Load bearing capacity of concrete filled steel columns

Transcription

1 Journal of Civil Engineering and Management ISS: (Print) (Online) Journal homepage: Load bearing apaity of onrete filled steel olumns Artiomas Kuranovas, Douglas Goode, Audronis Kazimieras Kvedaras & Shantong Zhong o ite this artile: Artiomas Kuranovas, Douglas Goode, Audronis Kazimieras Kvedaras & Shantong Zhong (9) Load bearing apaity of onrete filled steel olumns, Journal of Civil Engineering and Management, 15:1, 1-33, DOI: / o link to this artile: Published online: 14 Ot 1. Submit your artile to this journal Artile views: 3753 iew related artiles Citing artiles: 3 iew iting artiles Full erms & Conditions of aess and use an be found at

2 JOURAL OF CIIL EGIEERIG AD MAAGEME 9 15(1): 1 33 LOAD-BEARIG CAPACIY OF COCREE-FILLED SEEL COLUMS Artiomas Kuranovas 1, Douglas Goode, Audronis Kazimieras Kvedaras 3, Shantong Zhong 4 1, 3 Dept of Steel and imber Strutures, ilnius Gediminas ehnial University, Saulėtekio al. 11, L-13 ilnius, Lithuania University of Manhester, Manhester, M13 9PL, UK 4 Harbin Institute of Siene and ehnology, Harbin, Heilongjaing, 151, China 1 artiomas.kuranovas@st.vgtu.lt; dgoode@ukonline.uk; 3 akve@st.vgtu.lt; 4 zhongst@vip.451.om Reeived 14 Apr 8; aepted 17 July 8 Abstrat. his paper represents the analysis of 133 speimens of CFS experimental data. est results are ompared with EC4 provided method for determining the load-bearing apaity of these omposite elements. Several types of CFSs were tested: both irular and retangular ross-setions with solid and hollow onrete ore with axial load applied without and with moment, with sustained load and preloading. For irular ross-setion olumns there is a good agreement between the test failure load and the EC4 alulation for both short and long olumns with and without moment. For retangular ross-setion olumns the agreement is good exept when the onrete ylinder strength was greater than 75 MPa, when many tests failed below the strength predited by EC4. Preloading the steel tube before filling with onrete seems to have no effet on the strength. his paper also presents the stress distribution, onfinement distribution and omplete average longitudinal stress-strain urves for onrete-filled steel tubular elements. Based on the definition of the Unified heory, the CFS is looked upon as an entity of a new omposite material. In this paper, the researh ahievement of the strength and stability for entrifugal-hollow and solid onrete filled steel tube are introdued. hese behaviours relate to the hollowness ratio and the onfining indexes of orresponding solid CFS. If the hollow ratio equals to,4,5 and over, the -ε relationship exists in steady desending stage. he ritial stress of CFS elements stability is determined as an eentri member with the initial eentriity by use of finite element method. Keywords: omposite strutures, onrete-filled steel tubes, Euroode 4, omparison, analysis load-bearing apaity, hollow onrete-filled steel tubes, behaviour, stress state, Poisson s ratio, elastiity modulus. 1. Introdution Conrete-filled steel tubular (CFS) strutures is a type of the omposite steel-onrete strutures used presently in ivil engineering and onsists of steel tube and onrete ore inside it. he steel tube ats as a permanent formwork and an be of various ross-setions: irular, retangular, square and multi-side. Aording to the form of onrete ore, CFS members an be divided into types: with solid and hollow onrete ore. Elements with solid ore are formed by plaing plain onrete into the steel tube with ompation of it by vibrating. he hollow CFS is produed by spinning method. he point of prodution by spinning is that during this proess in the uniformly distributed plasti wet onrete entrifugation pressure appears, as the result of distanes between aggregates and other solid partiles; and wet onrete diminishes and exess water weakly bonded with other partiles is pressed out of onrete substane. Inreasing the onrete density helps to retain the ahieved form. Steel strutural hollow setions are the most effiient of all the strutural setions in resisting ompression load. By filling these setions with onrete either a signifiant inrease in load bearing apaity is ahieved or the olumn size an be redued. CFS olumns have many advantages over reinfored onrete olumns.. Overview of existing design odes for CFSs Different design regulations were produed for various ross-setions of CFS strutures. Different approahes and design philosophies have been adopted in different design odes (Xinbo et al. 6). In China, there are irular CFS struture design regulation, square struture design regulation, retangular struture design regulation, and irular hollow CFS struture design regulation. In these regulations, the design methods are different. In China and Japan, the standard for designing the omposite olumns is based on a simple method of superposition that uses the allowable stresses of the materials or the working stress method. ACI-318 adopts the traditional reinfored onrete approah. AS also uses the onept of reinfored onrete design. he AISC-LRFD is based on the onept of strutural steel. he Euroode 4, being a dediated ode JOURAL OF CIIL EGIEERIG AD MAAGEME ISS print / ISS online DOI: /

