BEHAVIOR OF SQUARE CONCRETE-FILLED TUBULAR COLUMNS UNDER ECCENTRIC COMPRESSION WITH DOUBLE CURVATURE DEFLECTION

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Rudolf Holt
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1 Otober 2-7, 28, Beijing, China BEHAVIOR OF SQARE CONCRETE-FILLED TBLAR COLNS NDER ECCENTRIC COPRESSION WITH DOBLE CRVATRE DEFLECTION T. Fujinaga, H. Doi 2 and Y.P. Sun 3 Assoiate Professor, Researh Center for rban Safety and Seurity, Kobe niversity, Kobe, Japan ABSTRACT : 2 Graduate Student, Dept. of Arhiteture Seurity, Kobe niversity, Kobe, Japan 3 Professor, Dept. of Arhiteture Seurity, Kobe niversity, Kobe, Japan ftaka@kobe-u.a.jp Objetive of this paper is to present experimental information about the behavior of square CFT olumns subjeted to eentri ompression with double urvature deformation, to investigate validity of the urrent design formula for slender CFT olumns, meanwhile to study its appliability to the middle-length olumns. Forty-three square CFT olumns were fabriated and tested. The experimental variables among the tests are, ) the bukling length to depth ratio of the olumn, 2) the onrete strength, 3) the moment gradient whih deforms the olumn into double urvature, and 4) the eentriity of the axial load. Experimental results have indiated that the flexural strength of slender square CFT olumns inreases with the onrete strength and the moment gradient. Comparison between the test results and the theoretial ones predited by the urrent design ode has shown that for the slender square CFT olumns with the bukling length to depth ratio of 2, the urrent design formula ould satisfatorily well predit the flexural strength in spite of the degree of moment gradient. For the middle-length square CFT olumns with the bukling length to depth ratio of, however, the urrent design formula overestimates the flexural strength when the olumn was under eentri ompression without moment gradient, i.e. under pure bending. On the other hand, for the middle-length olumns under eentri ompression with moment gradient, the urrent design formula ould be applied to evaluate their flexural strength with satisfatory auray. KEYWORDS: Conrete-filled tubular olumn, Slenderness ratio, Double urvature deformation, Eentri ompression, Square olumn. INTRODCTION In the urrent design standards for steel reinfored onrete strutures (hereafter refereed to as SRC standards) and the design guideline for onrete-filled tubular strutures (hereafter refereed to as CFT guideline) by the Arhitetural Institute of Japan, the ultimate apaity of a steel-onrete omposite slender olumn is alulated by simply superimpose the apaities of the onrete olumn and the steel olumn (, 2; 997). This simple superimposition method has suh advantages as to keep ontinuity in the alulation of apaity for the short and the slender olumns, and to ontain the up-to-date information on eah omponent, while the design formula beomes inevitably ompliated. In addition, for the olumns under onentri ompression, the urrent design standards not only provides alulation equations for short and slender olumns with slenderness ratio L k /D less than and equal to 4 and larger than and equal to 2, respetively, but also reommendation for the alulation for the middle-length olumn with L k /D varying between 4 and 2. However, for the olumns under ombined flexure and axial ompression, the urrent SRC standards only shows apaity design formulae for short and slender olumn, and approximates the alulation for the middle-length olumn by applying the equation for the short olumn, hene resulting disontinuity in the design equation. As to the apaity design equation for the middle-length olumns with L k /D varying between 4 and 2, Chung et al [24] haves proposed a method to obtain the ultimate apaity via linear interpolation between the short and the

2 Otober 2-7, 28, Beijing, China slender olumn. This method, however, involves tedious alulation proedure, while its onept is lear and mathematial expression is simple. Kido et al [25] have also proposed a theoretial approah for the alulation for the middle-length olumns, but in their proposal there is still disontinuity in the alulation. Fujinaga et al [25] have reently proposed a simple method for the middle-length CFT olumn. In this method, the ultimate apaity for the middle-length olumns is alulated by linear interpolation between the short and the slender olumn. Nevertheless, validity of their proposed method has not yet been verified with experimental results, neither the details of the moment modifiation fator C were mentioned in the method. On the other hand, experimental study on effets of the moment gradient in the olumns under double urvature on the ultimate apaity is sare. While Kilpatrik et al [997] have onduted systemati tests on the irular CFT olumns to investigate the effet of the moment gradient; there are no experimental results of square CFT olumns available. Furthermore, the moment amplifiation fator C due to the moment gradient for the middle-length olumn has not yet been investigated. Objetives of the researh is to obtain experimental information for the behavior of square CFT slender and middle-length olumns under double urvature deformation, and to investigate validity of the previous alulation methods through omparing the experimental results with the theoretial preditions. 2. OTLINES OF THE CRRENT DESIGN FORLAE 2.. Capaity Equations for the CFT Columns under Combined Flexure and Axial Compression Aording to the urrent SRC standards, ultimate flexural strength of the CFT olumns under ombined flexural and axial load an be obtained as follows: () For the olumn with L k /D ratio less than and equal to 2 N = N = + N s + s (2.) (2) For the olumn with L k /D ratio larger than 2 (i) When N < N or > s ( - N / N k ) / C N = N = + N s N k C (2.2) (ii) When N > N or < s ( - N / N k ) / C N = N + s N = N s N k C (2.3) where N,, s N, s are ultimate ompressive strength and ultimate flexural strength of the filled onrete setion, and those of the steel tube, respetively, s is ultimate flexural strength of steel tube under pure bending, N k is Euler s bukling load of the CFT olumn, N is ultimate ompressive strength of the filled onrete setion, and C is the moment amplifiation fator oment Amplifiation Fator C In the urrent SRC standard, the formula reommended in the plasti design guideline by the [, 975] is applied to alulate the moment amplifiation fator in the form of

