheared webs in the tube Area of the cross section of steel section Area of the web of steel section Area of the sheared plates under tension Area of the sheared plates under shear force Width of the non-sheared flange of a rectangular tube Diameter or width of the tube Yield strength of steel section Yield strength of the web of steel section Compressive strength of concrete 100 mm concrete cubic strength; Yield strength of steel tube Height of the sheared web of a rectangular tube Moment of inertia Height of the column Tested ultimate moment strength Moment strength according to modified EC4 method Axial load Axial load ratio Lateral load Tested ultimate lateral load strength Yield lateral load strength Interstory drift ratio Maximum interstory drift ratio Area moment Thickness of the tube Thickness of the non-sheared flange of a rectangular tube Thickness of the sheared web of a rectangular tube Thickness of the web of steel section Nominal shear strength Shear strength of concrete Shear strength of the web of steel section Shear strength of steel tube Shear strength in virtue of transverse stress σh of the sheared plate Shear strength in virtue of shear stress τ of the sheared plate Displacement Yield displacement Ultimate displacement corresponding to Pu Ultimate displacement where the post-peak remaining capacity of the column has dropped to 85% of the peak load Displacement ductility index Longitudinal stress Transverse stress Equivalent stress Shear stress Transverse stress of the sheared plate at the peak load point Shear stress of the sheared plate at the peak load point Asymmetric index of the shear stress in the sheared plate Shear span to depth ratio
ratio of 1.0. The concrete compressive strength was about 40 MPa. The 6 mm thick steel tube was terminated 5 mm from the ends of the columns. During the tests, the columns were subjected to cyclic lateral load and constant axial compression. It was concluded that steel tubes were very effective in preventing shear failure in short columns. Sakino et al. [5] investigated the cyclic behavior of eight square tubed RC short columns. The column sizes were 175 × 175 mm and 250 × 250 mm. In this case, the shear span to depth ratios varied between 1 and 2. The concrete compressive strength varied from 32 to 44 MPa. The width-to-thickness (D/t) ratio of the steel tube ranged between 30 and 77. It was concluded that the degree of confinement provided by the square steel tubes decreased as the D/t ratio of the steel tube and/or the concrete strength increased. It was also noted that the confining effect of the square steel tubes on the overall flexural behavior of the columns was more evident at high levels of applied axial compression. Aboutaha [6] investigated the cyclic behavior of three rectangular tubed RC columns. The cross-sectional dimensions were 500 × 300 mm and the column height was 1829 mm. The thickness of the steel tube was 8 mm and the axial load ratios of the three columns were 0, 0.12 and 0.16 respectively. Three similar RC columns were also tested under the same conditions and the results compared those obtained for the rectangular tubed RC columns. It was concluded that the ductility of the columns were obviously improved due to the confinement of the rectangular tube to the core concrete, while only a slight difference was noted in terms of the flexural strength. Zhang and Zhou [7,8] investigated the seismic behavior of tubed RC beam–columns. Circular and square tubed RC beam–columns were tested under combined axial compression and cyclic lateral shear force. The test results indicated that tubed RC beam–columns exhibited excellent ductility under high axial load ratio. 2. Experimental program 2.1. Details of specimens The test series presented in this study consisted of eight columns, including one common circular SRC (CSRC) column, three circular tubed SRC (CTSRC) columns, one common square SRC (SSRC) column and three square tubed SRC (STSRC) columns. The two common SRC columns were tested as comparison. Fig. 2 presents the details of the columns tested. In order to reproduce the boundary conditions as accurately as possible, the columns were embedded at their two ends in two RC blocks of 460 × 300 × 800 mm3 to avoid failure in the embeddings. As shown in Fig. 2, the steel tube was extended over the full height of the column but terminated 15 mm from its ends. A strengthening steel loop was welded at both ends of the circular tube to prevent the tube weld from fracturing due to the concrete bulging. And two strengthening steel loop spacing at 100 mm were welded at each end of square tubes to prevent the tube weld from fracturing. The size of strengthening steel loop was 6 mm thick and 20 mm high. The CSRC column (CSRC-70-5-1.5) was reinforced with four 9.47 mm grade 392 MPa longitudinal reinforcing bars, and the elongation ratio of the longitudinal bars after fracture was 0.24. Transverse reinforcement used consisted of 7.98 mm grade 363 MPa crossties spaced at 90 mm, and the elongation ratio of the transverse reinforcement after fracture was 0.22. The steel shape was 115 mm high and 115 mm wide. The thickness of the flange and the web was 9.64 mm and the grade of the steel shape was 296 MPa; and the elongation ratio of the flange and web after fracture was 0.28. The CTSRC columns were only consisted of circular tube, steel shape and concrete; neither longitudinal reinforcement nor transverse ties were used in the CTSRC columns. The steel shape used in CTSRC columns was 150 mm high and 85 mm wide. The
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Fig. 1. A tubed SRC column in a structural frame.
(a) Common SRC columns.
(b) Tubed SRC columns. Fig. 2. Details of test columns.
flange thickness of the steel shape was 9.64 mm and the grade of flange was 296 MPa, and the elongation ratio of the flange after
fracture was 0.28. The web thickness of the steel shape was 3 mm and the grade of web was 254 MPa, and the elongation ratio of
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Table 1 Parameters and test results of the test specimens. Cross section
Specimen
t (mm)
D/t
10 fcu (MPa)
fco (MPa)
fy (MPa)
N (kN)
Pu (kN)
n0
Circular
CSRC-70-5-1.5 CTSRC-70-5-1.5 CTSRC-70-4-1.5 CTSRC-70-3-1.5
– 3.00 3.00 3.00
– 75 75 75
75.1 75.1 75.1 75.1
56.4 56.4 56.4 56.4
– 346 346 346
1365 1365 1092 819
232.7 411.5 384.4 343.7
0.5 0.5 0.4 0.3
Square
SSRC-70-5-1.5 STSRC-70-5-1.5 STSRC-70-4-1.5 STSRC-70-3-1.5
– 3.00 3.00 3.00
– 66 66 66
75.1 75.1 75.1 75.1
56.4 56.4 56.4 56.4
– 254 254 254
1365 1365 1092 819
307.5 377.5 360.2 338.5
0.5 0.5 0.4 0.3
In the nomenclature of specimens, for example CTSRC-70-5-1.5, the five letters CTSRC denote that it is a Circular Tubed SRC column; the second number defines the cubic concrete strength (in this example equal to 70); the third number denotes the axial load ratio (in this case 5 stands for 0.5); the forth number denotes the shear span to depth ratio (the shear span to depth ratio of all the tested columns was 1.5). The elongation ratio of the circular and square tube after fracture was 0.32 and 0.38 respectively.
(a)
(b) Fig. 3. Schematic of test set-up and instrumentation layout.
the web after fracture was 0.38. The volume of the steel used in the CSRC column including reinforcement and steel shape was the same as the steel used in CTSRC columns including circular tube and steel shape. The longitudinal and transverse reinforcing bars used for the SSRC column were identical to those in the CSRC column. The steel shape was 125 mm high and 125 mm wide, and the material of steel shape was identical to those in the steel shape of the CSRC column. The STSRC columns were only consisted of square tube, steel shape and concrete; neither longitudinal reinforcement nor transverse ties were used in the STSRC columns. The steel shape used in STSRC columns was 140 mm high and 140 mm wide. The flange thickness of the steel shape was 5.76 mm and the grade of flange was 291 MPa, and the elongation ratio of the flange after fracture was 0.31. The web thickness of the steel shape was 3 mm and the grade of web was 254 MPa, and the elongation ratio of the web after fracture was 0.38. The volume of the steel used in the SSRC column including reinforcement and steel shape was the same as the steel used in STSRC columns including square tube and steel shape. The length L of the columns was 680 mm for the circular columns and 600 mm for the square columns, accordingly the shear span to depth ratio (λ) of the circular and square columns was 1.5. By using a diameter of 226 mm for the circular column and a width of 200 mm for the square columns, the two cross sections had the same area. The details of the tested columns are collected in Table 1 where the following variables have been reported: the thickness of steel tube t, the wide-to-thickness or diameter-to-thickness ratio of 10 the steel tube D/t; the 100 mm concrete cubic strength fcu ; the compressive strength of concrete fco that can be converted from 10 fcu ; the yield stress of the steel tube fy ; the axial load ratio n0 , where n0 = N /(fco Ac + fa Aa ), where N was the axial load applied during the test; Ac was the area of concrete; fa was the grade of the
steel shape and Aa was the area of the steel shape cross section; Pu was the tested lateral load strength of the columns. The steel grade obtained from tensile coupon test following Chinese code JGJ 101–96 [9], and the compressive strength of concrete obtained from compression coupon test following Chinese code GB 500102002 [10]. 2.2. Test set-up and instrumentation layout The test set-up is plotted in Fig. 3(a) schematically. The test set-up consisted of a lateral reaction system supporting the lateral MTS hydraulic actuator and a vertical system supporting the vertical hydraulic actuator. The lateral reaction system consisted of a rigid reaction wall, a 600 kN MTS hydraulic actuator and a stiff L beam. The vertical reaction system consisted of reaction racks, two rollers, 2500 kN hydraulic jack, a 2000 kN load cell and distribution beams. The axial load was applied using the vertical 2500 kN hydraulic jack and the lateral load was applied using the 600 kN MTS hydraulic actuator and the stiff L beam. Rollers were positioned between the rigid L beam and the distribution beam so that there was little friction between these components. The bottom end of the specimen was fully fixed to the ground, while the top end was free to move, keeping however its end cross section horizontal in respect that the pantograph system restrained the top end of the test column against rotation. Fig. 3(b) depicts the instrumentation layout for the specimens. Two LVDTs were used to measure horizontal displacement of the column at the top. Twelve strain gauges were placed at the mid-height of the columns, as shown in Fig. 3(b). There were three strain gauges at each side of the tube, including one transverse strain gauge, one longitudinal strain gauge and one 45° diagonal strain gauge. 2.3. Loading program The axial load was applied using the hydraulic jack until the specified load was reached at the beginning of the test. Fig. 4
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the slight bond cracks between concrete and the flanges of the steel section. The failure mode of CTSRC-70-4-1.5 and CTSRC-70-3-1.5 was similar with that of CTSRC-70-5-1.5 (see Figs. 5(c) and (d)), and the failure mode of three CTSRC columns was combined flexural and bond failure. The axial load ratio affected little on the failure mode of CTSRC columns. The failure mode of the three CTSRC columns indicated that shear connector studs should be used in a CTSRC short column to prevent the bond failure between concrete and flanges of the steel section. 3.2. Load (P) versus deflection (∆) response of circular columns
Fig. 4. Lateral load program.
