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  • Title Stability of Slender Reinforced Concrete Columns Subjected toBiaxially Eccentric Loads

    Author(s) IWAI, Satoshi; MINAMI, Koichi; WAKABAYASHI, Minoru

    Citation Bulletin of the Disaster Prevention Research Institute (1986),36(3-4): 137-157

    Issue Date 1986-12



    Type Departmental Bulletin Paper

    Textversion publisher

    Kyoto University

  • Bull. Disas. Prey. Res. Inst., Kyoto Univ., Vol. 36, Parts 3, 4, No. 321, December, 1986 137

    Stability of Slender Reinforced Concrete Columns

    Subjected to Biaxially Eccentric Loads

    By Satoshi IWAI, Koichi MINAMI and Minoru WAKABAYASHI

    (Manuscript received October 11, 1986)


    The elastic-plastic behavior of pin-ended reinforced concrete slender columns subjected to bi-axially eccentric loads is investigated experimentally and theoretically. The ultimate loads, longi-tudinal and transverse deformations and the behavior up to failure of the columns are examined in detail.

    A total of 36 column specimens with rectangular cross sections including square sections were tested. The ratios of column length to minimum depth ranged from 6 to 26. Loads were applied monotonically at each column end with equal eccentricities at various angles from an axis of sym-metry. The ultimate load carrying capacity of a slender column is reduced by additional eccentri-city due to lateral deflection even in a column having a length to depth ratio of 15. The numeri-cal analysis to solve the load-deformation response of the column predicts the test behavior very

    well. In the case of square columns, there is not much difference in the ultimate loads of the col-umns in spite of variation of the angle of eccentricity of the applied load. However, the remark-able effects of biaxial bending on the elastic-plastic behavior occurs with the rectangular columns. When the rectangular columns are subjected to biaxially eccentric load to cause bending about the near-strong axis, the ultimate loads and the deformation behavior are significantly affected by the bending about the weak axis of the section.

    1. Introduction

    Columns in building are designed conventionally on the basis of a structural anal-

    ysis of frames in the planes in which the principal axes of columns are constructed. However, since almost all columns are subjected to biaxial bending, the effects of bi-

    axial bending on the behavior of columns should be investigated. A number of

    experiments and analyses have been done to investigate the ultimate strength of short

    reinforced concrete columns under biaxially eccentric loading, and many strength

    formulations have been proposed for their design.

    Investigations on instability problems of relatively slender concrete columns have

    been extensively carried out in the area of no fear of strong earthquakes, while the

    shear resistance of short columns has been more investigated in Japan. In AIJ Stand-

    ard1), slender reinforced concrete columns are regulated by the following limitations

    of Art. 15.7; The ratio of the minimum depth or diameter of a member to the distance between

    the main supporting points shall be not less than 1/15 and 1/10 in case of using ordinary concrete and light weight concrete, respectively. These limitations, how-

    ever, are not applied when the structural safety of the column is certified by struc-


    tural calculation considering the effective slenderness ratio.

    In recent years, as the material strengths of concrete and steel increase more and

    more, the cross sections are able to be designed to compact and the members be-

    come to be slender. Moreover the reinforced concrete braces with slender propor-

    tions are sometimes used in a frame to resist earthquake forces. Therefore, clarifica-

    tion of the elastic-plastic behavior of slender reinforced concrete columns is very im-

    portant. The column behavior under biaxial loading becomes further complex due to the

    slenderness effects. There is very little available experimental information of the sta-

    bility of slender columns. In this paper, fundamental data from biaxially eccentric

    loading tests of slender columns with square and rectagular cross sections2).3) are re-

    ported. The objective of this study is to investigate the slenderness effects under biaxial bending on the ultimate strength and the deformation behavior up to the fail-

    ure of reinforced concrete columns.

    2. Outline of Experimental Work

    01 1(.5.