3 Otober 2-7, 28, Beijing, China 2 2 N =.5 π E I C.25, N k = + E I 2 s s N k l 5 k (2.4) where, 2 are the larger absolute end moment and smaller end moment, respetively, E and s E are the Young s modulus of onrete and of steel, respetively, I, s I are moment inertia of onrete and of steel, respetively, l k is bukling length of the olumn Strength of iddle-length Column Calulated by Interpolation In the design formula, the boundary of short olumn is L k /D=4, and the boundary of slender olumn is L k /D=2. Table Experimental Condition and Result Speimen Type L k /D e e 2 β σ B N =N e (mm) (mm) (=e 2 /e ) (N/mm 2 ) (kn) (knm) R2-27-C R (+) R (+) R R (-) R (-) B R (-) R (+) R (+) R R (-) R (-) C 3.5 R (-) R (+) R (+) B R R (-) R (-) C 35.8 R (-) R2-6-C R (+) R (-) B R2-6--.(+) R R (-) R2-6--.(-) C R-27-C R (+) R (+) R R (-) A R (-) R (-) R-27--.(+) R (+) R B R (-) R (-) C R-27--.(-) R-6-C A R-6--.(+) R-6--. B R-6--.(-) e, e 2 : Eentriity of upper end and bottom end, respetively, σ B : Compressive strength of onrete, N: Experimental maximum strength Then the flexural strength for middle-length olumn (4<L k /D<2) an be easily alulated by using linear interpolation method. 3. ECCENTRICALLY COPRESSIVE TESTS NDER DOBLE CRVATRE DEFORATION 3.. Outlines of Speimen A total of forty-three olumns were fabriated and tested. Figure shows details of the test olumns. All of the speimens were made of square steel tube with dimensions of 25x25x3.2mm (STKR4) and filled with onrete having targeted ompressive strength of 27 N/mm 2 or 6 N/mm 2. The experimental variables are; ) the L k /D ratio (2 and ), the onrete strength, the moment gradient expressed in term of 2 ratio, and the initial eentriity e (, 3, mm). PL-2x6 (SS4) (Endplate exist) -25x25x3.2 (STKR4) (No Endplate) (L/D=2),5(L/D=) 239(L/D=2),4(L/D=) Figure Speimen (mm) 65 2 Endplate A 65 2 Endplate B Welding seam f8 Welding seam f8 Hole for fill up

Otober 2-7, 28, Beijing, China Table 2 ixture of Conrete 2N loading mashine Depth Thikness Tension test Compression test Yield stress Tensile strength Yield stress Compressive strength (mm) (mm)

In Type A speimen, there are no steel plates at both ends of the olumn.

4 Otober 2-7, 28, Beijing, China Table 2 ixture of Conrete 2N loading mashine Depth Thikness Tension test Compression test Yield stress Tensile strength Yield stress Compressive strength (mm) (mm) (N/mm 2 ) (N/mm 2 ) (N/mm 2 ) (N/mm 2 ) σ (N/mm 2 ) σ = 38 N/mm Aording to the initial eentriity, the speimens were divided into three types. In Type A speimen, there are no steel plates at both ends of the olumn. On the other hand, in Type B speimen only one steel plate of 25mm in thikness was welded to the end of the olumn where the effet due to extra end onfinement is signifiant, while eah C type speimens had end plates at both ends. Table shows experimental onditions along with the primary test results of all speimens. The onrete strengths at the stage of testing are given in Table. Figure 2 displays the omplete stress-strain urve of the steel tube. The ompressive stress-strain urve shown in Figure 2 was obtained by onentri ompressive test on the short steel tube, while the tensile stress-strain urve was obtained by onduting tensile test of three standard oupons. The dotted line in Figure 2 expresses result where the axial ompressive strain of the steel tube was measured by strain gages σ Yt = 358 N/mm 2 σ t = 452 N/mm 2 Figure 2 Stress strain relationship ε (Endplate exist) (No Endplate) 25(L/D=2), 25(L/D=) Figure 3 Loading ondition 3.2 ing Apparatus Figure 3 shows the test apparatus, while Photos displays detail of end ondition. Eah speimen was at first loaded onentrially in elasti by a 2N apaity test mahine. After verifying the axial load had been applied in the enter of the olumn via the reords of the strain gages, the knife-edge (see Photo ) at the end of the olumn was slid to the targeted eentriity, and then the eentri loading was applied till large deformation. In addition to two displaement transduers measuring the axial deformation, eight displaement transduers were used to measure the lateral displaements along the length of the olumn. A total of twenty two strain gages were embedded on the surfae of the steel tube to measure the steel strain. Photo Loading situation Photo 2 Details of loading equipment