plots the lateral load diagram of the tested columns. At the beginning of the lateral load being applied process, each cycle was under force control with a maximum lateral force equal to 0.2, 0.4, 0.6, . . ., times the expected yield lateral force up to yielding. Thereafter, each cycle was under displacement control with a maximum displacement equal to 2, 3, 4, . . ., times the measured yield displacement up to failure. Except for the cycles before yielding, whose sole purpose was to crack the member to simulate real conditions and obtain elastic characteristics, all subsequent cycles were repeated twice. During the test, the axial load was maintained constant by re-adjusting the hydraulic jack. 3. Test results of circular columns 3.1. Failure mode of circular columns Failure pattern of the circular columns is depicted in Fig. 5. Fig. 5(a) illustrates the final failure pattern of CSRC-70-5-1.5. There was severe bond failure between the concrete and the flanges of steel section. The concrete cover spalled off, and then the main reinforcement buckled after the peak lateral load since the ties cannot prevent the main reinforcement bars from buckling after the cover spalling off. The concrete confined by ties crushed after the main reinforcement buckled. The shear capacity of the CSRC column dropped rapidly after the peak load. Fig. 5(b) depicts the final failure pattern of CTSRC-70-5-1.5 whose axial load level was the same as that of CSRC-70-5-1.5. No severe failure pattern occurred until the test was finished. Removing the tube after test, no severe failure was found except
(a) CSRC-70-5-1.5.
(b) CTSRC-70-5-1.5.
Fig. 6(a) depicts the lateral load (P) versus lateral deflection (∆) response of column CSRC-70-5-1.5. The lateral load strength dropped rapidly after the peak load point. CSRC-70-5-1.5 showed little ductility and energy dissipation capacity in respect that the main reinforcement buckled and the concrete was crushed after the peak load. Energy dissipation capacity of structural members plays an important role in the behavior of structures against earthquakes. Members with greater plastic deformation can dissipate more energy. Since the CSRC column failed immediately after the peak load, the plastic deformation of the column was very small and little energy was dissipated by the column. The lateral load (P) versus lateral deflection (∆) response of column CTSRC-70-5-1.5 was plotted in Fig. 6(b). The column showed excellent ductility and energy dissipation capacity owning to the excellent plastic deformation capacity of the columns. The lateral load strength dropped gradually after the maximum lateral load by virtue of the P–∆ effect. The P–∆ response of CTSRC-704-1.5 and CTSRC-70-3-1.5 plotted in Figs. 6(c) and (d) was very similar to that of CTSRC-70-5-1.5. The test results indicate that the axial load ratio affected little on the hysteretic behavior of CTSRC short columns. Fig. 7 depicts the comparisons on the envelopes of cyclic response of circular columns. The lateral load strength of CTSRC70-5-1.5 was 76.8% higher than that of CSRC-70-5-1.5. The comparison on the envelopes of the three CTSRC columns indicates that the lateral load strength increases with an increment in axial load ratio for CTSRC short columns. 3.3. Plastic deformation capacity and ductility of circular columns A structure is imposed displacements on the columns and walls in the earthquakes. The aim of the design recommended
(c) CTSRC-70-4-1.5.
Fig. 5. Failure modes of the circular columns.
(d) CTSRC-70-3-1.5.
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(a) CSRC-70-5-1.5.
(b) CTSRC-70-5-1.5.
(c) CTSRC-70-4-1.5.
(d) CTSRC-70-3-1.5. Fig. 6. Lateral load (P) versus lateral deflection (∆) of the circular columns.
Table 2 Test results of the columns.
Fig. 7. Comparisons on the envelopes of circular columns.
by Chinese regulations [11] or EC8 [12] is to give the structure a certain freedom of displacement. This capacity of deformation must occur in the plastic range, therefore the columns and walls should have enough plastic deformation ability. The maximum interstory drift ratio Ru of the tested columns is used to evaluate the plastic deformation capacity based on the measured displacement at failure: Ru =
∆0.85
(1) L in which ∆0.85 is the ultimate displacement when the post-peak remaining capacity of the column has dropped to 85% of the peak load. And L is the height of the column. The parameter Ru takes into account both inelastic and elastic behavior. It is generally assumed that a drift ratio of about Ru ≥ 4% represents a very good level of ductility [13]. Fig. 8 provides the lateral load (P)–drift
Group
Specimen
∆y (mm) ∆0.85 (mm) R0.85 (%)
µ∆
Circular columns
CSRC-70-5-1.5 CTSRC-70-5-1.5 CTSRC-70-4-1.5 CTSRC-70-3-1.5
2.71 5.17 4.52 5.12
8.65 (36.10) 37.50 (42.20)
1.27 (5.29) 5.51 (6.18)
3.19 6.96 8.29 8.21
Square columns
SSRC-70-5-1.5 STSRC-70-5-1.5 STSRC-70-4-1.5 STSRC-70-3-1.5
3.02 3.59 4.18 3.48
6.33 21.00 (32.50) 28.50
1.06 3.50 (5.42) 4.75
2.10 5.85 (7.77) 8.19
The results in the parentheses denote that the lateral strength of the column did not drop to 85% of the peak load until the test was finished.
ratio (R) of the circular columns. The average maximum interstory drift ratio of CSRC-70-5-1.5 was only Ru = 1.27% as listed in Table 2. The plastic deformation capacity of the three CTSRC short columns was much higher than that of CSRC-70-5-1.5. The average maximum interstory drift ratios of CTSRC-70-5-1.5, CTSRC-70-41.5 and CTSRC-70-3-1.5 were Ru = 5.29%, Ru = 5.51% and Ru = 6.18% respectively, representing an excellent ductility of the three CTSRC short columns. The test results indicate that the confinement of a thin circular tube can instinctively improve the ductility of a SRC short column. The lateral load strength of CTSRC70-5-1.5 and CTSRC-70-3-1.5 did not drop to 85% of the peak load until the test was finished, while the lateral load strength of CTSRC70-4-1.5 had dropped to 85% of the peak load during the test; denoting that the axial load ratio has no obviously effect on the plastic deformation capacity of the CTSRC columns tested in this paper.
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the column can continue carrying the applied specified axial load owing to the effective confinement of the tube to the concrete. Removing the tube after test, longitudinal bond cracks as well as diagonal shear cracks were found in the concrete. The failure mode of STSRC-70-5-1.5 is a combination of bond failure and shear failure. Failure mode of STSRC-70-4-1.5 was similar with that of STSRC-70-5-1.5. It was found that the concrete outside the steel flange was separated from the steel section. The bond failure of the two columns indicates that shear connector studs should be used in the STSRC short columns to prevent the bond failure between concrete and flanges of the steel section. The failure pattern of STSRC-70-3-1.5 presented in Fig. 9(d) illustrates that there was no bond or shear cracks in the concrete; the failure mode of this column was flexural failure. Compared with the failure mode of STSRC-70-4-1.5 and STSRC-70-5-1.5, it is concluded that the bond and shear failure tends to occur when columns are under a relative high axial load level.
Fig. 8. Lateral load versus drift ratio envelopes of circular columns.
Another means of evaluation the capacity of deformation is by calculating the ductility index µ∆ :
µ∆ =
∆0.85 ∆y
(2)
in which ∆y is the yield displacement [14]. The ductility index of CSRC-70-5-1.5 was 3.19 as depicted in Table 2, while the ductility index of CTSRC-70-5-1.5 was 6.96, which was much higher than that of CSRC-70-5-1.5. The test results listed in Table 2 indicate that the ductility index decreases with the increment in axial load ratio for CTSRC short columns. 4. Test results of square columns 4.1. Failure mode of square columns Failure mode of the tested square columns is depicted in Fig. 9. Fig. 9(a) depicts the final failure pattern of SSRC-70-5-1.5. There was obvious bond failure between the concrete and the flanges of steel section, and diagonal cracks were also found in the concrete after the test. The main reinforcement buckled and the concrete was crushed after the peak load, resulting in a rapid lateral load strength dropping; and the column could not continue to bear the specified axial load. The failure mode of SSRC-70-5-1.5 is a combination of bond failure and shear failure. Fig. 9(b) depicts the final failure pattern of STSRC-70-5-1.5 whose axial load level was the same as that of SSRC-70-5-1.5. The tube bulged at the end of the columns on account of the concrete being crushed and bulging at the end of the test, however
(a) SSRC-70-5-1.5.
(b) STSRC-70-5-1.5.
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4.2. Load (P) versus deflection (∆) response of square columns Fig. 10(a) depicts the lateral load (P) versus lateral deflection (∆) response of column SSRC-70-5-1.5. The lateral load strength dropped rapidly after the peak load point. And the column showed little ductility and energy dissipation capacity in respect that the main reinforcement buckled and the concrete was crushed after the peak load. Since the SSRC short column developed little plastic deformation after the peak load, it dissipated little energy at the post-peak stage. The P–∆ response of STSRC-70-5-1.5 plotted in Fig. 10(b) indicates that the column showed enough ductility and energy dissipating capacity. The lateral load strength decreased gradually after the peak lateral load. Since the column developed great plastic deformation, it dissipated much more energy than the SSRC column with the same steel ratio. The P–∆ response of STSRC-704-1.5 and STSRC-70-3-1.5 plotted in Fig. 10(c) and (d) was similar with that of STSRC-70-5-1.5. Fig. 11 depicts the comparisons on the envelopes of cyclic response of square columns. The lateral load strength of STSRC-705-1.5 was 22.8% higher than that of SSRC-70-5-1.5. The comparison on the envelopes of the three STSRC columns indicates that the lateral load strength increases with an increment in axial load ratio. 4.3. Plastic deformation capacity and ductility of square columns Fig. 12 provides the lateral load (P)–drift ratio (R) envelopes of the circular columns. The average maximum interstory drift
(c) STSRC-70-4-1.5. Fig. 9. Failure modes of the square columns.
(d) STSRC-70-3-1.5.
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(a) SSRC-70-5-1.5.