3 A. Kuranovas et al. Load-bearing apaity of onrete-filled steel olumns for omposite onstrution, ombines the design approah of both strutural steelwork and reinfored onrete olumns. Different limitations on the ompressive strength of onrete, steel yield strength, diameter-to-thikness ratio, steel ratio and onfining oeffiient are presribed in different odes. hese limitations are ompared and summarised in able 1. (3), Kuranovas (6), Kuranovas and Kvedaras (7), Zhong (1996), Zhong (1999), Zhang and Zhong (1998), Zhang and Zhong (1999). able 1. Comparison of the limitations in the different odes CH-JCJ CH-DL/ Item CH CECS f 3~5 3~8 3~8 k f ay 35~345 35~4 35~39 D/ t a ~ ~ 9 35/ f ay ~1 a a.4~.16.4~. ξ.3~.3 AISC- LRFD(99) EC4 f 6~65 5~6 k f ay ~355 JA-AIJ(97) 358/ f D/ t a 8E / fay 9 35/ fay ay a) b) ) d) Fig. 1. Short CFS stub olumns L / D( B) 4 : a) irular CFS with no moment, b) square CFS with no moment, ) square CFS with moment, d) hollow CFS with no moment a a.4 ξ ξ = 1.5A f / A f, k a ay k f is the 15 mm ube ompressive strength of onrete; f ay the yield strength of steel tube, A a, A areas of steel tube and onrete respetively, a a steel ratio; E the elastiity modulus of steel tube. Many researhers arry out tests whih they then ompare with a ode or their own partiular theory. Few look at others test results. his is partly beause it is diffiult and tedious to gather the information together. his paper, and its assoiated website ( ollets together information for 133 omposite olumn tests and ompares the test results with EC4; some typial graphs are also inluded in this paper. It is hoped that other researhers will ompare their theories with these data. he data over stati tests. 3. Databases he data olleted in the database on the website ( is subdivided into olumns of irular and retangular (mainly square) ross-setion and into short (defined in the paper as L / D( B) 4, Fig. 1) and long ( L / D( B) > 4, Fig. ) olumns with and without moment. he soure of the data is taken from Baohung and Hiroshi (3), Chung et. al (1), DL/585 (1999), Euroode 4 (5), Goode (1989), Goode (7), Gopal and Manoharan (3), Guolin and Zhong (6), Han (), Han and ao (3), Han and Yang (3), Han and Yao (), Han and Yao (3), Han et al. (4), Mursi et al. a) b) ) d) Fig.. Long CFS slenderness olumns L / D( B) > 4 : a) irular CFS with no moment, b) irular with moment, ) square CFS with no moment, d) square CFS with moment he information required and reported for eah test is: outer diameter (D) if irular ross-setion, or breath (B) and depth (H) if retangular; the thikness ( t a ) of the steel tube; the steel properties ( f ay ) and, for slenderness olumns, modulus of elastiity ( E a ); the onrete properties (onrete yield strength ( f yl ), ( f k in EC4)) and, for long olumns, its seant modulus of elastiity ( E ) to.4f k )); the length ( L ) of the olumn; the maximum load ahieved by the olumn in test ( u = est failure load). For olumns with an end moment, the initial eentriity of load at the top ( e t ) and bottom ( e b ) is required. he maximum lateral defletion at mid-height is also given when this has been reported by the researhers.

4 Journal of Civil Engineering and Management, 9, 15(1): If E a was not given, it was assumed to be GPa. If onrete ube strength ( f u ) would be given, the ylinder strength was taken.8fu. If E equation was not provided it was alulated from the (Xinbo et al. 6) E =.95( fyl 8) 1/ 3 GPa, where f yl is in MPa. 4. Analysis of test result and omparing with EC4 EC4 requires the harateristi onrete ylinder strength, f k, to be at least MPa and not more than 5 MPa unless its use is appropriately justified. For thin walled setion EC4 also inludes a loal bukling riteria. However, all tests have been ompared with e4 regardless of these limitations. he EC4 design equations are given and disussed by Douglas et al. he member has suffiient resistane if for both axes: Ed 1, (1) where pl Rd pl, Rd, plasti resistane to ompression, ( 1 η ( ta / Da )( fay / fk) ) γ pl, Rd = Aaη f ya / γma A fk 1 /, () where A a and A are the ross-setional area of the strutural steel and onrete; f ya and f k are their harateristi strengths in aordane with EC3 and EC; γ Ma and γ are partial safety fators at the ultimate limit states; t a the wall thikness of the steel tube; η 1 and η oeffiients; the other symbols are defined above. he eentriity of loading e is defined as: M max Ed / Ed. (3) he values of η 1 and η are: η1 = η1( 1 1e / Da ), (4) η = η ( 1 η )( 1e / Da ). For e > D a / 1, η 1 = and η =1.. he values of η 1 and η, when e = may be taken as follows: η1 = ,5λ 17λ (but ), ( λ) η =.5 3 (but 1. ). (5) he non-dimensional slenderness for the plane of bending onsidered is given by: λ = pl, Rd / r. (6) he elasti ritial load for the olumn length, be alulated from: ( ) r, shall r = π EI e/ L, (7) where ( EI ) e is effetive elasti flexural stiffness of rosssetions, and L is bukling length of a olumn. ( EI ) e= EaIa. 8Ed I, (8) where I a and I are moments of inertia of area for onsidered bending plane of the strutural steel and the onrete; E elastiity modulus for the strutural steel. a Ed = E m / γ, (9) E m mean value of onrete elastiity modulus When omparing EC4 with tests, the materials safety fators ( γ Ma and γ a ) have been taken as unity and onrete modulus as 1.35 beause.8e d=.8e /1. 35=.6E, to give the effetive elasti flexural stiffness ( EI ) e of the ross-setion, required for long olumns, as ( EI ) e= EaIa. 6EI. For olumns with an end moment, the ultimate strength omparison with EC4 is at the same axial load/moment ratio as in the test. In Figs 3 4 dispersion of EC4 vs test and ratio test/ec4 vs onrete strength for SC elements are provided and Figs 5 6 provides dispersions of EC4 vs test and ratio test/ec4 vs onrete strength for SR elements, Figs 7 8 for SRM, Figs 9 1 for SCH elements. Fig. 3. ests vs EC4 for short irular CFS olumns without moment Fig. 4. Ratio test/ec4 vs onrete strength for short irular CFS olumns without moment Fig. 5. ests ompared with EC4 for short retangular CFS olumns without moment

