STUDY ON AXIAL COMPRESSION BEARING CAPACITY OF REINFORCED CONCRETE FILLED STEEL TUBE MEMBERS

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1 Advaned Steel Constrution Vol. 12, No. 2, pp (2016) 94 STUDY ON AXIAL COMPRESSION BEARING CAPACITY OF REINFORCED CONCRETE FILLED STEEL TUBE MEMBERS Xiao-Xiong Zha *, Xiao-Li Li, Ning Wang and Cheng-Yong Wan Shenzhen Graduate Shool, Harbin Institute o Tehnology, Shenzhen , China *(Corresponding author: Zhaxx@hit.edu.n) Reeived: 30 May 2014; Revised: 30 January 2015; Aepted: 25 June 2015 ABSTRACT: The bearing apaity equation o reinored onrete illed steel tube (RCFST) members under axial loads is derived by using the ombined uniied and limit equilibrium theories. The onrete strength inrease due to the onstraint eet o the steel tube is taken into aount through the use o uniied theory; whereas the onrete strength inrease due to the onstraint eet o the stirrups is onsidered through the use o the limit equilibrium theory. Three-dimensional nonlinear inite element analysis and experimental tests were arried out and the orresponding results are reported in this paper. The omparisons o the numerial, experimental and theoretial results show that there are in good agreement between these three dierent methods. However, the present theoretial analysis model is not only simple and onvenient to use but also onsistent with existing Chinese design odes or CFST olumns. Keywords: Reinored onrete illed steel tube, Axial ompression bearing apaity, Uniied theory, Limit equilibrium theory, Finite element DOI: /IJASC INTRODUCTION Beause o many advantages, onrete illed steel tubes (CFST) are very popular in high rise buildings, bridges and oshore strutures. Extensive studies have been onduted on the stati and dynami analyses, and the ire perormane o CFST members [1-10]. For example, Han et al. [1], Yu et al. [2], Dundu et al. [3], Dai et al. [4] studied the ompressive strength o CFST members. Han et al. [1], Yu et al. [5], Prabhu et al. [6] investigated the axial ompression perormane o CFST members enased by various dierent materials, suh as onrete, FRP and CFRP. Wang et al. [7] studied the behavior o ire-exposed CFST olumns. More reently, Ma et al. [8] studied their seismi behavior o CFST olumns. Based on these studies, Chinese Codes [11] or design o onrete illed steel tubular members has been developed in A RCFST member is ormed by illing a steel tube with reinorement onrete. Beause o the large size o the setion the RCFST members may have smaller thiness o steel tube than CFST members, whih an ause trouble in mahining, onstrution and welding. Reinored onrete illed steel tubes (RCFST) have been used in multi-story buildings, partiularly, high-level buildings. Figure 1 shows a typial setion o a steel tube olumn and the orresponding olumn layout o Shenzhen Jingji inanial enter, whih is ranked as the tenth highest building in the world. Some studies have been onduted on the stati perormane o RCFST olumns [12-20]. Lie [14] gave the resistane o irular steel olumns illed with bar-reinored onrete. Chang et al. [15] and Zhu et al. [16] onduted experimental studies on the perormane o steel-reinored onrete-illed-steel tubular members. Wang et al. [18] studied on experimental perormane twin-olumn RCFT pier. Endo et al. [19] and Xiamuxi et al. [20] obtained the evaluation or axial

2 95 Study on Axial Compression Bearing Capaity o Reinored Conrete Filled Steel Tube Members ompressive strength o RCFST olumns and the results were validated using experimental data. But most studies on the mehanial properties at room temperature didn t onsider the onstraints o the stirrup on ore onrete. And they just simply onsidered the superposition o steel tube, onrete and longitudinal reinorement on the basis o a oeiient, not onsidering the synergy o steel tube and onrete. Notations K r Lateral onstant determined by tests, K 4 usually Axial ompressive strength o onrete onined by onrete stirrup Lateral pressure on onrete surrounded by stirrups A Area o single-layer stirrup Steel ratio ss1 yv d s A Area o onrete onined by stirrups, or 2 A = d 4 or s, Design strength o steel and onrete, respetively * Equivalent onining ator o multilayer stirrups Tensile strength o stirrup Hollow ratio, A /( A A ) h h Ddiameter o onrete olumn surrounded y, Charateristi strength o steel and by stirrups onrete, respetively s Spaing o stirrups B,C Parameters aording to setion types A sso Equivalent reinorement area o stirrup, da s ss1 A A, Ah sso s Area o onrete and hollow part in HCFST, respetively A, A s Area o onrete and steel tube v Stirrup ratio h, 1 Standard value o onining ator, h 0 y /(1.1 ) Conining ator o steel tube in CFST and RCFST respetively, and AS y AS y, 1 * A A Combined strength o CFST and RCFST, respetively A b Total area o reinorement in RCFST b s,, s A s Total area o RCFST, As=As+A Yield strength o reinorement in RCFST In this paper the behavior o RCFST members under axial ompression bearing apaity is studied through the theoretial analysis, inite element simulation and experimental tests. A theoretial analysis model is developed by using the ombined uniied and limit equilibrium theories. The present theoretial analysis model is not only simple and onvenient to use but also onsistent with existing Chinese design odes [11] or CFST olumns.