(b) STSRC-70-5-1.5.
(c) STSRC-70-4-1.5.
(d) STSRC-70-3-1.5. Fig. 10. Lateral load (P) versus lateral response (∆) of square columns.
Fig. 11. Comparisons on the envelopes of square columns.
ratio of SSRC-70-5-1.5 was only Ru = 1.06% as depicted in Table 2. The plastic deformation capacity of the three STSRC short columns was much higher than that of CSRC-70-5-1.5. The average maximum interstory drift ratios of STSRC-70-5-1.5, STSRC-70-41.5 and STSRC-70-3-1.5 were Ru = 3.50%, Ru = 5.42% and Ru = 4.75% respectively, indicating that the confinement of a thin square tube can instinctively improve the ductility of a SRC short column. The lateral load strength of CTSRC-70-4-1.5 did not drop to 85% of the peak load until the test was finished, while the lateral load strength of CTSRC-70-5-1.5 had dropped to 85% of the peak load during the test. The lateral load strength of CTSRC-70-3-1.5 had dropped to 85% of the peak load under the positive lateral load, while it did not drop to 85% of the peak load under the negative lateral load until the test was finished. The test results of the draft ratio indicates that the axial load ratio has no obviously effect on the plastic deformation capacity of the STSRC columns tested in this paper. The test results depicted in Table 2 indicate that the ductility index trends to decrease with an increment in axial load ratio for the tested STSRC columns.
Fig. 12. Lateral load versus drift ratio envelopes of square columns.
5. Comparison on the test results of circular and square columns A circular tube can improve the seismic behavior more effectively than a square tube in a tubed SRC column. The crosssection area and reinforcement of the CTSRC columns tested in this paper are equal to that of the STSRC columns. The test results depicted in Table 2 indicate that maximum interstory drift ratio of the CTSRC columns is higher than that of the STSRC columns. The comparison on the failure mode of CTSRC and STSRC columns indicate that a circular tube prevent the shear failure of the concrete more effectively than a square tube in a tubed SRC column.
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Von Mises yield criterion has been adopted to define the yield point of the steel:
σz =
(a) Sheared plate of circular tube.
σv2 + σh2 − σv σh + 3τ 2 = fy .
(4)
As depicted in Fig. 15, the stress states of the sheared plate of the three CTSRC columns were very similar: After the axial load had being applied to the specified value, there was only obvious longitudinal stress σv in the tube due to the bond and friction stress between the concrete and the tube. While σv deceased gradually as the cyclic lateral load was applied in respect that the bond and friction deteriorated before the peak load. After the peak load, σv increased obviously; the reason is that the friction force between the concrete and the tube increased due to the increment in the confinement stress of the tube to the core concrete. The transverse stress σh of the sheared plate in the tube increased gradually as the lateral load increased. The flexural moment at the mid-height of the columns is zero, hence σh in the sheared plate was generated in respect that the outer tube was confining the core concrete which was under shear deformation. After the peak load, the shear deformation of the core concrete decreased as the lateral load decreased since the failure mode of the three CTSRC columns was not shear failure. And then σh decreased with the shear deformation of the core concrete decreased. The shear stress τ of the sheared plate in the tube increased as the lateral load increased. After the peak load, τ decreased with the lateral load decreased in respect that the failure mode of the column was not shear failure and no severe plastic shear deformation occurred in the core concrete. The analysis result on the equivalent stress σz indicated that the sheared plate at the mid-height of the tube did not yield for the three CTSRC columns.
(b) Sheared plate of square tube.
Fig. 13. Sheared plate of the tube.
(a) Flexural deformation.
q
(b) Shear deformation.
Fig. 14. Deformation shape of column.
6. Elastic–plastic analysis on steel tube
6.2. Stress of square tubes of STSRC columns
In a tubed SRC column, the steel at the mid-height of tube is under a complex state of stress with a combination of axial compression, transverse tension and transverse shear. The elastic–plastic analysis method was adopted to analyze the stress state on the steel tube based on the measured strains [15]. Under lateral shear force, the plates parallel to the lateral shear force of the tube in the column is under shear stress (Fig. 13). The stress state of the sheared plate was analyzed in detail for the tested CTSRC and STSRC columns. The deformation of the tested short columns in this paper is depicted in Fig. 14. The deformation of the columns consisted of flexural deformation and shear deformation. In the elastic range, the flexural and shear deformation will increase in proportion as the shear force increases, while the case will alter after the peak lateral load. After the peak load, the resistance of the columns will decrease in respect of failing. For those columns with a flexural failure mode, after the peak lateral load the flexural deformation will increase rapidly as the lateral displacement increases, while the shear deformation will decrease with the reduced shear force. Regarding those columns experiencing shear failure, the shear deformation will increase dramatically and the flexural deformation will decrease after the peak lateral load.
The results of the analysis on the square tubes of STSRC-703-1.5 are provided in Fig. 16(a). The transverse stress σh of the sheared plate in the tube was rather low under lateral shear force for column STSRC-70-3-1.5, since the failure mode of the column was not shear failure and the flexural moment at the mid-height of the column was zero. The shear stress τ of the sheared plate in the tube increased as the lateral load increased for the column. At the post-peak stage, τ decreased with the lateral load decreased in respect that the failure mode the column was not shear failure and no severe plastic shear deformation emerged in the core concrete. Fig. 16(b) depicts the results of analysis on the square tube of STSRC-70-4-1.5. The transverse stress σh of the sheared plate in the tube increased as the lateral load increased before the peak load. The lateral load decreased at the post-peak stage, while σh kept increasing in respect that the failure mode of the column was shear failure. Plastic shear deformation increased rapidly as the lateral displacement increased after the peak load due to the shear failure mode of the core concrete. σh of the tube kept increasing with the increment in lateral displacement in respect that the tube confined the core concrete and prevent the concrete from severe shear failure. The shear stress τ of the sheared plate in the tube increased as the lateral load increased. At the post-peak stage, τ kept increasing in respect that the failure mode of the column was shear failure. Plastic shear deformation of the column increased rapidly with increment in lateral displacement, therefore the shear deformation as well as the shear stress τ of the sheared plate kept increasing. In this case, the degradation of the shear capacity in concrete core can be compensated by the steel tube as the σh and τ increased. Thereby the shear strength of the STSRC short columns with shear failure would not drop rapidly and the ductility was hence distinctively improved. The results of analysis on the equivalent stress σz indicated that the sheared plate at the midheight of the tube did not yield until after the peak load for this
6.1. Stress of circular tubes of CTSRC columns Fig. 15 depicts the analysis results of the CTSRC columns, in which P is the lateral load, σv and σh are the longitudinal and hoop stress of the steel at the mid-height of tube respectively; τ is the shear stress and σz is the equivalent stress determined from the following equation:
σz =
q σv2 + σh2 − σv σh + 3τ 2 .
(3)
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X. Zhou, J. Liu / Journal of Constructional Steel Research 66 (2010) 885–896
(a) CTSRC-70-3-1.5.
(b) CTSRC-70-4-1.5.
(c) CTSRC-70-5-1.5.
Fig. 15. Lateral load versus stress of the sheared web of the circular tubes.
(a) STSRC-70-3-1.5.
(b) STSRC-70-4-1.5.
(c) STSRC-70-5-1.5.
Fig. 16. Lateral load versus stress of the sheared web of the square tubes.
column. The results of analysis on the square tube of STSRC-70-51.5 depicted in Fig. 16(c) were similar with that of STSRC-70-4-1.5 in respect of their similar failure mode. 7. Nominal shear strength of tubed SRC columns The failure mode of STSRC-70-4-1.5 and STSRC-70-5-1.5 was shear failure, therefore the formula for the nominal shear strength of STSRC columns is proposed based on the test and analysis results of STSRC-70-4-1.5 and STSRC-70-5-1.5. The nominal shear capacity, Vn , of a STSRC column is equal to the sum of the contributions of three mechanisms; concrete Vc , web of the steel section Va,w , and outer tube Vt : Vn = Vc + Va,w + Vt .
Fig. 17. Shear force and shear stress in the sheared plate of a rectangular tube.
(5)
7.1. Shear strength provided by steel tube The shear strength provided by the sheared plate of the tube in a STSRC column can be calculated from the following equation: Vt = Vσ h + Vτ = σhp Aσ h + ατp Aτ
(6)
where Vσ h is the shear strength in virtue of transverse stress σh of the sheared plate, Vτ is the shear strength in virtue of shear stress τ of the sheared plate, σhp is the transverse stress of the sheared plate at the peak load point, τp is the shear stress of the sheared plate at the peak load point, Aσ h is the area of the sheared plates under tension (Figs. 17 and 18), Aτ is the area of the sheared plates under shear force (Figs. 17 and 18),
Fig. 18. Outer and inner force balance in the sheared plate.
X. Zhou, J. Liu / Journal of Constructional Steel Research 66 (2010) 885–896 Table 3 The stress in the sheared plate of the tube at the peak load point. Specimen STSRC-70-4-1.5 STSRC-70-5-1.5
σhp
τp
σhp + 8/9τp
(MPa)
(MPa)
(MPa)
54.7 59.8
67.8 72.8
115.0 124.5
Average value of (σhp + 8/9τp ) (MPa) 119.8
α is the asymmetric index of the shear stress in the sheared plate. Fig. 17 depicts the shear stress in the sheared plate of a rectangular tube where the moment of inertia I and area moment S of the tube around x axis can be calculated from Eqs. (7) and (8): I =
1
bh2 tf +
1
2 1
tw h3
(7)
6 1 (8) S = bhtf + tw h2 2 4 where b and tf are the width and thickness of the flange of the tube without shear stress respectively; h and tw are the height and thickness of the sheared web respectively. The maximal shear stress of the sheared web τmax can be calculated by the following expression: VS
τmax =
(9)
Itw
where V is the shear force. The shear force V can be evaluated from the combination of Eqs. (7)–(9): V =
=
Itw S
τmax =
3bh2 tf + h3 tw
3 bhtf + 12h2 tw
bhtf + 31 h2 tw btf + 12htw
bhtf + 13 h2 tw btf + 12htw
(2tw ) τmax .
tw τmax =
8 9
(10)
h (2tw ) τmax =
8 9
Aτ τmax .