5 4 A. Kuranovas et al. Load-bearing apaity of onrete-filled steel olumns Fig. 6. Ratio test/ec4 vs onrete strength for short retangular CFS olumns without moment Fig. 1. Ratio test/ec4 and test/cdg (Eqn. 1) vs wall thikness for short hollow irular CFS Fig. 7. ests vs EC4 for short retangular CFS olumns with moment Fig. 11. ests ompared with EC4 for long irular CFS olumns Fig. 8. Ratio test/ec4 vs onrete strength for short retangular CFS olumns with moment Fig. 1. Ratio test/ec4 vs slenderness for long CFS olumns without moment Fig. 9. ests ompared with EC4 for hollow short irular CFS olumns without moment Fig. 13. ests ompared with EC4 for long irular CFS with moment

6 Journal of Civil Engineering and Management, 9, 15(1): Fig. 14. Ratio est/ec4 vs onrete ylinder strength for long irular CFS olumns with moment Fig. 18. Ratio test/ec4 vs onrete ylinder strength for long retangular CFS olumns with moment Fig. 15. ests vs EC4 for long retangular CFS olumns without moment Fig. 19. ests ompared with EC4 for irular CFS olumns with moment and preload Fig. 16. Ratio test/ec4 vs onrete strength for long retangular CFS olumns without moment Fig.. Ratio test/ec4 against preload for long irular CFS olumns with moment and preload Fig. 17. ests ompared with EC4 long retangular CFS olumns with moment Fig. 1. Han's tests ompared with EC4 for retangular CFS olumns with moment and preload

7 6 A. Kuranovas et al. Load-bearing apaity of onrete-filled steel olumns Fig.. Ratio test/ec4 vs preload for retangular CFS olumns with moment and preload Fig. 3. ests vs EC4 for retangular CFS olumns with sustained load Fig. 4. Ratio test/ec4 vs sustained load for a long retangular CFS olumns Representations of dispersions EC4 vs test and ratio test/ec4 vs onrete strength for slenderness elements are provided in Figs Figs 11 1 represent values for LC and for LCM elements. Dispersions of EC4 vs test and ratio test/ec4 vs onrete strength for LR and LRM are presented in Figs and respetively. Figs 19 represent ratio test/ec4 vs preload for long irular and retangular olumns with moment and preload respetively. he dispersions of these ratios for long retangular olumns with sustained load are provided in Figs 3 4. For irular ross-setion olumns there is good agreement between the test failure load and the Euroode 4 alulation for both short and long olumns with and without moment. Short irular olumns without moment the overall average test/ec4 from 43 tests is 1.7 with a standard deviation of.141. Long irular olumns without moment the overall average test/ec4 from 357 tests is 1.18 with a standard deviation of,5. he 17 tests by Salani and Sims, whih were mortar filled, gave partiularly high results (average = 1.8; SD =.69); exluding these tests the average of the other 34 tests is 1.17 with SD of.176. Long irular olumns with moment the overall average test/ec4 from 54 tests is 1.15 with a standard deviation of.111. However, Gopal s 14 tests with fibre RC filling are higher than this (average 1.68) and Baohun s 14 tests all gave unsafe values (Av. test/ec4 =.87). Exluding both Gopal and Baohun s tests gives: average (6 tests) = 1.3 with a standard deviation =.113. Short hollow irular setion olumns the 6 tests have average test/ec4 of 1.16 with SD of.1. For retangular ross-setion olumns of agreement is good exept when the onrete ylinder strength was greater than 75 MPa (strength greater than 5 MPa is not allowed in EC4), when many tests failed below the strength predited by EC4. Short retangular setion olumns without moment the average test/ec4 from all the 185 tests is 1.9 with standard deviation.1. However, for higher strength onrete ( f yl > 75 MPa), and thus olumns of greater strength, the test results are lower than the EC4 approah predits; for the 3 tests, where f yl > 75 MPa, the average test/ec4 is.91 with standard deviation,8. Short retangular (square) olumns with moment the average test/ec4 of 9 tests is 1.1 with a standard deviation of.1. Long retangular olumns without moment the overall average test/ec4 from 18 tests is 1.4 with a standard deviation of.143. he 17 tests with a onrete strength greater than 75 MPa did not show any redution in the strength predited by EC4; average test/ec4 being 1.3, SD =.164. Long retangular with moment the average test/ec4 from 51 tests is 1.1 with SD of.181. Pre-load (up to 6% of the apaity of the steel) on the steel tube before filling with onrete seems to have no effet on the strength; the average test/ec4 for the 3 irular olumns (11 short, 1 long) being 1.15 (SD.13) and for the 19 retangular (1 short, 9 long) being 1.3 (SD.99). Sustained load 8 tests by Han et al (4) had an average sustained load of between 53% and 63% of their apaity for 1 or 18 days before being loaded to failure, the average test/ec4 is 1,5, whih was higher than their 6 omparison tests without sustained load (average 1.8).