5 Otober 2-7, 28, Beijing, China =.) =.5) =.) Setion( r =.) Setion( r =.85) Setion( r =.) Setion( r =.85) Setion( r =.) Setion( r =.85) = -.333) Setion( r =.) = -.667) Setion( r =.) = -.) Setion( r =.) Setion( r =.85) Setion( r =.85) Setion( r =.85) (a) L k /D=2 (Slender olumn), σ B =27N/mm Setion( r =.) =.) Setion( r =.) =.5) Setion( r =.) =.) Setion( r =.) = -.333) Setion( r =.) = -.667) Setion( r =.) = -.) (b) L k /D= (iddle-length olumn), σ B =27N/mm Figure 4 Comparison of strength (ontinue) 4. EXPERIENTAL RESLTS AND COPARISON WITH THEORETICAL PREDICTIONS 4. oment Versus Axial Load Relationship Figure 4 shows experimental flexural strengths along with several theoretial preditions. In Figure 4, the blak irles express the experimental results, while the theoretial results are represented by several urves; the blak solid line orresponds to the flexural strength of the CFT olumn alulated by the SRC standard, where effet of the slenderness has been taken into onsideration, and the dotted line expresses the ultimate flexural strength of the CFT setion. For the middle-length olumns, a blak line is further plotted as shown in Figure 4 (b) and (d) to

6 Otober 2-7, 28, Beijing, China represent the flexural strength omputed by linear interpolation between the flexural strengths of short and slender olumns by SRC standard. As obvious from Figure 4 (a) and (), the theoretial results alulated by urrent SRC standard agree well with the experimental results of the slender olumns in spite the onrete strength, while the theoretial preditions tend to underestimate the experimental ones as the moment gradient beomes larger. For the middle-length olumns, however, the SRC standard seems to overestimate the experimental result for the olumns under pure bending,, i.e. without moment gradient. This disrepany is mainly due to that in the SRC standard, the flexural strength of the middle-length olumn with L k /D ratio varying between 4 and 2 is omputed by using the equation for the short olumn. It is apparent, on the other hand, that the theoretial results alulated by linear interpolation ould onservatively predit the test results in spite of the moment gradient. From the above-mentioned omparisons and observation, one an see that flexural strength of the middle-length square CFT olumn an be reasonably predited by linear interpolation between the flexural apaities of the short and slender olumns alulated by the urrent SRC standard. To better understand differene between the experimental and theoretial flexural strengths, relationships between the exess ratios and the exess angles of flexural strength, whih are defined in Figure 5, are plotted in Figure 6. For the slender olumns with L k /D ratio of 2, the ratio of the experimentally measured strength to the theoretial results varies between.2 and,24, having an average of.3. For the middle-length olumns with L k /D ratio of, the flexural strength ratio varies between.9 and.29 when the SRC equation for short olumn is diretly applied to alulate the flexural strength. On the other hand, the linear interpolation method an give a more reasonable predition to the 5 5 Setion( r =.) =.) Setion( r =.85) Setion( r =.) = -.667) Setion( r =.85) Setion( r =.) =.) Setion( r =.85) Setion( r =.) = -.) Setion( r =.85) () L k /D=2 (Slender olumn), σ B =6N/mm 2 5 Setion( r =.) =.) 5 Setion( r =.) =.) 5 Setion( r =.) = -.) (d) L k /D= (iddle-length olumn), σ B =6N/mm Figure 4 Comparison of strength (the rest)