(11)
It is concluded from Eq. (11) that the asymmetric index of the shear stress in the sheared plate is equal to 8/9. Fig. 18 plots the outer and inner force balance in the sheared plate. Aσ h equals to Aτ since the angle of the concrete crack under shear force is θ = 45°. Therefore Eq. (6) can be simplified as: Vt = Vσ h + Vτ = σhp Aσ h + ατp Aτ =
8
Vt = σhp Aσ +
9
8
σhp + τp Aτ . 9
(12)
τp Aτ = σh + τ Aτ = 119.8Aτ
= 0.56f215 Aτ = 0.56f215 Aw
Specimen
Pu (kN)
Vn (kN)
Vn /Pu (kN m)
STSRC-70-4-1.5 STSRC-70-5-1.5
360.2 377.5
350.0 370.6
0.97 0.98
Table 5 Comparison on the results from the test and proposed method for the columns with flexural failure. Specimen
Mu (kN m)
MEC 4 (kN m)
Mu /MEC 4 (kN m)
CTSRC-70-3-1.5 CTSRC-70-4-1.5 CTSRC-70-5-1.5 STSRC-70-3-1.5
132.2 145.5 156.3 124.5
105.8 113.5 122.6 98.1
1.25 1.28 1.27 1.27
Vc = 0.17 1 +
N
14Ag
p
fco D2 .
(14)
Quantity N /Ag shall be expressed in MPa. Plastic shear capacity is adopted to evaluate the shear strength provided by the web of the steel section. Va,w = fa,w Aa,w
(15)
where fa,w and Aa,w are the yield strength and area of the web of steel section. 7.3. Shear strength of tubed SRC columns
Vn = 0.17 1 +
N
14Ag
fco D2 + fa,w Aa,w + 0.56f215 Aw .
p
(16)
For circular members, the area used to compute Vn shall be taken as the product of the diameter and effective depth of the concrete section [10,16]. The equivalent width of a circular column is 1.76r, where r is the radius of the cross section. Comparison of test results and predictions based on the proposed method are listed in Table 4 where Pu is the tested maximum lateral load and Vn is the predicted shear strength of the columns. The predictions compared well with the test results of the two columns with shear failure. 8. Nominal moment strength of tubed SRC columns
Table 3 depicts the (σhp + 8/9τp ) of the sheared plates in the two STSRC columns with shear failure. The test results indicate that the axial load ratio has no obvious effect on (σhp + 8/9τp ), therefore it is proposed that the effect of axial load ratio on the shear strength provided by the sheared plate of the tube may not be considered. Then Eq. (12) can be simplified using the average value of (σhp + 8/9τp ): 8
Table 4 Comparison on the results from the test and proposed formula for the columns with shear failure.
The formula for the nominal shear strength of STSRC columns is a modified ACI formula [16] based on the test and analysis results of the two STSRC columns with shear failure:
(2tw ) τmax
In a thin-walled steel tube used in the STSRC columns, b ≈ h and tw = tf ; then Eq. (10) can be simplified as: V =2
895
9
8.1. Tested moment strength of the columns The height of the plastic hinge of the columns with flexural failure was about D/2, so the tested moment strength (Mu ) of the columns with flexural failure can be calculated by the following equation [7]: Mu = Pu (L/2 − D/2) + N ∆u /2
(17)
where L is the length of the column; Pu is the ultimate lateral load strength; ∆u is the displacement corresponding to Pu . The tested moment strength (Mu ) of the four columns with flexural failure was listed in Table 5.
(13)
where f215 = 215 MPa and Aw is the total cross-section area of the sheared two webs. 7.2. Shear strength provided by concrete and web of steel section The shear strength provided by concrete can be evaluated from a modified ACI method [16] based on the test results:
8.2. Nominal moment strength of CTSRC and STSRC columns In the calculation of the nominal moment capacity of a SRC column in accordance with EC4 [1], the following assumptions are adopted:
• There is full interaction between the steel and concrete sections until failure occurs;
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Fig. 19. Comparisons between test results and EC4 Code of CTSRC columns with flexural failure.
2. For CTSRC short columns, the lateral load strength increases with an increment in axial load ratio. The ductility index decreases with an increment in axial load ratio, while the axial load ratio affects little on the plastic deformation capacity of CTSRC short columns. 3. For STSRC short columns, under a relative high axial load level (n0 ≥ 0.4 in this paper), the failure mode is a combination of bond failure and shear failure. The plastic deformation capacity of STSRC short columns with shear failure reaches a high level in respect that the tube prevents the core concrete form severe shear failure. The shear strength of STSRC columns increases with an increment in axial load ratio, while the axial load ratio has no considerable effect on the plastic deformation capacity of the STSRC short columns. 4. The steel tube in a tubed SRC short column will not yield at the peak lateral load point, hence the confinement of the tube to the core concrete will keep increasing. Therefore the lateral load strength of tubed SRC short columns cannot drop sharply after the peak load. 5. A circular tube prevents the shear failure of the concrete more effectively than a square tube in a tubed SRC column. 6. Shear connector studs should be used in CTSRC and STSRC short columns to prevent the bond failure between concrete and flanges of the steel section. 7. A modified ACI design method is adopted to calculate the nominal shear strength of STSRC columns as well as CTSRC columns. Acknowledgements
Fig. 20. Comparisons between test results and EC4 Code of STSRC columns with flexural failure.
• Geometric imperfections and residual stresses are taken into account in the calculation, although this is usually done by using an equivalent initial out-of-straightness, or member imperfection; • Plane sections remain plane whilst the column deforms. It is proposed that the flexural strength of tube SRC columns is then calculated based on the compressive strength of the confined concrete fcc and on the assumptions proposed of the EC4. The compressive strength of tubed concrete fcc have been proposed by Zhang [7] and Liu [17]. The M–N interaction curves for uniaxial bending of the four tubed SRC columns with flexural failure were calculated according to the modified EC4 method in this paper, as shown in Figs. 19 and 20, where N and M are the axial load and moment, respectively. Comparisons on the tested ultimate moment strength and the predicted moment are listed in Table 5. The test results are higher than the predictions in virtue of strain hardening of the steel shape. 9. Conclusions The experimental and analysis results of eight short columns tested under combined quasi-static axial compressive and cyclic lateral loads were discussed in this paper. The test results indicated that the common SRC short columns suffered brittle shear failure with poor ductility, while the ductility of tubed SRC short columns was excellent due to the effective confinement of the outer thin steel tube to the core concrete. Based on the test and analysis results, it can be concluded as follows: 1. Tubed SRC short columns exhibit higher lateral load strength, displacement ductility, more stable hysteresis loops, and greater energy dissipation ability than common SRC short columns in respect of the effective confinement of the thin tube to the core concrete.
This research is financially supported by National Natural Science Foundation of China (50708027) and Key Projects in the National Science & Technology Pillar Program in the Eleventh Five-year Plan Period (2006BAJ01B02), which are gratefully acknowledged. References [1] Eurocode 4: Design of steel and concrete structures, part 1.1, general rules and rules for buildings. Brussels (Belgium): European Committee for Standardization, 1996. [2] ANSI/AISC 360-05. Specification for structural steel buildings. American Institute of Steel Construction, Inc.; 2005. [3] ANSI/AISC 341-05. Seismic provisions for structural steel buildings. American Institute of Steel Construction, Inc.; 2005. [4] Tomii M, Sakino K, Xiao Y. Ultimate moment of reinforced concrete short columns confined in steel tube. In: Pacific conf. on earthquake engrg. 1987. [5] Sakino K, Sun YP, Aklan A. Effects of wall thickness of steel tube on the behavior of square tubed R/C columns. In: 11th world conf. on earthquake engrg. 1996. [6] Aboutaha RS, Machado RI. Seismic resistance of steel-tubed high-strength reinforced-concrete columns. Journal of Structural Engineering 1999;125(5): 485–94. [7] Sumei Zhang, Jiepeng Liu. Seismic behavior and strength of square tube confined reinforced-concrete (STRC) columns. Journal of Constructional Steel Research 2007;63(9):1194–207. [8] Xuhong Zhou, Sumei Zhang, Jiepeng Liu. Seismic behavior and steel tube confined reinforced-concrete beam–columns. Journal of Building Structures 2008;29(5):19–28. [9] JGJ 101-96 Specification of testing methods for earthquake of resistant buildings. PR China: Ministry of Construction; 1997. [10] GB 50010-2002. Code for design of concrete structures. PR China: Ministry of Construction; 2002. [11] GB 50011-2001. Code for seismic design of buildings. PR China: Ministry of Construction; 2001. [12] Eurocode 8. Design provisions for earthquake resistance of structures. AFNOR–2000. XP ENV 1998-1-1, XP ENV 1998-1-2, ENV 1998-1-3. [13] ACI-ASCE Committee 441. High strength concrete columns: State of the art. ACI Structure Journal 1997;94(3):323–35. [14] Taghi Kazemi Mohammad, Morshed Reza. Seismic shear strengthening of R/C columns with ferrocement jacket. Cement & Concrete Composites 2005;27: 834–42. [15] Zhang Sumei, Guo Lanhui, Ye Zaili, Wang Yuyin. Behavior of steel tube and confined high strength concrete for concrete-filled RHS tubes. Advances in Structural Engineering 2005;8(5):101–16. [16] ACI Committee 318. Building code requirements for structural concrete (ACI318-02) and commentary (ACI318R-02). American Concrete Institute; 2002. [17] Liu Jiepeng, Zhang Sumei, Zhang Xiaodong, Guo Lanhui. Behavior and strength of circular tube confined reinforced-concrete (CTRC) columns. Journal of Constructional Steel Research 2009;65(7):1447–58.