8 Journal of Civil Engineering and Management, 9, 15(1): Strutural behaviour 5.1. Constitutive relationship of steel A typial stress σ i strain ε i relationship for steel used in ivil engineering under 3D stress state is shown in Fig. 5 (Zhang and Zhong 1999). he following assumptions are made: a) the strain hardening is simplified by a straight line d, b) the failure is onsidered to be a horizontal straight line de. where [ D ] s is the stiffness matrix for the steel, [ ] s elasti stiffness matrix ([ ] e ) the plasti range is [ D] ep = [ D] e [ D] p, where [ ] p D the D in the elasti range, and in D the plasti stiffness matrix. s s1 s3 1 In the plasti range εi = 1εi, ε i = 1εi s ; while in the strain hardening range, f au / f ay = Constitutive relationship of onrete ore here are many theories to desribe the behaviour of onrete under triaxial ompression. he onstitutive relationship for onrete ore of CFSs is expressed using plasti-frature theory in whih the strains onsists of elasti, plasti and frature strains. Under 3D ompression, total strain is: el pl fr dε ij = dεij dεij dεij, (1) where supersripts e, p, f mean for elasti, plasti and frature strains respetively; l and r mean for longitudinal and radial strains respetively. ypial onstitutive relationships of onrete ore 3D, D and uniaxial stress state are presented in Fig. 6 (Zhang and Zhong 1998). Fig. 5. ension and ompression steel σ ε relationships he relation urve of stress intensity with strain intensity for steel under omplex stress states is similarly to the stress strain relation urve under simply tension. here are 5 stages: elasti, elasto-plati, plasti, strengthening and damage (Zhong 1996). he equations of stress and strain are as follows: σ i = [( σ11 σ) ( σ σ33) (1) 1/ ( σ σ ) ( σ σ σ )] Fig. 6. Conrete σ ε relationships for uniaxial, D ε i = [( ε11 ε) ( ε ε33) and 3D stress state 3 () 3 1/ ( ε33 ε11) ( ε1 ε3 ε31) ]. he onstitutive relationship for onrete ore in a 3D stress state an be expressed using plasti-frature In the elasti range, the proportional limit of steel theory as follows: fap=. 8f ay ; the Poisson s ratio ν a=. 83 ; the elasti- { dσ } = [ D] { dε }, (13) 5 ity modulus Ea=.6 1 /mm. In the elasto-plasti range, the tangent modulus of steel t ( fay σi ) σi Ea = Ea ; the Poisson s ratio ( fay fap) f p t ( σi fap) ν a = f ap, f ay and f au are ( fay fap) proportional limit, yield stress and ultimate tensile strength respetively. he onstitutive relationship for the steel an be expressed as follows: { d } = [ D] { dε } σ, (11) ij s ij where [ D ] a 6 6 stiffness matrix. here are 6 unknown parameters in this equation and they an be obtained by regression of experimental load-strain urves for onentrially loaded CFSs Strutural behaviour of CFSs he strutural behaviour of CFS elements are onsiderably affeted by the differene between the Poisson s ratios of the steel tube and onrete ore. In the initial stage of loading, the Poisson s ratio for the onrete is lower than that of steel. hus, the steel tube has no onfining effet on the onrete ore. As longitudinal strain inreases, the lateral expansion of onrete gradually

