Behavior of high strength concrete columns under eccentric loads

Peer review under responsibility of Housing and Building National Research Center.

Figures & data

Fig. 1.a Reinforcement arrangement along column height.

Fig. 1.b Columns section dimension and reinforcement.

Fig. 1.c Columns setup and details.

Fig. 1.d Columns setup demec points and details.

Fig. 4.a Load-concrete compressive strain for tested columns.

Fig. 4.b Load-stirrup tensile strain for tested columns.

Fig. 6.a Solid 65 elements, ANSYS manual set.

Fig. 6.b Link8, 3–D spar element ANSYS manual.

Fig. 6.c Compressive uni-axial stress-strain curve for concrete MacGregor [6].

Fig. 6.d Applied boundary conditions on the model.

Fig. 9.a Experimental and analytical cracking patterns at failure for half of column S2–E15.

Fig. 9.b Experimental and analytical cracking patterns at failure for half of column S1–R.

Table 1 Mechanical properties of steel bars.

Steel diameter (mm)	Steel grade	Actual area (mm^2)	Yield strength (MPa)	Ultimate strength (MPa)	Elongation%
Φ6	Mid steel	28.4	340	489.4	20
Φ8		51.13	290	453.8	18.8
Φ10	High grade steel	77.31	650	728.3	6.0
Φ12		108.27	580	726.9	16.7
Φ16		200.0	540	728	18.75

Table 2 Properties of tested square columns in the experimental program.

Groups	Columns^⁎	fcu MPa	Long. steel	Long. steel ratio, μ%	Column height (H), m	(H/t)	e/t	Ties diameters (mm)
Ref.	S1–R	65	4Φ12	2.0	1.5	10	0.10	Φ6
A	S2–E15	71.5	4Φ12	2.0	1.5	10	0.15	Φ6
	S3–E20	71.5	4Φ12	2.0	1.5	10	0.20	Φ6
B	S4–s12	65	4Φ12	2.0	1.8	12	0.10	Φ6
	S5–s15	71.5	4Φ12	2.0	2.25	15	0.10	Φ6
C	S6–L2.7	65	8Φ10	2.7	1.5	10	0.10	Φ6
	S7–L3.0	65	6Φ12	3.0	1.5	10	0.10	Φ6
	S10–3.5	65	4Φ16	3.5	1.5	10	0.10	Φ6
D	S8–St8	65	4Φ12	2.0	1.5	10	0.10	Φ8
	S9–St10	65	4Φ12	2.0	1.5	10	0.10	Φ10

* All tested columns are square columns with dimension of 150 × 150 mm.

Fig. 2 Column S1–R, reference column at first crack and after failure.

Fig. 3 Load-mid height displacement for tested columns.

Fig. 5 View of tested columns compression side after failure.

Table 3 Test results for all tested columns in the experimental program.

Columns	Group	fcu MPa	Load at first crack (KN)	Type of first crack	Disp. at failure (mm)	Failure load (KN)	Modes of failure
S1–R	Ref.	65	750	Vertical compression	5.5	970	Compression failure
S2–E15	A	71.5	880	(Vertical compression + horizontal tension)	9.0	985	Compression failure
S3–E20		71.5	760	(Vertical compression + Horizontal tension)	10.4	887	Compression failure
S4–S12	B	65	720	Vertical compression	11.0	849	Compression failure
S5–S15		71.5	840	Vertical compression	15.0	984	Compression failure
S6–L2.7	C	65	440	Vertical compression	7.2	840	Compression failure
S7–L3.0		71.5	1360	No cracks appeared before ultimate load	2.26	1360	Compression failure
S10–L3.5		71.5	1490	No cracks appeared before ultimate load	4.0	1490	Compression failure
S8–St8	D	65	960	(Vertical compression + horizontal tension)	12.7	1067	Compression failure
S9–St10		65	1080	(Vertical compression + horizontal tension)	7.8	1262	Compression failure

Table 4 Properties of analyzed columns in the analytical parametric study.