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Journal of Constructional Steel Research journal homepage: www.elsevier.com/locate/jcsr
Seismic behavior and strength of tubed steel reinforced concrete (SRC) short columns Xuhong Zhou a , Jiepeng Liu b,∗ a
School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China
b
Architectural Design and Research Institute, Harbin Institute of Technology, Harbin, 150090, China
article
info
Article history: Received 19 October 2009 Accepted 28 January 2010 Keywords: Tubed SRC Short column Axial load ratio Plastic deformation capacity Nominal shear strength
abstract The seismic behavior of tubed SRC short columns has been investigated by testing eight specimens subjected to combined constant axial compression and lateral cyclic load. Three circular tubed SRC columns (CTSRC) and three square tubed SRC (STSRC) columns were tested in this research with two common SRC columns for comparison. Different axial load ratios (n0 = 0.3, 0.4 and 0.5) have been adopted for the constant axial load. The test results indicate that the shear strength, plastic deformation capacity, ductility index, and energy dissipating capacity of the tubed SRC short columns were much higher than those of the SRC columns with the same steel ratio and axial compressive load. The lateral load strength of CTSRC and STSRC short columns increased with an increment in axial load level, while the axial load ratio has no obvious effect on the plastic deformation capacity of CTSRC and STSRC short columns. The steel tubes prevented the shear failure of the concrete more effectively in the circular columns than in the square ones. Shear connector studs should be used in CTSRC and STSRC short columns to prevent bond failure between concrete and flanges of the steel section. A modified ACI design method was adopted to calculate the nominal shear strength of STSRC columns as well as CTSRC columns. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction A tubed steel reinforced concrete (SRC) column as depicted in Fig. 1 is a special SRC column where reinforcement cage is in the form of an outer thin steel tube. The outer circular or square tube does not pass through the beam-to-column connection, therefore no axial load is directly applied on the steel tube and the tube confines the core concrete more effectively. This leads to an efficient use of the steel tube in preventing the concrete cover from spalling off and the longitudinal steel from buckling. At the same time, the strength and ductility of the concrete core will increase owing to the confinement of the steel tube. This approach leads to a pronounced enhancement in both strength and ductility of the overall column behavior. SRC columns can provide considerable advantages compared to open steel columns. SRC columns do not require any check on the thickness of the walls of the steel section, and the complete encasement of a steel section usually provides enough fire protection to satisfy the most stringent practical requirements [1]. In virtue
∗ Corresponding address: PO Box 2551, 202 Haihe Road, Nan’gang District, Harbin Institute of Technology (2nd District), Harbin 150090, China. Tel.: +86 0 451 8628 2083; fax: +86 0 451 86282083. E-mail address: [email protected] (J. Liu). 0143-974X/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2010.01.020
of the advantages, SRC columns are widely used in the construction of high rise buildings. In a SRC column, longitudinal and transverse reinforcements should be used to provide good confinement to the concrete [1–3]. However, the reinforcement does not confine the concrete cover, which will spall off during the occurrence of an earthquake. When subjected to combined high axial load and cyclic lateral load, the concrete cover tends to spall off rapidly. In such a situation, the transverse ties are not able to effectively prevent the longitudinal bars and the flanges of the encased steel shape from buckling, leading to a rapid decrease of the axial load strength and flexural strength. The existence of reinforcement in the SRC columns also makes the concrete casting difficult in construction. In order to increase the confinement to concrete and improve the concrete casting quality, it is proposed to replace the longitudinal and transverse reinforcement by a thin steel tube outside the concrete core, and the outside tube is terminated near the beam (tubed SRC). In such a manner, the steel tube confines the entire concrete column and the concrete casting becomes easier. To the knowledge of the authors no work has been published on the behavior of tubed SRC columns. Only limited research has been carried out in this area. Tomii et al. [4] firstly investigated the seismic behavior of square tubed reinforced concrete (RC) short columns. The objective of the research was to prevent the RC short columns from shear failure. The tested columns were 175 × 175 mm with a 350 mm height and a shear span to depth
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Nomenclature Ac Ag As Aw Aa Aa,w Aσ h Aτ b D fa fa,w fco 10 fcu fy h I L Mu MEC N n0 P Pu Py R Ru S t tf tw ta,w Vn Vc Va,w Vt Vσ h Vτ
∆ ∆y ∆u ∆0.85
µ∆ σv σh σz τ σhp τp α λ
Area of the concrete of the cross section Gross area of the cross section of SRC column Area of the steel tube of the cross section Total cross-section area of the two sheared webs in the tube Area of the cross section of steel section Area of the web of steel section Area of the sheared plates under tension Area of the sheared plates under shear force Width of the non-sheared flange of a rectangular tube Diameter or width of the tube Yield strength of steel section Yield strength of the web of steel section Compressive strength of concrete 100 mm concrete cubic strength; Yield strength of steel tube Height of the sheared web of a rectangular tube Moment of inertia Height of the column Tested ultimate moment strength Moment strength according to modified EC4 method Axial load Axial load ratio Lateral load Tested ultimate lateral load strength Yield lateral load strength Interstory drift ratio Maximum interstory drift ratio Area moment Thickness of the tube Thickness of the non-sheared flange of a rectangular tube Thickness of the sheared web of a rectangular tube Thickness of the web of steel section Nominal shear strength Shear strength of concrete Shear strength of the web of steel section Shear strength of steel tube Shear strength in virtue of transverse stress σh of the sheared plate Shear strength in virtue of shear stress τ of the sheared plate Displacement Yield displacement Ultimate displacement corresponding to Pu Ultimate displacement where the post-peak remaining capacity of the column has dropped to 85% of the peak load Displacement ductility index Longitudinal stress Transverse stress Equivalent stress Shear stress Transverse stress of the sheared plate at the peak load point Shear stress of the sheared plate at the peak load point Asymmetric index of the shear stress in the sheared plate Shear span to depth ratio
ratio of 1.0. The concrete compressive strength was about 40 MPa. The 6 mm thick steel tube was terminated 5 mm from the ends of the columns. During the tests, the columns were subjected to cyclic lateral load and constant axial compression. It was concluded that steel tubes were very effective in preventing shear failure in short columns. Sakino et al. [5] investigated the cyclic behavior of eight square tubed RC short columns. The column sizes were 175 × 175 mm and 250 × 250 mm. In this case, the shear span to depth ratios varied between 1 and 2. The concrete compressive strength varied from 32 to 44 MPa. The width-to-thickness (D/t) ratio of the steel tube ranged between 30 and 77. It was concluded that the degree of confinement provided by the square steel tubes decreased as the D/t ratio of the steel tube and/or the concrete strength increased. It was also noted that the confining effect of the square steel tubes on the overall flexural behavior of the columns was more evident at high levels of applied axial compression. Aboutaha [6] investigated the cyclic behavior of three rectangular tubed RC columns. The cross-sectional dimensions were 500 × 300 mm and the column height was 1829 mm. The thickness of the steel tube was 8 mm and the axial load ratios of the three columns were 0, 0.12 and 0.16 respectively. Three similar RC columns were also tested under the same conditions and the results compared those obtained for the rectangular tubed RC columns. It was concluded that the ductility of the columns were obviously improved due to the confinement of the rectangular tube to the core concrete, while only a slight difference was noted in terms of the flexural strength. Zhang and Zhou [7,8] investigated the seismic behavior of tubed RC beam–columns. Circular and square tubed RC beam–columns were tested under combined axial compression and cyclic lateral shear force. The test results indicated that tubed RC beam–columns exhibited excellent ductility under high axial load ratio. 2. Experimental program 2.1. Details of specimens The test series presented in this study consisted of eight columns, including one common circular SRC (CSRC) column, three circular tubed SRC (CTSRC) columns, one common square SRC (SSRC) column and three square tubed SRC (STSRC) columns. The two common SRC columns were tested as comparison. Fig. 2 presents the details of the columns tested. In order to reproduce the boundary conditions as accurately as possible, the columns were embedded at their two ends in two RC blocks of 460 × 300 × 800 mm3 to avoid failure in the embeddings. As shown in Fig. 2, the steel tube was extended over the full height of the column but terminated 15 mm from its ends. A strengthening steel loop was welded at both ends of the circular tube to prevent the tube weld from fracturing due to the concrete bulging. And two strengthening steel loop spacing at 100 mm were welded at each end of square tubes to prevent the tube weld from fracturing. The size of strengthening steel loop was 6 mm thick and 20 mm high. The CSRC column (CSRC-70-5-1.5) was reinforced with four 9.47 mm grade 392 MPa longitudinal reinforcing bars, and the elongation ratio of the longitudinal bars after fracture was 0.24. Transverse reinforcement used consisted of 7.98 mm grade 363 MPa crossties spaced at 90 mm, and the elongation ratio of the transverse reinforcement after fracture was 0.22. The steel shape was 115 mm high and 115 mm wide. The thickness of the flange and the web was 9.64 mm and the grade of the steel shape was 296 MPa; and the elongation ratio of the flange and web after fracture was 0.28. The CTSRC columns were only consisted of circular tube, steel shape and concrete; neither longitudinal reinforcement nor transverse ties were used in the CTSRC columns. The steel shape used in CTSRC columns was 150 mm high and 85 mm wide. The
X. Zhou, J. Liu / Journal of Constructional Steel Research 66 (2010) 885–896
887
Fig. 1. A tubed SRC column in a structural frame.
(a) Common SRC columns.
(b) Tubed SRC columns. Fig. 2. Details of test columns.
flange thickness of the steel shape was 9.64 mm and the grade of flange was 296 MPa, and the elongation ratio of the flange after
fracture was 0.28. The web thickness of the steel shape was 3 mm and the grade of web was 254 MPa, and the elongation ratio of
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X. Zhou, J. Liu / Journal of Constructional Steel Research 66 (2010) 885–896
Table 1 Parameters and test results of the test specimens. Cross section
Specimen
t (mm)
D/t
10 fcu (MPa)
fco (MPa)
fy (MPa)
N (kN)
Pu (kN)
n0
Circular
CSRC-70-5-1.5 CTSRC-70-5-1.5 CTSRC-70-4-1.5 CTSRC-70-3-1.5
– 3.00 3.00 3.00
– 75 75 75
75.1 75.1 75.1 75.1
56.4 56.4 56.4 56.4
– 346 346 346
1365 1365 1092 819
232.7 411.5 384.4 343.7
0.5 0.5 0.4 0.3
Square
SSRC-70-5-1.5 STSRC-70-5-1.5 STSRC-70-4-1.5 STSRC-70-3-1.5
– 3.00 3.00 3.00
– 66 66 66
75.1 75.1 75.1 75.1
56.4 56.4 56.4 56.4
– 254 254 254
1365 1365 1092 819
307.5 377.5 360.2 338.5
0.5 0.5 0.4 0.3
In the nomenclature of specimens, for example CTSRC-70-5-1.5, the five letters CTSRC denote that it is a Circular Tubed SRC column; the second number defines the cubic concrete strength (in this example equal to 70); the third number denotes the axial load ratio (in this case 5 stands for 0.5); the forth number denotes the shear span to depth ratio (the shear span to depth ratio of all the tested columns was 1.5). The elongation ratio of the circular and square tube after fracture was 0.32 and 0.38 respectively.