9 8 A. Kuranovas et al. Load-bearing apaity of onrete-filled steel olumns beomes greater than expansion of steel tube (Fig. 7). At this stage, the onrete ore beomes triaxially and steel tube biaxially stressed (Kuranovas, Kvedaras 7) (Fig. 8). he steel tube under a biaxial state annot sustain the normal yield stress, ausing a transfer of load from tube to the ore. he load transfer mehanism is similar, square and irular CFS elements. In the first stage of loading the steel tube sustains most of the load until it yields (point a in Fig. 9). At this point (a) there is a load transfer from steel tube to the onrete ore. he steel tube exhibits a gradual derease in load sharing until the onrete reahes its maximum ompressive strength (a to b). After this stage of loading (point b), there is redistribution of load from onrete ore to the steel tube. At this point (b) the steel exhibits a hardening behaviour with almost the same slope as in uniaxial stress-strain hardening relationship ( E ). t Fig. 9. σa εa relationship Even though the load transfer mehanism in irular and square CFS is similar, the maximum onfined ompressive stress of onrete ore in irular olumns is higher than square olumn. his an be explained in terms of a larger onfining effet of irular steel tubes, whih is desribed in following setions. 6. Load-bearing apaity of H-CFSs by other methods EC, EC4 and other soures provide design proedures and reommendation only for enhaned, CFS with solid onrete ore elements. For hollow CFS elements no design reommendations are provided beause of lak information, analyzis and test results. One of few methods for determining load-bearing apaity is the Unified theory (Zhong 1996, 1999; Zhang and Zhong 1999) and, aording to it, the member is onsidered as a unified body. Fig. 7. Stress ondition in steel tube and onrete ore at different stages of loading: ν a > ν (a), ν a < ν (b) he typial σ ε relationship shown in Fig. 6 onsists of elasti (oa), elastoplasti (ab), and hardening (bd) stages. Having suh diagrams, it is easy to find the elastiity modulus E a and hardening modulus E a of CFS ' element Unified theory he ontent of Unified theory are: the onrete-filled steel tube is regarded as an unified body, whih is a omposite material, and its behaviour is hanged with the hange of physis parameters of materials, geometrial parameters of members, types of ross-setions and stresses states. he hanges are ontinually, relatively, while the design is unified. In a word, the behaviour of CFSs have unifiation, ontinuity and relativity. From Unified theory, a unified design formula of CFSs is produed. It an be used to design all of the members with different ross-setions. It makes a onveniene of design work. And it is benefiially to draw up a unified standard for various CFS members. Unified design formulas are provided as follows (Zhang and Zhong 1999): when ϕ A a. 1 fa, (14) Fig. 8. Distribution of stresses in H-CFS element

10 Journal of Civil Engineering and Management, 9, 15(1): when 5 1.4ϕ ϕ A 5 a 1.71M 1.4ϕ <. 1, 1 1, when axial fore is tension 7 M βm ( 1.4 / ) βm (1.4 / exp ex 7 (15) fa, (16) ) 7 (17) M 5 1, (18) t M where, M, and are applied axial fore, moment torsion and shear fore, respetively. Relations between / ; M / M and / ratios for CFSs are presented in Fig. 3 (Zhang and Zhong 1999). Fig. 3. olume surfae of -M- relations here are 4 terms equations. When =, these formulas are hanged to 3 terms equations; when = =, it will be hanged to terms. And when it is axial ompression or axial tension design formulas. o matter what forms of members, solid or hollow setions or various ross-setions, these formulas an be used to design; the denominators of these formulas are resisting fores of members, whih should be taken parameters for various members only. Hene, it is very onveniently for design. Resisting axial ompression = A a f s, (19) resisting axial tension = k A f, () t 1 a resisting bending moment M = γmwa fa, (1) resisting torsion moment v = γwa fa, () resisting shearing fore = γ Aa fa, (3) where geometrial parameters of ross-setion A a, A a, W a and W a are total area of member of ross-setion, area of steel tube, bending and torsion setion modulus, respetively. It is a differene for various ross-setions. he physial parameters f a, f a and f are omposite design strength of ompression, shearing of CFS and design ompressive strength of steel, respetively. Coeffiient k 1 for solid member is equal to 1.1, for hollow member 1.. For lattied members onsisted of, 3 and 6 CFSs, bearing apaity in plain should be alulated by following formula (Zhong 1996, 1999; Zhang and Zhong 1999): 7 ϕ 5 βm ϕ M (1 ) ex 1. (4) he omposite ompression design strength: for solid ross-setion y fa = ( 1.1 Bkξ Ckξ ) fk ( 1.1 Bk ξ Ck ξ ) f, fa = for irular hollow ross-setion k ' fa = fa kh B =.1759 f C =.138 fk /.39, for otagonal ross-setion: B =.141f y / , y / , ξ ψf C =.7 fk for square and retangular ross-setion: B =.131f /.6, / 35.73,,, (5) (6) (7) y (8) C =.7 fk /.6, where ξ, ξ is design onfining index of solid member, ξ = af /1. 1f k ; ξ = af / f ; a steel ratio of solid ' member, a = A a / A ; ξ design onfining index of hollow member, ξ = a f / f ; a steel ratio of hollow ' ' ' member; ψ hollowness ratio, ψ = AH /( Aa Aa ) ; A a total area of member; A a area of steel tube; A H area of hollow part; f ompression strength of steel; and f ompression strength of onrete. For hollow CFS member, the ompression strength of onrete should be taken 1.1f owing to the onrete maintained by steam pouring. he ompression strength an be enhaned by 1%.