Col. No.	Group name	Column name^⁎	fcu MPa	Long. steel	Long. steel ratio^⁎⁎, μ	Height of column (H), m	(H/t)	e /t	Ties Φ (mm)
1	Ref.	S1–R	65	4Φ12	2.0	1.5	10	0.10	Φ6
2	A	S2–E15	71.5	4Φ12	2.0	1.5	10	0.15	Φ6
3		S3–E20	71.5	4Φ12	2.0	1.5	10	0.20	Φ6
4	B	S4–S12	65	4Φ12	2.0	1.8	12	0.10	Φ6
5		S5–S15	71.5	4Φ12	2.0	2.25	15	0.10	Φ6
6	C	S6–L2.7	65	8Φ10	2.7	1.5	10	0.10	Φ6
7		S7–L3.0	71.5	6Φ12	3.0	1.5	10	0.10	Φ6
8		S10–L3.5	71.5	4Φ16	3.5	1.5	10	0.10	Φ6
9	D	S8–St8	65	4Φ12	2.0	1.5	10	0.10	Φ8
10		S9–St10	65	4Φ12	2.0	1.5	10	0.10	Φ10
Rectangular columns
11	Ref	R1–R	68.5	4Φ18	2.2	3.0	10	0.10	Φ6
12	A	R2–E15	68.5	4Φ18	2.2	3.0	10	0.15	Φ6
13		R3–E20	68.5	4Φ18	2.2	3.0	10	0.20	Φ6
14	B	R4–S12	68.5	4Φ18	2.2	3.6	12	0.10	Φ6
15		R5–S15	68.5	4Φ18	2.2	4.5	15	0.10	Φ6
16	C	R6–L2.8	68.5	4Φ20	2.8	3.0	10	0.10	Φ6
17		R7–L3.3	68.5	4Φ22	3.3	3.0	10	0.10	Φ6
18	D	R8–St8	68.5	4Φ18	2.2	3.0	10	0.10	Φ8
19		R9–St10	68.5	4Φ18	2.2	3.0	10	0.10	Φ10

* Column dimensions 150 × 150 mm for square columns and 150 × 300 mm for rectangular columns.

⁎⁎ Longitudinal steel yield stress = 580 MPa for Φ12, Φ16, Φ18, Φ20, and Φ22, but for Φ10 is 650 MPa. Mild steel yield stress for both Φ6, Φ8 = 300 MPa.

Fig. 7.a Comparisons between columns load capacity from both experimental and analytical analyses.

Fig. 7.b Comparisons between columns maximum mid-height displacement from both experimental and analytical analyses.

Fig. 8 Comparison between analytical and experimental mid height displacements.

Table 5 Comparison between test and analytical results.

Column name	Group name	Experimental		Analytical		$\frac{P_{\text{exp}.}-P_{\text{anal}.}}{P_{\text{exp}.}}\%$	$\frac{{\mathrm{\Delta }}_{\text{exp}.}-{\mathrm{\Delta }}_{\text{anal}.}}{{\mathrm{\Delta }}_{\text{exp}.}}\%$
		Pu (KN)	Δ(mm)	Pu (KN)	Δ(mm)
S1–R	Ref.	970	5.5	891	5.6	8	−2
S2–E15	A	984	9	784	7	20	22
S3–E20		886	9.25	671	7.8	24	15
S4–S12	B	848	8.3	826	7	3	15
S5–S15		984	15	780	13	20	13
S6–L2.7	C	840	7.2	925	4.9	−8	30
S7–L3.0		1360	2.3	1007	7.4	26	−220
S10–L3.5		1490	4	1007	7.1	32	−78
S8–St8	D	1067	9	931	7.7	13	14
S9–St10		1262	7.8	940	7.5	25	4

Table 6 Results of rectangular columns from analytical simulation.

Column No.	Group No.	Pu (KN)	$\frac{P-P_{\text{ref}.}}{P_{\text{ref}.}}\%$	Δ(mm)	$\frac{\mathrm{\Delta }-{\mathrm{\Delta }}_{\mathit{ref}.}}{{\mathrm{\Delta }}_{\mathit{ref}.}}\%$
R1–R	Ref.	1975	0	13.4	0
R2–E15	A	1728	−12.5	16	23
R3–E20		1490	−24.5	17.5	31
R4–S12	B	1887	−4.5	19.2	43
R5–S15		1712	−13.3	26	94
R6–L2.8	C	1998	1.2	14.5	8.2
R7–L3.3		2001	1.3	14	4.4
R8–St8	D	1995	−1	16	19
R9–St10		1998	1.2	16	19

Fig. 10 Load mid-height displacement for rectangular reference column & group A.

Fig. 11 Interaction diagram for some tested columns.

Table 7 Difference between experimental results and interaction diagram.

Column No.	PExp. (KN)	PACI (KN)	PECP (KN)	$\frac{P_{\text{exp}.}-P_{\text{ACI}}}{P_{\text{exp}.}}\%$	$\frac{P_{\text{exp}.}-P_{\text{ECP}}}{P_{\text{exp}.}}\%$
S1–R	970	875	920	9.8	5.15
S2–E15	984	720	810	26.8	17.7
S3–E20	886	680	800	23.2	9.7
S4–S12	848	910	970	−7.3	−14.4
S5–S15	984	925	980	6	0.4
S6–L2.7	840	1075	1100	−28	−30
S7–L3.0	1360	825	990	39.3	27.2
S8–St8	1067	830	900	22.2	15.6
S9–St10	1262	775	835	38.6	33.8
S10–L3.5	1490	860	925	42.3	38