(a)
(b) Fig. 3. Schematic of test set-up and instrumentation layout.
the web after fracture was 0.38. The volume of the steel used in the CSRC column including reinforcement and steel shape was the same as the steel used in CTSRC columns including circular tube and steel shape. The longitudinal and transverse reinforcing bars used for the SSRC column were identical to those in the CSRC column. The steel shape was 125 mm high and 125 mm wide, and the material of steel shape was identical to those in the steel shape of the CSRC column. The STSRC columns were only consisted of square tube, steel shape and concrete; neither longitudinal reinforcement nor transverse ties were used in the STSRC columns. The steel shape used in STSRC columns was 140 mm high and 140 mm wide. The flange thickness of the steel shape was 5.76 mm and the grade of flange was 291 MPa, and the elongation ratio of the flange after fracture was 0.31. The web thickness of the steel shape was 3 mm and the grade of web was 254 MPa, and the elongation ratio of the web after fracture was 0.38. The volume of the steel used in the SSRC column including reinforcement and steel shape was the same as the steel used in STSRC columns including square tube and steel shape. The length L of the columns was 680 mm for the circular columns and 600 mm for the square columns, accordingly the shear span to depth ratio (λ) of the circular and square columns was 1.5. By using a diameter of 226 mm for the circular column and a width of 200 mm for the square columns, the two cross sections had the same area. The details of the tested columns are collected in Table 1 where the following variables have been reported: the thickness of steel tube t, the wide-to-thickness or diameter-to-thickness ratio of 10 the steel tube D/t; the 100 mm concrete cubic strength fcu ; the compressive strength of concrete fco that can be converted from 10 fcu ; the yield stress of the steel tube fy ; the axial load ratio n0 , where n0 = N /(fco Ac + fa Aa ), where N was the axial load applied during the test; Ac was the area of concrete; fa was the grade of the
steel shape and Aa was the area of the steel shape cross section; Pu was the tested lateral load strength of the columns. The steel grade obtained from tensile coupon test following Chinese code JGJ 101–96 [9], and the compressive strength of concrete obtained from compression coupon test following Chinese code GB 500102002 [10]. 2.2. Test set-up and instrumentation layout The test set-up is plotted in Fig. 3(a) schematically. The test set-up consisted of a lateral reaction system supporting the lateral MTS hydraulic actuator and a vertical system supporting the vertical hydraulic actuator. The lateral reaction system consisted of a rigid reaction wall, a 600 kN MTS hydraulic actuator and a stiff L beam. The vertical reaction system consisted of reaction racks, two rollers, 2500 kN hydraulic jack, a 2000 kN load cell and distribution beams. The axial load was applied using the vertical 2500 kN hydraulic jack and the lateral load was applied using the 600 kN MTS hydraulic actuator and the stiff L beam. Rollers were positioned between the rigid L beam and the distribution beam so that there was little friction between these components. The bottom end of the specimen was fully fixed to the ground, while the top end was free to move, keeping however its end cross section horizontal in respect that the pantograph system restrained the top end of the test column against rotation. Fig. 3(b) depicts the instrumentation layout for the specimens. Two LVDTs were used to measure horizontal displacement of the column at the top. Twelve strain gauges were placed at the mid-height of the columns, as shown in Fig. 3(b). There were three strain gauges at each side of the tube, including one transverse strain gauge, one longitudinal strain gauge and one 45° diagonal strain gauge. 2.3. Loading program The axial load was applied using the hydraulic jack until the specified load was reached at the beginning of the test. Fig. 4
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the slight bond cracks between concrete and the flanges of the steel section. The failure mode of CTSRC-70-4-1.5 and CTSRC-70-3-1.5 was similar with that of CTSRC-70-5-1.5 (see Figs. 5(c) and (d)), and the failure mode of three CTSRC columns was combined flexural and bond failure. The axial load ratio affected little on the failure mode of CTSRC columns. The failure mode of the three CTSRC columns indicated that shear connector studs should be used in a CTSRC short column to prevent the bond failure between concrete and flanges of the steel section. 3.2. Load (P) versus deflection (∆) response of circular columns
Fig. 4. Lateral load program.
plots the lateral load diagram of the tested columns. At the beginning of the lateral load being applied process, each cycle was under force control with a maximum lateral force equal to 0.2, 0.4, 0.6, . . ., times the expected yield lateral force up to yielding. Thereafter, each cycle was under displacement control with a maximum displacement equal to 2, 3, 4, . . ., times the measured yield displacement up to failure. Except for the cycles before yielding, whose sole purpose was to crack the member to simulate real conditions and obtain elastic characteristics, all subsequent cycles were repeated twice. During the test, the axial load was maintained constant by re-adjusting the hydraulic jack. 3. Test results of circular columns 3.1. Failure mode of circular columns Failure pattern of the circular columns is depicted in Fig. 5. Fig. 5(a) illustrates the final failure pattern of CSRC-70-5-1.5. There was severe bond failure between the concrete and the flanges of steel section. The concrete cover spalled off, and then the main reinforcement buckled after the peak lateral load since the ties cannot prevent the main reinforcement bars from buckling after the cover spalling off. The concrete confined by ties crushed after the main reinforcement buckled. The shear capacity of the CSRC column dropped rapidly after the peak load. Fig. 5(b) depicts the final failure pattern of CTSRC-70-5-1.5 whose axial load level was the same as that of CSRC-70-5-1.5. No severe failure pattern occurred until the test was finished. Removing the tube after test, no severe failure was found except
(a) CSRC-70-5-1.5.
(b) CTSRC-70-5-1.5.
Fig. 6(a) depicts the lateral load (P) versus lateral deflection (∆) response of column CSRC-70-5-1.5. The lateral load strength dropped rapidly after the peak load point. CSRC-70-5-1.5 showed little ductility and energy dissipation capacity in respect that the main reinforcement buckled and the concrete was crushed after the peak load. Energy dissipation capacity of structural members plays an important role in the behavior of structures against earthquakes. Members with greater plastic deformation can dissipate more energy. Since the CSRC column failed immediately after the peak load, the plastic deformation of the column was very small and little energy was dissipated by the column. The lateral load (P) versus lateral deflection (∆) response of column CTSRC-70-5-1.5 was plotted in Fig. 6(b). The column showed excellent ductility and energy dissipation capacity owning to the excellent plastic deformation capacity of the columns. The lateral load strength dropped gradually after the maximum lateral load by virtue of the P–∆ effect. The P–∆ response of CTSRC-704-1.5 and CTSRC-70-3-1.5 plotted in Figs. 6(c) and (d) was very similar to that of CTSRC-70-5-1.5. The test results indicate that the axial load ratio affected little on the hysteretic behavior of CTSRC short columns. Fig. 7 depicts the comparisons on the envelopes of cyclic response of circular columns. The lateral load strength of CTSRC70-5-1.5 was 76.8% higher than that of CSRC-70-5-1.5. The comparison on the envelopes of the three CTSRC columns indicates that the lateral load strength increases with an increment in axial load ratio for CTSRC short columns. 3.3. Plastic deformation capacity and ductility of circular columns A structure is imposed displacements on the columns and walls in the earthquakes. The aim of the design recommended
(c) CTSRC-70-4-1.5.
Fig. 5. Failure modes of the circular columns.
(d) CTSRC-70-3-1.5.
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(a) CSRC-70-5-1.5.
(b) CTSRC-70-5-1.5.
(c) CTSRC-70-4-1.5.
(d) CTSRC-70-3-1.5. Fig. 6. Lateral load (P) versus lateral deflection (∆) of the circular columns.
Table 2 Test results of the columns.
Fig. 7. Comparisons on the envelopes of circular columns.
by Chinese regulations [11] or EC8 [12] is to give the structure a certain freedom of displacement. This capacity of deformation must occur in the plastic range, therefore the columns and walls should have enough plastic deformation ability. The maximum interstory drift ratio Ru of the tested columns is used to evaluate the plastic deformation capacity based on the measured displacement at failure: Ru =
∆0.85
(1) L in which ∆0.85 is the ultimate displacement when the post-peak remaining capacity of the column has dropped to 85% of the peak load. And L is the height of the column. The parameter Ru takes into account both inelastic and elastic behavior. It is generally assumed that a drift ratio of about Ru ≥ 4% represents a very good level of ductility [13]. Fig. 8 provides the lateral load (P)–drift
Group
Specimen
∆y (mm) ∆0.85 (mm) R0.85 (%)
µ∆
Circular columns
CSRC-70-5-1.5 CTSRC-70-5-1.5 CTSRC-70-4-1.5 CTSRC-70-3-1.5
2.71 5.17 4.52 5.12
8.65 (36.10) 37.50 (42.20)
1.27 (5.29) 5.51 (6.18)
3.19 6.96 8.29 8.21
Square columns
SSRC-70-5-1.5 STSRC-70-5-1.5 STSRC-70-4-1.5 STSRC-70-3-1.5
3.02 3.59 4.18 3.48
6.33 21.00 (32.50) 28.50
1.06 3.50 (5.42) 4.75
2.10 5.85 (7.77) 8.19
The results in the parentheses denote that the lateral strength of the column did not drop to 85% of the peak load until the test was finished.
ratio (R) of the circular columns. The average maximum interstory drift ratio of CSRC-70-5-1.5 was only Ru = 1.27% as listed in Table 2. The plastic deformation capacity of the three CTSRC short columns was much higher than that of CSRC-70-5-1.5. The average maximum interstory drift ratios of CTSRC-70-5-1.5, CTSRC-70-41.5 and CTSRC-70-3-1.5 were Ru = 5.29%, Ru = 5.51% and Ru = 6.18% respectively, representing an excellent ductility of the three CTSRC short columns. The test results indicate that the confinement of a thin circular tube can instinctively improve the ductility of a SRC short column. The lateral load strength of CTSRC70-5-1.5 and CTSRC-70-3-1.5 did not drop to 85% of the peak load until the test was finished, while the lateral load strength of CTSRC70-4-1.5 had dropped to 85% of the peak load during the test; denoting that the axial load ratio has no obviously effect on the plastic deformation capacity of the CTSRC columns tested in this paper.