11 3 A. Kuranovas et al. Load-bearing apaity of onrete-filled steel olumns he omposite shearing design strength: 3 1/ 8 fs = a ξ fa. (9) he bukling oeffiient of axial ompression is: ϕ = k, (3) ϕ where oeffiient ϕ is bukling oeffiient of irular solid CFS member, as shown in able. he values of k for solid and hollow setions are: for irular 1., for 16-side member.95, for otagon.9 and for square and retangular.85. ϕ is presented in able 3. he oeffiient of plasti development γ M, γ and γ are listed in able 4. Results show: the higher the steel ratio α a, loadbearing apaity and the bigger slope of plasti-hardening stages; the smaller hollowness ratio ψ, the higher loadbearing apaity and the more similar their behaviour to solid CFS members; in the only ase, when the hollowness is big and steel ratio is small, there is desending stage on the a εa urve; the failure of hollow CFS members starts from the inside surfae of the onrete tube beause the onrete is there in biaxial ompression; the above alulated urves are very lose to the test urves for both solid and hollow CFS elements. able. Coeffiients k and k H Cross-setions Cirular and Otagonal Square a 16-side k Coef. k H..4.5 able 3. Coeffiient ϕ λ S35 S355 S35 S able 4. Coeffiients γ M, γ and γ Coef. γ M γ For all types of solid ross-setions For all types of hollow ross-setions.483ξ ξ.483ξ ξ 1.471ξ ξ.471ξ ξ 1 γ.953ξ ξ.953ξ ξ. 9 In Fig. 31 it an be notied that for solid CFS there is no desending stage in a εa diagram, but for H- CFS suh stage exists, and the plasti stage is shortened while hollow ratio is inreased, finally, the brittle damage ours. he desending stage ours in H-CFSs, beause the strength indexes at the point of elasto-plasti stage and the elastiity modulis are lower than that of solid one. And they are dereasing with inreasing the hollowness ratio ψ. Fig. 31. ratios ψ a εa relationship related with hollowness On the elasti range of H-CFSs under axial ompression, both the onrete ore and the steel tube are under uniaxial stress state. here is no onfinement from the steel to the onrete ore. he elastiity modulus at this stage with different ross-setion geometries is expressed as follows: p p Ea = f a / εa, (31) p p where f a and ε a are the average proportional limit stress and strain of H-CFSs, respetively. p y fa= (.19f ay / ) f a, (3) p ε a =.67 f ay / Ea. (33) y Different ross-setion geometries have different f ay and E a. In the elasto-plasti range, the tangent modulus of an H-CFS element is haraterised by the following equation: where y ( A fa B σ) σ E y p p a ( f f ) f t Ea = 1 1, (34) a a a ' p ' E 1 = 1 a f p a E A, = a f B a E y 1 1. (35) a f y a Ea fa In the hardening phase, the tangent modulus is: 6.. Other methods ' a E = 4ξ 15. (36) Goode (7) proposes to alulate load-bearing apaity of H-CFS elements by Eq. 35: pl, R= Aa f y A k fk, (37) where k oeffiient of inreased onrete strength in entrifuged ore, whih an be alulated by Eq. 36: k = d 39.7t.434t s / t.1133 f k s.34 f d 55.6d, k (38)

12 Journal of Civil Engineering and Management, 9, 15(1): where d, t s, t are external diameter of onrete ore, thiknesses of steel tube and onrete ore respetively. A. K. Kvedaras (1999) proposes to alulate the strength of H-CFS as sum of fores ating omposite ross-setion (Eq. 39): pl, R= au u, (39) where au, u are load-bearing apaities of steel shell and onrete ore orrespondingly and an be determined by Eqs. 4, 41: = f A, (4) au u y k a = 1. 3 f A. (41) C. D. Goode (1989) suggests evaluating ultimate load value of omposite member by modified EC4 formula Eq. (4), whih aording author predit well loadbearing apaity of CFS member: pl, Rd =.68 fk A 6 f y At /( D t). (4) Kuranovas (6) proposes to determine ultimate load of H-CFS element with evaluation of stress redistribution in onrete ore. For non-slender L / D 4 elements ultimate load an be alulated by pl, R= kf A fa, y Aa, (43) where k oeffiient taking into aount the inrease of strength. As result of testing results, proessing for k oeffiient determination mathematial model of progression was derived. k = 1 ma / A na f / A, (44) a where m = 5 for one-layered, m = 7 for doublelayered elements, n =.1 for one-layered, n =.9 for double-layered elements. Evaluation of all suggested Eqs. (37 44) is presented by Kuranovas (6) and the results show that Eqs. (43 44) predit results with ultimate load for H-CFS elements with average value 1. of predit and test ratio and with variation oeffiient of,3 value. And most of predited results are less than experimental ones. Results obtained from Eqs. (39 41) give orresponding values of 1. and.8 orrespondingly and very well predit strength of omposite members. Eqs. 43, 44 evaluate the phenomenon of strength inrease from multilayering of onrete ore and more preisely predit ultimate loads than other sientists suggested. Fig. 3 shows dispersion of experimental results vs predited values aording to Eq Conlusions Investigations show that the behaviour of hollow CFS elements is more ompliated than that of solid ones, beause of omplex stress states none of stresses in hollow onrete ore are evenly distributed through the thikness of its ross-setion. At present it is a lak of information for H-CFSs designing. Different approahes and design philosophies have been adopted in different design odes. Euroode 4 is a very good, and safe, preditor of strength for all types of irular ross-setion CFS olumns a Fig. 3. Dispersion of experimental results vs predited values and ould be safely used for onrete with ylinder strength up to 1 MPa. For retangular setion CFS olumns Euroode 4 should be used with aution, when the onrete ylinder strength is greater than 75 MPa as the failure load in the majority of tests, when f > 75 MPa, was less than that yl predited by the EC4 approah. (ote: EC4 limits the onrete strength to 5 MPa.) he fator,85 whih is usually applied to the ylinder strength to relate it to the uniaxial strength in the stress blok is omitted, in EC4, for filled tubes, probably beause of the onfining effet of the tube. Omitting this fator for all sizes of tube and onrete strength seems very arbitrary and, for a greater safety, it is suggested that for retangular setion tubes this,85 fator should be inluded, when onrete with a ylinder strength greater than 75 MPa is used. Pre-load of the steel tube, up to 6% of the apaity of the steel, before filling with onrete, seems to have had little effet on the strength of the olumn. Sustained load of up to 63% of the olumn s apaity for up to 18 days did not redue the strength of the 8 olumns, when subsequently tested to failure. he simplified k fator method and seond order analysis of Euroode 4 gave similar results. For the 54 irular olumns the average test/ec4 ratio by the k fator method gave And also 1.15 by the seond order analysis; for the 51 retangular olumns the ratio was 1.11, by the k fator method and 1.16 using the seond order analysis. he establishment of Unified theory provides a new researh method and design method of CFSs. he Unified theory analyses the onrete-filled steel tube as a unified body, whih is omposite material and onsists of steel tube and onrete ore. Behaviour of this element hanged with physial parameters of materials, geometrial parameters and the type of ross-setion. he hanges are ontinuous relatively, while the design is unified. Further investigations, tests, FEM and strutural analyses are neessary.

