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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(34): 137157
Issue Date 198612
URL http://hdl.handle.net/2433/124940
Right
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)
Abstract
The elasticplastic behavior of pinended reinforced concrete slender columns subjected to biaxially eccentric loads is investigated experimentally and theoretically. The ultimate loads, longitudinal 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 symmetry. The ultimate load carrying capacity of a slender column is reduced by additional eccentricity due to lateral deflection even in a column having a length to depth ratio of 15. The numerical analysis to solve the loaddeformation 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 columns in spite of variation of the angle of eccentricity of the applied load. However, the remarkable effects of biaxial bending on the elasticplastic behavior occurs with the rectangular columns. When the rectangular columns are subjected to biaxially eccentric load to cause bending about the nearstrong 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
138 S. IW AI, K. MINAMI and M. WAKABAY ASHI
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 elasticplastic 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
12014:14012o1 .1 120 " 471 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
g
.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, _
8010454060 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(193) 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 (102) 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 specimens 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 8D10 longitudinal bars
(gross reinforcement ratios of 0.0396 and 0.0264, respectively) and 4.5 mm hoops spaced 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 metalform. The compressive strength of the concrete was 270340 kgf/cm2 (26
33 N/mm2) and the tensile yield strength of main reinforcement was 3,5003,700 kgf/
cm2 (340360 N/mm2). Age of specimens at test was 40210 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 pinended 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 midheight 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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