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the column can continue carrying the applied specified axial load owing to the effective confinement of the tube to the concrete. Removing the tube after test, longitudinal bond cracks as well as diagonal shear cracks were found in the concrete. The failure mode of STSRC-70-5-1.5 is a combination of bond failure and shear failure. Failure mode of STSRC-70-4-1.5 was similar with that of STSRC-70-5-1.5. It was found that the concrete outside the steel flange was separated from the steel section. The bond failure of the two columns indicates that shear connector studs should be used in the STSRC short columns to prevent the bond failure between concrete and flanges of the steel section. The failure pattern of STSRC-70-3-1.5 presented in Fig. 9(d) illustrates that there was no bond or shear cracks in the concrete; the failure mode of this column was flexural failure. Compared with the failure mode of STSRC-70-4-1.5 and STSRC-70-5-1.5, it is concluded that the bond and shear failure tends to occur when columns are under a relative high axial load level.
Fig. 8. Lateral load versus drift ratio envelopes of circular columns.
Another means of evaluation the capacity of deformation is by calculating the ductility index µ∆ :
µ∆ =
∆0.85 ∆y
(2)
in which ∆y is the yield displacement [14]. The ductility index of CSRC-70-5-1.5 was 3.19 as depicted in Table 2, while the ductility index of CTSRC-70-5-1.5 was 6.96, which was much higher than that of CSRC-70-5-1.5. The test results listed in Table 2 indicate that the ductility index decreases with the increment in axial load ratio for CTSRC short columns. 4. Test results of square columns 4.1. Failure mode of square columns Failure mode of the tested square columns is depicted in Fig. 9. Fig. 9(a) depicts the final failure pattern of SSRC-70-5-1.5. There was obvious bond failure between the concrete and the flanges of steel section, and diagonal cracks were also found in the concrete after the test. The main reinforcement buckled and the concrete was crushed after the peak load, resulting in a rapid lateral load strength dropping; and the column could not continue to bear the specified axial load. The failure mode of SSRC-70-5-1.5 is a combination of bond failure and shear failure. Fig. 9(b) depicts the final failure pattern of STSRC-70-5-1.5 whose axial load level was the same as that of SSRC-70-5-1.5. The tube bulged at the end of the columns on account of the concrete being crushed and bulging at the end of the test, however
(a) SSRC-70-5-1.5.
(b) STSRC-70-5-1.5.
891
4.2. Load (P) versus deflection (∆) response of square columns Fig. 10(a) depicts the lateral load (P) versus lateral deflection (∆) response of column SSRC-70-5-1.5. The lateral load strength dropped rapidly after the peak load point. And the column showed little ductility and energy dissipation capacity in respect that the main reinforcement buckled and the concrete was crushed after the peak load. Since the SSRC short column developed little plastic deformation after the peak load, it dissipated little energy at the post-peak stage. The P–∆ response of STSRC-70-5-1.5 plotted in Fig. 10(b) indicates that the column showed enough ductility and energy dissipating capacity. The lateral load strength decreased gradually after the peak lateral load. Since the column developed great plastic deformation, it dissipated much more energy than the SSRC column with the same steel ratio. The P–∆ response of STSRC-704-1.5 and STSRC-70-3-1.5 plotted in Fig. 10(c) and (d) was similar with that of STSRC-70-5-1.5. Fig. 11 depicts the comparisons on the envelopes of cyclic response of square columns. The lateral load strength of STSRC-705-1.5 was 22.8% higher than that of SSRC-70-5-1.5. The comparison on the envelopes of the three STSRC columns indicates that the lateral load strength increases with an increment in axial load ratio. 4.3. Plastic deformation capacity and ductility of square columns Fig. 12 provides the lateral load (P)–drift ratio (R) envelopes of the circular columns. The average maximum interstory drift
(c) STSRC-70-4-1.5. Fig. 9. Failure modes of the square columns.
(d) STSRC-70-3-1.5.
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(a) SSRC-70-5-1.5.
(b) STSRC-70-5-1.5.
(c) STSRC-70-4-1.5.
(d) STSRC-70-3-1.5. Fig. 10. Lateral load (P) versus lateral response (∆) of square columns.
Fig. 11. Comparisons on the envelopes of square columns.
ratio of SSRC-70-5-1.5 was only Ru = 1.06% as depicted in Table 2. The plastic deformation capacity of the three STSRC short columns was much higher than that of CSRC-70-5-1.5. The average maximum interstory drift ratios of STSRC-70-5-1.5, STSRC-70-41.5 and STSRC-70-3-1.5 were Ru = 3.50%, Ru = 5.42% and Ru = 4.75% respectively, indicating that the confinement of a thin square tube can instinctively improve the ductility of a SRC short column. The lateral load strength of CTSRC-70-4-1.5 did not drop to 85% of the peak load until the test was finished, while the lateral load strength of CTSRC-70-5-1.5 had dropped to 85% of the peak load during the test. The lateral load strength of CTSRC-70-3-1.5 had dropped to 85% of the peak load under the positive lateral load, while it did not drop to 85% of the peak load under the negative lateral load until the test was finished. The test results of the draft ratio indicates that the axial load ratio has no obviously effect on the plastic deformation capacity of the STSRC columns tested in this paper. The test results depicted in Table 2 indicate that the ductility index trends to decrease with an increment in axial load ratio for the tested STSRC columns.
Fig. 12. Lateral load versus drift ratio envelopes of square columns.
5. Comparison on the test results of circular and square columns A circular tube can improve the seismic behavior more effectively than a square tube in a tubed SRC column. The crosssection area and reinforcement of the CTSRC columns tested in this paper are equal to that of the STSRC columns. The test results depicted in Table 2 indicate that maximum interstory drift ratio of the CTSRC columns is higher than that of the STSRC columns. The comparison on the failure mode of CTSRC and STSRC columns indicate that a circular tube prevent the shear failure of the concrete more effectively than a square tube in a tubed SRC column.
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Von Mises yield criterion has been adopted to define the yield point of the steel:
σz =
(a) Sheared plate of circular tube.
σv2 + σh2 − σv σh + 3τ 2 = fy .
(4)
As depicted in Fig. 15, the stress states of the sheared plate of the three CTSRC columns were very similar: After the axial load had being applied to the specified value, there was only obvious longitudinal stress σv in the tube due to the bond and friction stress between the concrete and the tube. While σv deceased gradually as the cyclic lateral load was applied in respect that the bond and friction deteriorated before the peak load. After the peak load, σv increased obviously; the reason is that the friction force between the concrete and the tube increased due to the increment in the confinement stress of the tube to the core concrete. The transverse stress σh of the sheared plate in the tube increased gradually as the lateral load increased. The flexural moment at the mid-height of the columns is zero, hence σh in the sheared plate was generated in respect that the outer tube was confining the core concrete which was under shear deformation. After the peak load, the shear deformation of the core concrete decreased as the lateral load decreased since the failure mode of the three CTSRC columns was not shear failure. And then σh decreased with the shear deformation of the core concrete decreased. The shear stress τ of the sheared plate in the tube increased as the lateral load increased. After the peak load, τ decreased with the lateral load decreased in respect that the failure mode of the column was not shear failure and no severe plastic shear deformation occurred in the core concrete. The analysis result on the equivalent stress σz indicated that the sheared plate at the mid-height of the tube did not yield for the three CTSRC columns.
(b) Sheared plate of square tube.
Fig. 13. Sheared plate of the tube.
(a) Flexural deformation.
q
(b) Shear deformation.
Fig. 14. Deformation shape of column.
6. Elastic–plastic analysis on steel tube
6.2. Stress of square tubes of STSRC columns
In a tubed SRC column, the steel at the mid-height of tube is under a complex state of stress with a combination of axial compression, transverse tension and transverse shear. The elastic–plastic analysis method was adopted to analyze the stress state on the steel tube based on the measured strains [15]. Under lateral shear force, the plates parallel to the lateral shear force of the tube in the column is under shear stress (Fig. 13). The stress state of the sheared plate was analyzed in detail for the tested CTSRC and STSRC columns. The deformation of the tested short columns in this paper is depicted in Fig. 14. The deformation of the columns consisted of flexural deformation and shear deformation. In the elastic range, the flexural and shear deformation will increase in proportion as the shear force increases, while the case will alter after the peak lateral load. After the peak load, the resistance of the columns will decrease in respect of failing. For those columns with a flexural failure mode, after the peak lateral load the flexural deformation will increase rapidly as the lateral displacement increases, while the shear deformation will decrease with the reduced shear force. Regarding those columns experiencing shear failure, the shear deformation will increase dramatically and the flexural deformation will decrease after the peak lateral load.
The results of the analysis on the square tubes of STSRC-703-1.5 are provided in Fig. 16(a). The transverse stress σh of the sheared plate in the tube was rather low under lateral shear force for column STSRC-70-3-1.5, since the failure mode of the column was not shear failure and the flexural moment at the mid-height of the column was zero. The shear stress τ of the sheared plate in the tube increased as the lateral load increased for the column. At the post-peak stage, τ decreased with the lateral load decreased in respect that the failure mode the column was not shear failure and no severe plastic shear deformation emerged in the core concrete. Fig. 16(b) depicts the results of analysis on the square tube of STSRC-70-4-1.5. The transverse stress σh of the sheared plate in the tube increased as the lateral load increased before the peak load. The lateral load decreased at the post-peak stage, while σh kept increasing in respect that the failure mode of the column was shear failure. Plastic shear deformation increased rapidly as the lateral displacement increased after the peak load due to the shear failure mode of the core concrete. σh of the tube kept increasing with the increment in lateral displacement in respect that the tube confined the core concrete and prevent the concrete from severe shear failure. The shear stress τ of the sheared plate in the tube increased as the lateral load increased. At the post-peak stage, τ kept increasing in respect that the failure mode of the column was shear failure. Plastic shear deformation of the column increased rapidly with increment in lateral displacement, therefore the shear deformation as well as the shear stress τ of the sheared plate kept increasing. In this case, the degradation of the shear capacity in concrete core can be compensated by the steel tube as the σh and τ increased. Thereby the shear strength of the STSRC short columns with shear failure would not drop rapidly and the ductility was hence distinctively improved. The results of analysis on the equivalent stress σz indicated that the sheared plate at the midheight of the tube did not yield until after the peak load for this
6.1. Stress of circular tubes of CTSRC columns Fig. 15 depicts the analysis results of the CTSRC columns, in which P is the lateral load, σv and σh are the longitudinal and hoop stress of the steel at the mid-height of tube respectively; τ is the shear stress and σz is the equivalent stress determined from the following equation:
σz =
q σv2 + σh2 − σv σh + 3τ 2 .