13 3 A. Kuranovas et al. Load-bearing apaity of onrete-filled steel olumns Referenes Baohung, C.; Hiroshi, H. 3. Eentriity ratio effet on the behavior of eentrially loaded CFS olumns, in Pro. ASSCCA'3 International Conferene Advanes in Strutures (ASCCS-7), Sydney, Australia, 3, Chung, J.; Matsui, C.; suda, K. 1. Simplified design formula of slender onrete-filled steel tubular beamolumns, Strutural Engineering and Mehanis 1(1): DL/ : Design ode for onrete filled steel tubes. China, Euroode 4: Design of omposite steel and onrete struture. Part 1. 1: General Rules and Rules for Buildings. British Standards Institution, London, 5. Goode, C. D. 7. ASCCS database of onrete-filled steel tube olumns [ited 16 April 7]. Available from Internet: < ass>. Goode, C. D Four tests. Unpublished. Manhester University, Gopal, S. R.; Manoharan, P. D. 3. Strutural behavior of slender olumns infilled with fibre reinfored onrete, in Pro. ASSCCA'3 International Conferene Advanes in Strutures (ASCCS-7), Sydney, Australia, 3, Han, L. H.. he influene of onrete ompation on the strength of onrete filled steel tubes, Advanes in Strutural Engineering 3(): Han, L.-H; Yao, G.-H.. ests on stub olumns of onretefilled RHS setions, Journal of Construtional Steelwork 58: Han, L.-H.; Yang, Y.-F. 3. Analysis of thin-walled steel RHS olumns filled with onrete under long-term sustained loads, hin-walled Strutures 41: Han, L.-H.; Yao, G.-H. 3. Influene of onrete ompation on the strength of onrete-filled steel RHS olumns, Journal of Construtional Steel Researh 59(6): Han, L.-H.; Yao, G. 3. Behaviour of onrete-filled hollow strutural steel (HSS) olumns with pre-load on the steel tubes, Journal of Construtional Steel Researh 59(8): Han, L.-H.; Zhong,.; Wei, L. 4. Effets of sustained load on onrete-filled hollow strutural steel olumns, Journal of Strutural Engineering ASCE 9: Kuranovas, A. 6. Influene of interation between hollow onrete filled steel tubes omponents to their strength, in Pro. of an 8th International Conferene on Steel- Conrete Composite and Hybrid Strutures, Harbin, China, 6. Harbin: Harbin University of Siene and ehnology, Kuranovas, A.; Kvedaras, A. K. 7. Behaviour of hollowonrete steel tubular omposite elements, Journal of Civil Engineering and Management 13(): Kuranovas, A.; Kvedaras, A. K. 7. Centrifugally manufatured hollow onrete-filled steel tubular olumns, Journal of Civil Engineering and Management 13(4): Kvedaras, A. K heory and pratie of onrete filled steel tubes: Habilitation thesis. ilnius: ehnika. 8 p. Mursi, M.; Uy, B.; Bradford, M. A. 3. Interation bukling of onrete filled olumns using high-strength steel, in Pro. ASSCCA'3 International Conferene Advanes in Strutures (ASCCS-7), Sydney, Australia, 3, Šapalas, A Compressive strength of onrete element of annular ross-setion with outer steel shell: Dotoral dissertation. ilnius: ehnika. 13 p. ao, Z.; Han, L. H. 3. ests and mehanis model for onrete-filled double skin steel tubular stub olumns, in Pro. ASSCCA'3 International Conferene Advanes in Strutures (ASCCS-7), Sydney, Australia, 3, Xinbo, M.; Zhang, S.; Goode, C. D. 6. Comparison of design methods for irular onrete filled steel tube olumns in different odes, in Pro of an 8th International Conferene on Steel-Conrete Composite and Hybrid Strutures, Harbin, China, 6. Harbin: Harbin University of Siene and ehnology, Zhong, S ew onept and development of researh on CFS members, in Pro. of nd International Symposium on Civil Infrastruture Systems (Main theme: Composite and Hybrid Strutures), De 9 1, 1996, Hong Kong. Zhong, S High-rise buildings of onrete filled steel tubular strutures. Heilongjiang Siene and ehnology Publishing House, P. R. China. Zhong, S.; Guolin, X. 6. he strength and stability of entrifugal-hollow onrete-filled steel tube (h-fst) olumns under axial ompression, in Pro. of an 8th International Conferene on Steel-Conrete Composite and Hybrid Strutures, Harbin, China, 6. Harbin: Harbin University of Siene and ehnology, Zhong, S.; Zhang, S A new method from China to determine load-arrying apaity for CFS members, in Pro. of an Engineering Foundation Conferene: Composite onstrution in steel and onrete II, 1998, Zhong, S.; Zhang, S.-M Appliation and development of onrete-filled steel tubes (CFS) in high-rise buildings, Advanes in Strutural Engineering (): BEOŠERDŽIŲ PLIEIIŲ AMZDIIŲ KOLOŲ LAIKOMOJI GALIA A. Kuranovas, C. D. Goode, A. K. Kvedaras, S.. Zhong S a n t r a u k a Straipsnyje analizuojami 133 betonšerdžių plieninių strypų bandinių eksperimentiniai duomenys. Duomenys lyginami su eurokode 4 pateiktais kompozitinių elementų laikomosios galios nustatymo metodais. Analizuojami šie betonšerdžių plieninių strypų bandinių tipai: pilnaviduriai ir tuščiaviduriai, apskrito ir stačiakampio skerspjūvio kolonos, kurių galuose veikia arba neveikia momentas, su iš anksto pridėta arba ilgalaike apkrova. Apskrito skerspjūvio kolonų laikomosios galios bandymų rezultatai atitinka skaičiavimų reikšmes, apskaičiuotas pagal eurokode 4 pateiktu metodu. Stačiakampio skerspjūvio elementų laikomosios galios reikšmių bandymo rezultatai puikiai atitinka teorines reikšmes, kai betono ritininis stipris nesiekia 75 MPa. Išankstinis elementų apkrovimas poveikio elementų laikomajai galiai beveik neturi. aip pat nagrinėjami betonšerdžių elementų įtempių būvių pasiskirstymas, betono apspaudimo poveikis ir išilginių deformaijų ir įtempių kreivės. Pateikiama S.. Zhong Unifikuota teorija, kuri nagrinėja kompozitinį elementą kaip visumą. Straipsnyje nagrinėjamos kompozitinio plieninio ir betoninio elemento stiprumo ir pastovumo sąlygos. okių elementų