3 Xiao-Xiong Zha, Xiao-Li Li, Ning Wang and Cheng-Yong Wan 96 Figure 1. Typial Setion o Steel Tube Column and Building Elevation o King Key Finanial Center 2. THEORETICAL DERIVATION OF RCFST MEMBERS In general, the onrete in RCFST is restrained by both the outside steel tube and inside stirrups as shown in Figure 2. The onstraints will enhane the onrete ompressive strength, whih will be disussed separately in the ollowing analyses. Outside steel tube Reinorement Reinorement Stirrup Stirrup a) Single-layer reinorement setion b) Multilayer reinorement setion Figure 2. Cross Setion Diagram o RCFST 2.1 The Equivalent Strength o Core Conrete rom Stirrups Aording to the oniguration o the reinorement, the ore onrete o a RCFST member an be treated as a single layer material or a multilayer material, as shown in Figure 3. Both ases will be disussed in this paper. The equivalent strengths o the ore onrete in both ases are to be developed.

4 97 Study on Axial Compression Bearing Capaity o Reinored Conrete Filled Steel Tube Members The seond layer stirrup The irst layer stirrup The irst layer stirrup a) Single-layer reinorement setion b) Multilayer reinorement setion Figure 3. Core Conrete Conined by Stirrups diagram o RCFST The ompressive strength o onrete onined by stirrups (1) Axial ompressive strength o onrete onined by single-layer stirrups Aording to limit equilibrium theory rom the theory o reinorement onrete, i the spaing o spiral stirrups or welded stirrups is not larger than 80 mm and d s /5 (where d s is the diameter o the onrete olumn surrounded by stirrups), the strength improvement o ore onrete due to the eet o stirrups should be onsidered (Slater et al. [21]), as shown in Figure 4. ' p p p p Stirrup ' Figure 4. Conrete under Three-way Pressure In this ase, the longitudinal ompressive strength o onrete onined by stirrups an be determined as ollows: Kr (1) r 2A ss 1 yv (2) ds s Aording to Eqs. 1, 2 and in general the lateral onstraint oeiient is taken as K=4, it yields 2A (3) ss0 yv (1 ) Aor

5 Xiao-Xiong Zha, Xiao-Li Li, Ning Wang and Cheng-Yong Wan 98 Assuming v is the stirrup reinorement ratio, the onining ator o steel tube an be deined as ollows yv v (4) So the axial ompressive strength o the onined single-layer onrete stirrup an be expressed as: 1 2 (5) (2) Axial ompressive strength o onrete onined by multilayer stirrups Conrete in a RCFST olumn o multilayer stirrups an be divided into i+1 parts, as the shadow part shown in Figure 3 (b). As ar as the whole member is onerned, the eets o individual layer stirrups on the onrete an be alulated using a superposition method. Hene, the errule eet inreases gradually rom outside to inside. Assuming that A i is the area divided by the i th and (i+1)-th layer stirrups, i is the errule oeiient o the i th layer stirrups, A ssoi is the equivalent reinorement area o the i th layer stirrups, v is the stirrup ratio, and i is the onrete strength restrained by the i th layer stirrup, Eq. 4 an be expressed as ollows A yv ssoi yv i v (6) Ai when i 1, when i 1, (1 2 ) (7) i i k k 1 1 i (12 ) (8) Aording to the above ormulas, the ompressive strength o onrete onined by the multilayer stirrups is equal to the ordinary onrete strength multiplied a stirrup enhanement oeiient Equivalent strength o ore onrete within the outside steel tube The total bearing apaity o onrete within the steel tube inluding plain onrete with no stirrups and the onrete onined by stirrups an be given by Eq. 9, inluding the shadow and blank parts shown in Figure 3. n 1 2 (9) N A A A A i i i i i i1 i1 Substituting Eq. (6) into (9), it yields n n A ssoi yv * N A 2 Ai A 2yv Assoi A 12 A Sine n (10) i1 i i1

