New simple equations for effective length factors

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

Figures & data

Fig. 1 Braced and sway frames.

Fig. 2 Buckling length factor (K) for prevent of sway (Braced) columns.

Fig. 3 Buckling length factor (K) for permitted of sway (Unbraced) columns.

Table 1 Comparison of K-factors obtained by P.W., and French Rules with exact results (side sway is prevented).

GA	GB	exact	P.W.	% Diff.	French	% Diff.
		value			Rule [7]
0.1	0.4	0.603	0.603	0.06	0.608	0.88
0.25	0.25	0.611	0.613	0.28	0.619	1.30
0.1	0.9	0.648	0.648	0.00	0.651	0.42
0.25	0.75	0.672	0.672	0.07	0.677	0.79
0.5	0.5	0.686	0.687	0.10	0.692	0.92
0.1	1.9	0.683	0.684	0.21	0.685	0.36
0.25	1.75	0.716	0.718	0.24	0.721	0.68
0.5	1.5	0.751	0.752	0.07	0.756	0.62
1	1	0.774	0.774	−0.03	0.778	0.49
0.5	4.5	0.792	0.794	0.26	0.798	0.77
1	4	0.840	0.841	0.06	0.844	0.43
2.5	2.5	0.877	0.877	0.02	0.879	0.20
0.5	9.5	0.806	0.808	0.29	0.813	0.88
1	9	0.858	0.859	0.09	0.862	0.52
2.5	7.5	0.913	0.913	0.00	0.914	0.15
5	5	0.930	0.930	0.04	0.931	0.11
50	4	0.952	0.952	0.00	0.953	0.11
50	10	0.977	0.977	0.02	0.977	0.04
100	50	0.994	0.994	0.01	0.994	0.01

Table 2 Comparison of K-factors obtained by P.W., and French Rules with exact results (side sway is permitted).

GA	GB	exact	P.W.	% Diff.	French	% Diff.
		value			Rule [7]
0.1	0.4	1.083	1.078	−0.45	1.093	0.96
0.25	0.25	1.083	1.080	−0.29	1.095	1.15
0.1	0.9	1.159	1.158	−0.09	1.170	0.99
0.25	0.75	1.162	1.164	0.21	1.178	1.40
0.5	0.5	1.164	1.169	0.40	1.183	1.65
0.1	1.9	1.286	1.283	−0.22	1.290	0.30
0.25	1.75	1.295	1.297	0.14	1.306	0.84
0.5	1.5	1.307	1.314	0.53	1.326	1.44
1	1	1.317	1.327	0.79	1.342	1.87
0.5	4.5	1.575	1.575	0.03	1.577	0.15
1	4	1.634	1.638	0.23	1.647	0.78
2.5	2.5	1.711	1.716	0.28	1.732	1.23
0.5	9.5	1.777	1.783	0.34	1.774	−0.15
1	9	1.874	1.881	0.36	1.881	0.36
2.5	7.5	2.092	2.093	0.06	2.104	0.59
5	5	2.228	2.222	−0.26	2.236	0.36
50	4	2.949	2.956	0.24	2.973	0.81
50	10	3.948	3.940	−0.21	3.939	−0.22
100	50	7.476	7.513	0.49	7.393	−1.12