14 Journal of Civil Engineering and Management, 9, 15(1): elgsena pagal teoriją priklauso nuo tuštumos santykio ir apspaudimo indekso, kurie grindžiami pilnavidurio elemento reikšmėmis. Jeigu tuštumos santykis lygus,4,5 ir daugiau, -ε sąryšis yra kritimo stadijoje. Elgsenos stadijos keičiasi pagal tuštumos koefiientą. Reikšminiai žodžiai: kompozitinės konstrukijos, betonšerdžiai, plieniniai vamzdžiai, eurokodas 4, lyginimas, laikomosios galios analizė, betonšerdžiai plieniniai elementai, elgsena, įtempių būviai, Puasono koefiientas, tamprumo modulis. Artiomas KURAOAS. PhD student at the Department of Steel and imber Strutures, ilnius Gediminas ehnial University, Lithuania. A graduate of Civil Engineering at ilnius Gediminas ehnial University (). MS of Civil Engineering (4) at ilnius Gediminas ehnial University. Member of the Counil on all Buildings and Urban Habitat (CBUH) and the International Assoiation for Steel-Conrete Composite Strutures (ASCCS). Researh interests: strutural mehanis, omposite elements and behaviour of their omponents, engineering software for strutural elements design. Douglas GOODE. PhD, University of Manhester, UK. Member of International Assoiation for Steel-Conrete Composite Strutures (ASCCS). Author of the biggest database whih ontains more than 18 test results of onrete-filled steel tube olumns. Researh interests: steel, onrete, omposite steel-onrete strutures. Audronis Kazimieras KEDARAS. Prof Dr Habil at the Department of Steel and imber Strutures and Diretor of the Innovatory Sientifi Institute of Speial Strutures Kompozitas of ilnius Gediminas ehnial University. Member of the International Assoiation for Bridge and Strutural Engineering (IABSE) and ASCCS, invited AO expert (1996, ). Researh interests: steel, omposite steel-onrete and timber strutures. Shantong ZHOG. Prof, Harbin University of Siene and ehnology, China, honour president of International Assoiation for Steel-Conrete Composite Strutures (ASCCS). Researh interests: steel, onrete, steel-onrete omposite omponents, strutural mehanis. Author and o-author of over 1 publiations. Researh interests: finite element analysis, omposite strutures.