6 99 Study on Axial Compression Bearing Capaity o Reinored Conrete Filled Steel Tube Members n yv Assoi * i1 (11) A Eq. 10 is simpliied as ollows N 1 2 (12) * * A 2.2 Axial Compression Bearing Capaity o RCFST by steel tube Combined strength by steel tube Aording to the CFST uniied theory [13], the ompressive strength o the CFST olumn an be expressed as ollows: s 2 B C (13) The strength o onrete in Eq. 12 replaing 13, we have the ormula o the ombined strength o RCFST olumns: * 2 * B C B C (14) s As y where, 1 *, y B B , C and A * C Axial ompression bearing apaity Outside steel tube Reinorement Outside steel tube Reinorement Figure 5. Cross Setion Diagram o RCFST without Stirrup Aording to superposition priniple, the axial ompression bearing apaity o RCFST members is obtained by the sum o the axial ompression bearing apaity o longitudinal bar and CFST members onined by stirrups, as shown in Figure * N A A A B C A (15) sb s s b b s b b

7 Xiao-Xiong Zha, Xiao-Li Li, Ning Wang and Cheng-Yong Wan 100 The above desription demonstrates that the axial ompression bearing apaity o RCFST members is related to the errule oeiient o stirrups and steel tube, reinorement ratio and strength o longitudinal reinorement. I the errule oeiient or the reinorement ratio beomes higher, the overall load-bearing apaity beomes stronger Compared with the ormula o national ode when it is CFST When the reinorement ratio is zero, the RCFST redues to the CFST. Beause Ab 0 * 0, Eq. 15 is simpliied into Eq. 16. Nsb As s A b b A B C s As B C A s s and (16) By omparing Eqs. 13 and 16, it an be seen that the ormula o RCFST is in a good agreement with the ormula reommended in Chinese design ode or CFST members. Furthermore Eq. 15 an be regarded as an extension o the Chinese national design ode or RCFST members. 3. FINITE ELEMENT SIMULATION OF RCFST MEMBERS 3.1 The material onstitutive relation Core onrete o RCFST is simulated by using the plasti-damage onstitutive model (Ludovi et al. [22]). The uniaxial ompressive stress-strain model o onrete is utilized as suggested by Hognestad (Jerey et al. [23]), whih is simpliied as the elasti-peretly plasti model, as shown in Figure 6. Tensile in elasti part is similar with ompressive parts, and the ultimate tensile strength is taken as one-tenth o the ompressive strength. The steel model uses the bilinear model. Poisson's ratio is taken as 0.25 or onrete and 0.3 or steel. 3.2 The Finite Element Model Figure 6. The Constitutive Relation o Conrete and Steel The three-dimensional solid element (C3D8R) is used to simulate the ore onrete and steel tube o CFST members (Lu and Zhao [24]). The truss element (T3D2) is adopted to simulate the

8 101 Study on Axial Compression Bearing Capaity o Reinored Conrete Filled Steel Tube Members unidiretional reinored bars. For the onveniene o applying boundary onditions, two rigid irular plates are used in the inite element analysis (FEA) model to simulate the upper and lower over plates o the CFST member. All boundary onditions and loads are diretly loaded on the rigid plates. Reinored skeleton rame and onrete are ontated by using the Embedded region deined in ABAQUS. Element meshes o ore onrete and reinorement are shown in Figure7. Figure 7. Model Meshes o Core Conrete and Reinorement Figure 8. Deormation Model Fixed displaement onstraints are imposed to the bottom rigid plate. On the top rigid plate all other degrees o reedom exept or the axial displaement are ixed. The axial loading is added on the enter o the top plate. The problem is solved by using the displaement loading method. 3.3 Finite Element Results Beore the parametri analysis o the inite element analysis, inite element model is veriied in this setion. From the omparison between inite element simulation and its theoretial value under dierent parameters, it is ound inite element value is slightly higher than the theoretial value, but the error is very small. Figure 8 plots a typial deormed shape o the RCFST olumn. Load (kn) y s=20mm s=40mm 6000 s=80mm s=120mm 4000 s=160mm 2000 s=200mm s=300mm 0 x Displaemnet (mm) Figure 9. The Inluene o Stirrup Spaing or Load-displaement Curve