7 Otober 2-7, 28, Beijing, China n = N / Nmax O Exess ratio = OB/OA Degree of exess ratio = θ B A θ m = / max Figure 5 Definition of exess ratio Exess ratio F 27 F 6 L k /D = θ Exess ratio L k /D = F 27 F 27(Slender olumn) F 27( interporation) F 6 F 6(Slender olumn) F 6( interporation) θ (a) L k /D=2 (Slender olumn) (b) L k /D= (iddle-length olumn) Figure 6 Comparison about exess ratio flexural strength for the middle-length CFT olumns, with the strength ratio varying between.5 and.29 and an average of oment Amplifiation Fator C In order to obtain experimental results for the moment amplifiation fator, the experimental moment versus axial load urves were at first approximated by onduting regression analysis on the experimental flexural strengths for eah moment gradient as shown in Figure 7. Then the experimental moment amplifiation fators were alulated as the differene between the experimentally measured strength and the strength drawn from the approximated moment-axial load urve shown in Figure 7. Figure 8 shows experimental moment amplifiation fators along with the theoretial urves reommended by the plasti design guideline for steel strutures [, 975]. The bold solid lines and dotted lines in Figure 8 represent equation for the moment amplifiation fator based on elasti theory and the approximate equation, respetively. Axial fore is normalized by Euler s load (see Eqn. (2.4)). For the slender olumns with L k /D ratio of 2, in the ase of F =27N/mm 2, the approximate equation agreed well with the test results as the moment ratio 2 is equal to -.. As beomes larger, i.e. the moment gradient beomes smaller, the disrepany between the experimental and the theoretial results beomes wider, but the approximate equation ould still trae the tendeny of the moment amplifiation fator along with the axial load. In the ase of F =6N/mm 2, although the experimental data is few, the approximate formula traed the tendeny of moment amplifiation fator C as well as in the ase of F =27N/mm 2 2 =.5 2 =.5. For the middle-length olumns with L k /D ratio of, the experimental moment amplifiation fators were less than the alulated results obtained either by the elasti theoretial equation or by the approximate equation, whih means that the design formula for the slender CFT olumns reommended in the urrent standards would underestimate the axial apaity of the middle-length CFT olumns. C Theoretial formula Approximate formula L k /D = N / N k (a) L k /D= =-. C F 27 F 6 2 =.5 2 =. 2 = = =. L k /D = N / N k. (b) L k /D= Figure 8 Comparison of moment modified fator C =-.

8 Otober 2-7, 28, Beijing, China 5. CONCRDING REARKS Experiments of slender and middle-length square CFT olumns under eentrially ompression with doubleurvature defletion were onduted to examine the effet of moment gradient on the flexural strength of olumn. Comparing the experimental results with the theoretial preditions leads to the following onlusions: ) For the slender square CFT olumns with the bukling length to depth ratio of 2, the urrent design formula ould satisfatorily well predit the flexural strength in spite of the degree of moment gradient. 2) For the middle-length square CFT olumns with the bukling length to depth ratio of, the urrent design formula overestimated the flexural strength when the olumn was under eentri ompression without moment gradient, i.e. under pure bending. On the other hand, for the middle-length olumns under eentri ompression with moment gradient, the urrent design formula ould be applied to evaluate their flexural strength with satisfatory auray. 3) oment amplifiation fator, whih was alulated bakward from experimental result, ompared well with the elasti theoretial and approximate equations. Approximate equation predits well the results for the olumns with L k /D= 2 and 2 =-.. However, for the olumns with L k /D=, auray is muh lower regardless of the moment gradient. REFERENCES Arhitetural Institute of Japan (2). Standards for Strutural Calulation of Steel Reinfored Conrete Strutures Arhitetural Institute of Japan (997). Reommendations for Conrete Filled Steel Tubular Strutures Chung, J. and Kimura, J. (24). Strength Formula of CFT Short Beam-Column. Summaries of Tehnial Papers of Annual eeting, Kido,. and Tsuda, K. (25). Design Formula for Conrete Filled Steel Tubular Column Subjeted to Axial Load and Bending oment. Journal of Strutural Engineering Vol.5B, Fujinaga, T., Chang, Y.K. and itani, I. (25). A Study on Strength of Slender CFT Beam-Columns. Journal of Strutural Engineering Vol.5B, Kilpatrik, A.E. and Rangan, B.V. (997). s on High-Strength Composite Conrete Columns, Researh Report No /97, Shool of Civil Engineering Curtin niversity of Tehnology Arhitetural Institute of Japan (975). Reommendations for the Plasti Design of Steel Strutures ACKNOWLEDGENT The Authors wish to express their gratitude to the staff of Department of Arhiteture, Kobe niversity for their help in experimental work. This investigation is supported by a grant-in-aid of researh for steel strutures JSSC.

WRAP-AROUND GUSSET PLATES

WRAP-AROUND GUSSET PLATES Where a horizontal brae is loated at a beam-to-olumn intersetion, the gusset plate must be ut out around the olumn as shown in Figure. These are alled wrap-around gusset plates.