Determination of Modelling Error Statistics for Cold-Formed Steel Columns

Table 7

Results of Chi-square goodness-of-fit test for modelling error of test database compression members.

Design standard	Type of compression member	Failure mode	Nos@	Assumed distribution (DOF)	Computed Chi-square value	Allowable Chi-square value
						At α = 5%	At α = 1%
ASCE 10-15	Column	Flexural buckling	14	Normal (2)	0.556	5.99	9.21
				Lognormal (2)	0.354
				Uniform (2)	0.722
		Flexure-torsion buckling	33	Normal (8)	1.837	15.51	20.09
				Lognormal (8)	1.057
				Uniform (8)	1.523
		Local buckling	10	Normal (1)	0.875	3.84	6.63
				Lognormal (1)	0.753
				Uniform (1)	0.853
	Stub column	Yielding	27	Normal (6)	0.572	12.59	16.81
				Lognormal (6)	0.525
				Uniform (6)	0.311
		Local buckling	10	Normal (1)	0.223	3.84	6.63
				Lognormal (1)	0.242
				Uniform (1)	0.226
AISI S100-16 & AS/NZS 4600: 2018	Column	Flexural buckling	14	Normal (2)	0.820	5.99	9.21
				Lognormal (2)	0.523
				Uniform (2)	0.986
		Flexure-torsion buckling	34	Normal (8)	1.801	15.51	20.09
				Lognormal (8)	1.116
				Uniform (8)	1.647
		Local buckling	23	Normal (5)	0.576	11.07	15.09
				Lognormal (5)	0.477
				Uniform (5)	0.839
		Distortion buckling	40	Normal (10)	0.379	18.31	23.21
				Lognormal (10)	0.442
				Uniform (10)	0.244
	Stub column	Yielding	17	Normal (3)	0.190	7.81	11.34
				Lognormal (3)	0.204
				Uniform (3)	0.060
		Local buckling	32	Normal (8)	3.455	15.51	20.09
				Lognormal (8)	1.682
				Uniform (8)	0.902
		Distortion buckling	42	Normal (11)	0.811	19.68	24.73
				Lognormal (11)	1.031
				Uniform (11)	1.322
EN 1993-1-3: 2006	Column	Flexural buckling	39	Normal (10)	1.183	18.31	23.21
				Lognormal (10)	0.978
				Uniform (10)	1.156
		Flexure-torsion buckling	57	Normal (16)	0.856	26.30	32.00
				Lognormal (16)	0.473
				Uniform (16)	0.902
		Local and distortion buckling	3	Normal (0)	1.260	—	—
				Lognormal (0)	1.266
				Uniform (0)	1.717
	Stub column	Local and distortion buckling	74	Normal (22)	0.408	33.92	40.29
				Lognormal (22)	1.023
				Uniform (22)	0.781

^@Number of Specimens from the test database critical in particular failure mode.