9 Xiao-Xiong Zha, Xiao-Li Li, Ning Wang and Cheng-Yong Wan 102 Figure 9 shows the inluene o the number o stirrups on the ultimate bearing apaity o the RCFST olumn (Wang [25]). It an be seen rom the igure that the ultimate load inreases with the derease o the spaing o the stirrups. Table 1 gives a omparison o the inite element results with the theoretial values. Through the parameter analysis, it is ound that the inluene o the steel tube errule oeiient and slenderness ratio on the load-displaement urve o RCFST members are similar to CFST members. Aording to the results o inite element simulation, reinorement ratio, the strength o longitudinal reinorement and the stirrup spaing are the key parameters, whih should be onsidered in the experimental tests. Table 1. Partial Value o Finite Element Simulation Compared with the Theoretial Value Longitudinal Steel Steel pipe Conrete Reinorement reinoreme Stirrup Theoretial Simulation ratio intensity strength ratio nt intensity spaing value value y (MPa) (MPa) b s (mm) N (MPa) (kn) N 0 (kn) b N0 N Mean value AXIAL COMPRESSION TEST RESEARCH 4.1 General Situation o Test Material Tensile tests o reinorement and steel tube were arried out by using hydrauli universal material testing mahine. The sample size was determined aording to the tensile test o metalli materials. The length o reinorement speimens is 500 mm. Figure 10 shows some o the speimens tested or the steel tube and reinorement. The speimens tested or onrete is shown in Figure 11 (Wang [25]), whih is the standard ubi speimen o 150*150*150 mm. a) Steel tube speimens b) Reinorement material speimens Figure 10. Steel Speimens

10 103 Study on Axial Compression Bearing Capaity o Reinored Conrete Filled Steel Tube Members Figure 11. Conrete Standard Cube Speimens The yield and ultimate strengths or the steel were obtained in the steel tensile tests, whih show that both the steel tube and reinorement have very good dutility. The onrete ubi ompressive 150 strength is used to alulate the ompressive strength o the prism by using : k2 u, k (where k 2 is the onversion ator,or ordinary strength onrete, k ) Speimens The axial ompressive tests inluded CFST speimens and RCFST speimens, and all steel tubes were o the same size. RCFST speimens were divided into three groups aording to the strength o internal longitudinal reinorement, and there were three kinds o longitudinal reinorement ratios and two stirrup spaings in eah group speimens. The setion size o the over plates was 500mm 500mm, with an idential thiness o 16 mm. All parameters o speimens are listed in Table 2. The experiment was arried out in arhiteture lab o South China University o Tehnology. The speimens were made by the proedure: (1) abriation o steel reinorement age, (2) welding reinorement to the bottom plate, (3) welding steel tube to the bottom plate, (4) pouring onrete into the steel tube. During the asting o onrete, a 50 mm plug-in vibrator was used to vibrate the onrete. Ater the onrete is asted, the speimen was ured or 12 hours in an environment with ixed temperature and humidity onditions. Ater the onrete was ured, the top steel plate was welded to the speimen (Jamaluddin et al. [26]). Table 2. Parameters o the Speimens under Axial Compression Sample number D (mm) t (mm) L (mm) (MPa) y u (MPa) b (MPa) (MPa) yv b s (mm) A A % 100 A % 100 A % 50 A % 100 A % 100 A % 100 A % 50 A % 100 A % 100 A % 100 A % 50 A % 100

11 Xiao-Xiong Zha, Xiao-Li Li, Ning Wang and Cheng-Yong Wan 104 Note: In the table, D is the ross-setion diameter o the speimen, t is thiness the steel tube L is the length o members, is the yield strength o steel, y u is the ube rushing strength o onrete, is yield strength o the longitudinal reinorement, b is the yield strength o stirrup, yv is the ratio o longitudinal reinorement, s is the stirrup spaing. b Test proedure (1) The test instrument and equipment Axial ompression tests were perormed in the 1500T hydrauli pressure testing mahine, as shown in Figure 12. Colleting devie o strains and displaements was DH3816 stati strain gauge. (2) Figure T Hydrauli Pressure Testing Mahine (2) Loading and data aquisition In the axial ompression test, the parameters needed to determine were the longitudinal stress-strain relationship o reinorement, the stress-strain relationship o the steel tube in both the longitudinal and hoop diretions. In order to obtain the required parameters, our groups o strain gauges were plaed on the middle o the external surae o the steel tube, whih were purposed to measure the longitudinal and hoop strains (see Figure 13). Figure 13. Strain Gauge Arrangement o Steel Tube and Reinorement In addition, our internal longitudinal strain gauges were used to measure the axial tension and ompression strain o longitudinal reinorement (Nie et al. [27]). To determine the axial and lateral displaements o the speimens, two axial displaement meters and two lateral displaement meters were plaed in the middle o the olumn (Hou et al. [28]). 4.2 Experimental Results In the axial ompression test proess, short olumns generally do not all, so when the axial displaement omponent reahes a ertain extent or when the axial deormation is large, the test is stopped or unloaded.