(3)
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(a) CTSRC-70-3-1.5.
(b) CTSRC-70-4-1.5.
(c) CTSRC-70-5-1.5.
Fig. 15. Lateral load versus stress of the sheared web of the circular tubes.
(a) STSRC-70-3-1.5.
(b) STSRC-70-4-1.5.
(c) STSRC-70-5-1.5.
Fig. 16. Lateral load versus stress of the sheared web of the square tubes.
column. The results of analysis on the square tube of STSRC-70-51.5 depicted in Fig. 16(c) were similar with that of STSRC-70-4-1.5 in respect of their similar failure mode. 7. Nominal shear strength of tubed SRC columns The failure mode of STSRC-70-4-1.5 and STSRC-70-5-1.5 was shear failure, therefore the formula for the nominal shear strength of STSRC columns is proposed based on the test and analysis results of STSRC-70-4-1.5 and STSRC-70-5-1.5. The nominal shear capacity, Vn , of a STSRC column is equal to the sum of the contributions of three mechanisms; concrete Vc , web of the steel section Va,w , and outer tube Vt : Vn = Vc + Va,w + Vt .
Fig. 17. Shear force and shear stress in the sheared plate of a rectangular tube.
(5)
7.1. Shear strength provided by steel tube The shear strength provided by the sheared plate of the tube in a STSRC column can be calculated from the following equation: Vt = Vσ h + Vτ = σhp Aσ h + ατp Aτ
(6)
where Vσ h is the shear strength in virtue of transverse stress σh of the sheared plate, Vτ is the shear strength in virtue of shear stress τ of the sheared plate, σhp is the transverse stress of the sheared plate at the peak load point, τp is the shear stress of the sheared plate at the peak load point, Aσ h is the area of the sheared plates under tension (Figs. 17 and 18), Aτ is the area of the sheared plates under shear force (Figs. 17 and 18),
Fig. 18. Outer and inner force balance in the sheared plate.
X. Zhou, J. Liu / Journal of Constructional Steel Research 66 (2010) 885–896 Table 3 The stress in the sheared plate of the tube at the peak load point. Specimen STSRC-70-4-1.5 STSRC-70-5-1.5
σhp
τp
σhp + 8/9τp
(MPa)
(MPa)
(MPa)
54.7 59.8
67.8 72.8
115.0 124.5
Average value of (σhp + 8/9τp ) (MPa) 119.8
α is the asymmetric index of the shear stress in the sheared plate. Fig. 17 depicts the shear stress in the sheared plate of a rectangular tube where the moment of inertia I and area moment S of the tube around x axis can be calculated from Eqs. (7) and (8): I =
1
bh2 tf +
1
2 1
tw h3
(7)
6 1 (8) S = bhtf + tw h2 2 4 where b and tf are the width and thickness of the flange of the tube without shear stress respectively; h and tw are the height and thickness of the sheared web respectively. The maximal shear stress of the sheared web τmax can be calculated by the following expression: VS
τmax =
(9)
Itw
where V is the shear force. The shear force V can be evaluated from the combination of Eqs. (7)–(9): V =
=
Itw S
τmax =
3bh2 tf + h3 tw
3 bhtf + 12h2 tw
bhtf + 31 h2 tw btf + 12htw
bhtf + 13 h2 tw btf + 12htw
(2tw ) τmax .
tw τmax =
8 9
(10)
h (2tw ) τmax =
8 9
Aτ τmax .
(11)
It is concluded from Eq. (11) that the asymmetric index of the shear stress in the sheared plate is equal to 8/9. Fig. 18 plots the outer and inner force balance in the sheared plate. Aσ h equals to Aτ since the angle of the concrete crack under shear force is θ = 45°. Therefore Eq. (6) can be simplified as: Vt = Vσ h + Vτ = σhp Aσ h + ατp Aτ =
8
Vt = σhp Aσ +
9
8
σhp + τp Aτ . 9
(12)
τp Aτ = σh + τ Aτ = 119.8Aτ
= 0.56f215 Aτ = 0.56f215 Aw
Specimen
Pu (kN)
Vn (kN)
Vn /Pu (kN m)
STSRC-70-4-1.5 STSRC-70-5-1.5
360.2 377.5
350.0 370.6
0.97 0.98
Table 5 Comparison on the results from the test and proposed method for the columns with flexural failure. Specimen
Mu (kN m)
MEC 4 (kN m)
Mu /MEC 4 (kN m)
CTSRC-70-3-1.5 CTSRC-70-4-1.5 CTSRC-70-5-1.5 STSRC-70-3-1.5
132.2 145.5 156.3 124.5
105.8 113.5 122.6 98.1
1.25 1.28 1.27 1.27
Vc = 0.17 1 +
N
14Ag
p
fco D2 .
(14)
Quantity N /Ag shall be expressed in MPa. Plastic shear capacity is adopted to evaluate the shear strength provided by the web of the steel section. Va,w = fa,w Aa,w
(15)
where fa,w and Aa,w are the yield strength and area of the web of steel section. 7.3. Shear strength of tubed SRC columns
Vn = 0.17 1 +
N
14Ag
fco D2 + fa,w Aa,w + 0.56f215 Aw .
p
(16)
For circular members, the area used to compute Vn shall be taken as the product of the diameter and effective depth of the concrete section [10,16]. The equivalent width of a circular column is 1.76r, where r is the radius of the cross section. Comparison of test results and predictions based on the proposed method are listed in Table 4 where Pu is the tested maximum lateral load and Vn is the predicted shear strength of the columns. The predictions compared well with the test results of the two columns with shear failure. 8. Nominal moment strength of tubed SRC columns
Table 3 depicts the (σhp + 8/9τp ) of the sheared plates in the two STSRC columns with shear failure. The test results indicate that the axial load ratio has no obvious effect on (σhp + 8/9τp ), therefore it is proposed that the effect of axial load ratio on the shear strength provided by the sheared plate of the tube may not be considered. Then Eq. (12) can be simplified using the average value of (σhp + 8/9τp ): 8
Table 4 Comparison on the results from the test and proposed formula for the columns with shear failure.
The formula for the nominal shear strength of STSRC columns is a modified ACI formula [16] based on the test and analysis results of the two STSRC columns with shear failure:
(2tw ) τmax
In a thin-walled steel tube used in the STSRC columns, b ≈ h and tw = tf ; then Eq. (10) can be simplified as: V =2
895
9
8.1. Tested moment strength of the columns The height of the plastic hinge of the columns with flexural failure was about D/2, so the tested moment strength (Mu ) of the columns with flexural failure can be calculated by the following equation [7]: Mu = Pu (L/2 − D/2) + N ∆u /2
(17)
where L is the length of the column; Pu is the ultimate lateral load strength; ∆u is the displacement corresponding to Pu . The tested moment strength (Mu ) of the four columns with flexural failure was listed in Table 5.
(13)
where f215 = 215 MPa and Aw is the total cross-section area of the sheared two webs. 7.2. Shear strength provided by concrete and web of steel section The shear strength provided by concrete can be evaluated from a modified ACI method [16] based on the test results:
8.2. Nominal moment strength of CTSRC and STSRC columns In the calculation of the nominal moment capacity of a SRC column in accordance with EC4 [1], the following assumptions are adopted:
• There is full interaction between the steel and concrete sections until failure occurs;
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Fig. 19. Comparisons between test results and EC4 Code of CTSRC columns with flexural failure.
2. For CTSRC short columns, the lateral load strength increases with an increment in axial load ratio. The ductility index decreases with an increment in axial load ratio, while the axial load ratio affects little on the plastic deformation capacity of CTSRC short columns. 3. For STSRC short columns, under a relative high axial load level (n0 ≥ 0.4 in this paper), the failure mode is a combination of bond failure and shear failure. The plastic deformation capacity of STSRC short columns with shear failure reaches a high level in respect that the tube prevents the core concrete form severe shear failure. The shear strength of STSRC columns increases with an increment in axial load ratio, while the axial load ratio has no considerable effect on the plastic deformation capacity of the STSRC short columns. 4. The steel tube in a tubed SRC short column will not yield at the peak lateral load point, hence the confinement of the tube to the core concrete will keep increasing. Therefore the lateral load strength of tubed SRC short columns cannot drop sharply after the peak load. 5. A circular tube prevents the shear failure of the concrete more effectively than a square tube in a tubed SRC column. 6. Shear connector studs should be used in CTSRC and STSRC short columns to prevent the bond failure between concrete and flanges of the steel section. 7. A modified ACI design method is adopted to calculate the nominal shear strength of STSRC columns as well as CTSRC columns. Acknowledgements
Fig. 20. Comparisons between test results and EC4 Code of STSRC columns with flexural failure.
• Geometric imperfections and residual stresses are taken into account in the calculation, although this is usually done by using an equivalent initial out-of-straightness, or member imperfection; • Plane sections remain plane whilst the column deforms. It is proposed that the flexural strength of tube SRC columns is then calculated based on the compressive strength of the confined concrete fcc and on the assumptions proposed of the EC4. The compressive strength of tubed concrete fcc have been proposed by Zhang [7] and Liu [17]. The M–N interaction curves for uniaxial bending of the four tubed SRC columns with flexural failure were calculated according to the modified EC4 method in this paper, as shown in Figs. 19 and 20, where N and M are the axial load and moment, respectively. Comparisons on the tested ultimate moment strength and the predicted moment are listed in Table 5. The test results are higher than the predictions in virtue of strain hardening of the steel shape. 9. Conclusions The experimental and analysis results of eight short columns tested under combined quasi-static axial compressive and cyclic lateral loads were discussed in this paper. The test results indicated that the common SRC short columns suffered brittle shear failure with poor ductility, while the ductility of tubed SRC short columns was excellent due to the effective confinement of the outer thin steel tube to the core concrete. Based on the test and analysis results, it can be concluded as follows: 1. Tubed SRC short columns exhibit higher lateral load strength, displacement ductility, more stable hysteresis loops, and greater energy dissipation ability than common SRC short columns in respect of the effective confinement of the thin tube to the core concrete.
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