Design Forces of Horizontal Braces Unlocated at Middle of Columns considering Random Initial Geometric Imperfections

Table 3

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Horizontal braces located at 0.6L					Horizontal braces located at 0.7L
λc	n	Statistical character	Fn/P (%)	1.2 × Fn/P (%)	λc	n	Statistical character	Fn/P (%)	1.2 × Fn/P (%)
50	4	μ = −2.0375; σ = 1.0702	1.63	1.96	50	4	μ = −0.7927; σ = 0.4124	2.03	2.44
		μΙn = 0.6923; σΙn = 0.3946					μΙn = −0.1401; σΙn = 0.5870
		a1 = 0.2300					a1 = 0.2980
50	6	μ = −1.1544; σ = 0.5958	2.37	2.84	50	6	μ = −1.1693; σ = 0.6279	3.05	3.66
		μΙn = 0.2089; σΙn = 0.4510					μΙn = 0.1563; σΙn = 0.6624
		a1 = 0.2810					a1 = 0.3720
50	8	μ = −1.1907; σ = 0.5662	3.16	3.79	50	8	μ = −1.4877; σ = 0.6906	3.96	4.75
		μΙn = 0.2647; σΙn = 0.5743					μΙn = 0.4434; σΙn = 0.5127
		a1 = 0.3850					a1 = 0.3360
50	10	μ = −1.5193; σ = 0.7332	4.03	4.84	50	10	μ = −1.7635; σ = 0.8433	5.13	6.15
		μΙn = 0.4805; σΙn = 0.5294					μΙn = 0.6485; σΙn = 0.4866
		a1 = 0.3760					a1 = 0.3520
75	4	μ = −1.0674; σ = 0.5176	1.87	2.24	75	4	μ = −1.3492; σ = 0.7566	2.61	3.13
		μΙn = 0.0317; σΙn = 0.6390					μΙn = 0.2587; σΙn = 0.6496
		a1 = 0.3530					a1 = 0.3660
75	6	μ = −1.1134; σ = 0.7718	2.88	3.46	75	6	μ = −1.8843;σ = 0.8356	4.21	5.05
		μΙn = −0.0331; σΙn = 0.8046					μΙn = 0.5768; σΙn = 0.5375
		a1 = 0.3060					a1 = 0.3110
75	8	μ = −1.9497; σ = 1.1104	3.85	4.62	75	8	μ = −2.4379; σ = 1.1773	5.78	6.94
		μΙn = 0.6112; σΙn = 0.6170					μΙn = 0.7872; σΙn = 0.5883
		a1 = 0.3910					a1 = 0.4260
75	10	μ = −2.3161; σ = 1.3239	5.48	6.58	75	10	μ = −3.2291; σ = 1.5906	7.66	9.19
		μΙn = 0.8144; σΙn = 0.5938					μΙn = 1.0570; σΙn = 0.5564
		a1 = 0.3810					a1 = 0.4610
100	4	μ = −0.9750; σ = 0.4261	2.33	2.79	100	4	μ = −1.4045; σ = 0.6492	3.03	3.63
		μΙn = −0.1504; σΙn = 0.5849					μΙn = 0.2742; σΙn = 0.6987
		a1 = 0.3720					a1 = 0.3880
100	6	μ = −1.7184; σ = 0.7460	3.3	3.96	100	6	μ = −2.5231; σ = 1.1984	4.88	5.85
		μΙn = 0.4839; σΙn = 0.5801					μΙn = 0.7677; σΙn = 0.7717
		a1 = 0.4270					a1 = 0.4480
100	8	μ = −2.3836; σ = 1.1715	4.82	5.78	100	8	μ = −3.3931; σ = 1.8379	6.97	8.36
		μΙn = 0.7768; σΙn = 0.6407					μΙn = 1.0623; σΙn = 0.7615
		a1 = 0.4240					a1 = 0.4580
100	10	μ = −2.8440; σ = 1.4411	6.75	8.1	100	10	μ = −4.3562; σ = 2.5071	9.39	11.27
		μΙn = 0.9566; σΙn = 0.6333					μΙn = 1.2740; σΙn = 0.7612
		a1 = 0.4340					a1 = 0.4760

F_n/P: refer to Figure 5 for the definition of the characteristic value.