12 105 Study on Axial Compression Bearing Capaity o Reinored Conrete Filled Steel Tube Members Figure 14. Slip Line and Failure State The experimental phenomenon (Figure 14) shows that the damage orm o RCFST speimens is neither bending ailure nor shear ailure, but the loal buling. The examination o the internal onrete shows that there is no evidene o debonding rom the steel tube although onrete rushing in some plaes. A detailed omparison o the theoretial, inite element analysis and experimental results o the short olumn is given in Table 3. It an be seen rom Figure 15 that the dutility o the RCFST members is better than that o CFST members. For suh good dutile strutural members it is general to take the ompressive load at the strain value o as the bearing load o the member (Degtyarev [29]). Load (kn) y A-1 A A A A x Displaement (mm) a )The irst set o speimens y Load (kn) 8000 Load (kn) y A-1 A A A A x Displaemnt (mm) b) The seond set o speimens 6000 A A3-6-1 A A A x Displament (mm) ) The third set o speimens Figure 15. Loading-displaement Curve o RCFST Short Columns

13 Xiao-Xiong Zha, Xiao-Li Li, Ning Wang and Cheng-Yong Wan 106 Speimen number Table 3. Axial Compression Bearing Capaity o Short Columns Theoretial Finite element Trial N value N (kn) value N 0 (kn) N 0 N N e value N (kn) A A A A A A A A A A A A A Mean value e 5. CONCLUSIONS This paper has presented the theoretial, numerial and experimental investigations on the ultimate bearing load apaity o RCFST olumns. The theoretial study is perormed by using the ombined uniied and limit equilibrium theories. The numerial study is done by using the inite element method. The theoretial and FEA results are validated by the experimental data. From the results obtained the ollowing onlusions an be drawn: 1) Addition o longitudinal reinorement in RCFST short olumns an signiiantly inrease the bearing apaity o the olumns, in whih both longitudinal reinorement and stirrups play important role in this strength inrease. 2) Short olumns are neither in bending ailure nor in shear ailure, but in the loal buling ailure o the steel tube. 3) The proposed theoretial ormula or alulating the ompressive strength o RCFST olumns is onsistent with existing design ode or CFST olumns. That is, it redues to the design ormula o CFST when the reinorement ratio is 0. REFERENCES [1] Han, L.H. and An, Y.F., Perormane o Conrete-enased CFST Stub Columns under Axial Compression, Journal o Construtional Steel Researh, 2014, Vol. 93, pp [2] Yu, M. at al., A Uniied Formulation or Cirle and Polygon Conrete-illed Steel Tube Columns under Axial Compression, Engineering Strutures, 2013, Vol. 49, pp [3] Dundu, M., Compressive Strength o Cirular Conrete Filled Steel Tube Columns, Thin-Walled Strutures, 2012, Vol. 56, pp [4] Dai, X. and Lam, D., Numerial Modelling o the Axial Compressive Behaviour o Short onrete-illed Elliptial Steel Columns, Journal o Construtional Steel Researh, 2010, Vol. 66, pp

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15 Xiao-Xiong Zha, Xiao-Li Li, Ning Wang and Cheng-Yong Wan 108 [25] Wang, N., Stati and Dynami Perormane Researh o Bar-reinore Conrete Filled Steel Tubular Component [D]. 2013, Shenzhen: Harbin Institute o Tehnology. (in Chinese) [26] Jamaluddin, N. et al., An experimental study on elliptial onrete illed olumns under axial ompression, Journal o Construtional Steel Researh, 2013, Vol. 87, pp [27] Nie, J.G, Wang, Y.H. and Fan, J.S., Experimental Researh on Conrete Filled Steel Tube Columns under Combined Compression-bending-torsion Cyli Load, Thin-Walled Strutures, 2013, Vol. 67, pp [28] Hou, C., Han, L.H. and Zhao, X.L., Conrete-illed Cirular Steel Tubes Subjeted to Loal Bearing Fore: Experiments, Journal o Construtional Steel Researh, 2013, Vol. 83, pp [29] Degtyarev, V.V., Strength o Composite Slabs with End Anhorages, Part I: Analytial Model, Journal o Construtional Steel Researh, 2013.