    L- 600 -41 ri--:74611 680

    (a) C series (LID = 5.7) + Load Pokft

    1201-4:1-40-12o1 .1 120 " 4-71 2 0

    ,1(d) Square cross section 1800 4 1880 (A, B, C series) (b) B series (L/D . 15.7)

    01 1, 7120

    3000 1 3080

    (c) A series (LID . 25.7) 22.."

    1S Strain 1111


    .ioniammiamninlIMMIL vorcaumwou1111"


    .1!m" ipf

    (e) RS series (i/b = 10) (g) Rectangular cross section

    (RS, RL series)

    ,1 I Strain Gages Strain Gages

    IiiIIIRIBMIIIIIIIIIIMMI111111111 II 1 1111111111111111111111, _

    8-010454060 40141301 110011241241201201 1100 1120140 3000

    (f) RL series (lib = 25) Fig. 1 Geometry of test specimen (units in mm).

  • Stability of Slender Reinforced Concrete Columns Subjected to Biaxially Eccentric Loads 139

    Table 1 Mix proportion of concrete and material properties (unit : 1 Vein' =0.098 kN/mm2).

    Test Series C B A

    Mixing Ratios by Weight Water 0. 67 0. 65 0. 66 0. 62

    Cement 1 1 1 1 Sand 1.97 1.91 1.91 1.90 Gravel 2. 74 2. 76 2. 76 2. 75

    Specific Gravities

    Cement 3. 16 3. 16 3. 16 3. 16 Sand 2. 61 2. 62 2. 45 2. 48 Gravel 2. 58 2.60 2. 50 2.54

    Concrete Compressive Strength Fc (kg/cm2) 275 281 311 316

    Strain at Compressive StrengthEP(19-3) 2.59 2.30 2.41 2. 43

    Splitting Tensile Strength (kg/cm2) - 30. 1 26. 2 28. 9

    Reinforcement Upper Yield Strength (t/cm2) 3. 72 3. 72 3.63 3.77

    Lower Yield Strength (t/cm2) 3.54 3. 62 3. 49 3. 68 Ultimate Strength (t/cm2) 5. 27 5. 17 5. 50 5. 18 Elongation (10-2) 18. 2 16. 9 22. 6 27. 2

    A total of 36 column specimens were tested. Their column length to minimum

    section depth rations, 1/D or i/b, ranged from 6 to 26. The geometry of test speci-mens is shown in Fig. 1. The columns had a 12 cm (b) x 12 cm (D) square cross sec-

    tion or a 12 cm (b) X 18 cm (D) rectangular cross section with 8-D10 longitudinal bars

    (gross reinforcement ratios of 0.0396 and 0.0264, respectively) and 4.5 mm hoops spac-ed 6 cm apart. The mix proportion of concrete and the properties of materials are

    listed in Table L The concrete was cast in the horizontal position using a machin-

    ed metal-form. The compressive strength of the concrete was 270-340 kgf/cm2 (26-

    33 N/mm2) and the tensile yield strength of main reinforcement was 3,500-3,700 kgf/

    cm2 (340-360 N/mm2). Age of specimens at test was 40-210 days.

    Photo 1 and Fig. 2(a) show a specimen placed in the loading apparatus. Both

    ends of the column were supported by universal bearings to simulate pin-ended con-

    ditions. The bearings were greased to minimize friction. Load was applied mono-

    tonically at each column end with equal eccentricities, e, at various angles, 0, from an axis of symmetry, as given in Fig. 1. Transverse deflections, u and v in the prin-

    cipal axes of the section, denoted by x and y, respectively, and torsional rotation, a,

    at the mid-height of the column (Fig. 2(b)), rotations of both column ends, 0, and Ow (where added subscripts, u and 1, represented upper end and lower end, respec-

    tively), about the x and y axes of the section, respectively, and axial deformation, w,

  • 140 S. IW AI, K. MINAMI and M. W AKABAY ASHI

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