A 24-foot-tall steel column (W14 × 82) with Fy = 50 ksi has pins at both ends. Its weak axis is braced at midheight, but the column is free to buckle the full 24 feet in the strong direction. Determine the safe load capacity for this column.

Question

A 24-foot-tall steel column (W14 × 82) with [latex]F_{ y } [/latex]= 50 ksi has pins at both ends. Its weak axis is braced at midheight, but the column is free to buckle the full 24 feet in the strong direction. Determine the safe load capacity for this column.

Accepted Answer

Properties of the W14 × 82:

A = 24.1 in.²

[latex]r_{x}[/latex]= 6.05"

[latex]r_{y}[/latex]= 2.48"

Compute the slenderness ratio about both axes to determine the critical direction for buckling.

[latex]\frac{K \ell}{r_{x}}=\frac{24^{\prime} imes 12 in. / ft. }{6.05^{\prime \prime}}=47.6[/latex]

[latex]\frac{K \ell}{r_{y}}=\frac{12^{\prime} imes 12 in . / ft. }{2.48^{\prime \prime}}=58.1[/latex]

The larger slenderness ratio governs; therefore, the weak axis (y) buckling is used in determining [latex]F_{ a }[/latex].

From Table 9.2,

Interpolating for[latex]K \ell / r=58.1 ; F_{ a}=23.04 ksi[/latex]

[latex] herefore P_{ ext {allowable }}=F_{ a } imes A=23.04 k / in .^{2} imes 24.1 in .^{2}=555 k[/latex]

Table 9.2

Table C-50 Allowable Stress For compression Members of 50-ksi Specified Yield Stress [latex] ext { Steel }^{ a }[/latex]
[latex]\frac{K l}{r}[/latex]	[latex]\begin{gathered}F_{a} \ ext { (ksi) }\end{gathered}[/latex]	[latex]\frac{K l}{r}[/latex]	[latex]\begin{gathered}F_{a} \ ext { (ksi) }\end{gathered}[/latex]	[latex]\frac{K l}{r}[/latex]	[latex]\begin{gathered}F_{a} \ ext { (ksi) }\end{gathered}[/latex]	[latex]\frac{K l}{r}[/latex]	[latex]\begin{gathered}F_{a} \ ext { (ksi) }\end{gathered}[/latex]	[latex]\frac{K l}{r}[/latex]	[latex]\begin{gathered}F_{a} \ ext { (ksi) }\end{gathered}[/latex]
1	29.94	41	25.69	81	18.81	121	10.20	161	5.76
2	29.87	42	25.55	82	18.61	122	10.03	162	5.69
3	29.80	43	25.40	83	18.41	123	9.87	163	5.62
4	29.73	44	25.26	84	18.20	124	9.71	164	5.55
5	29.66	45	25.11	85	17.99	125	9.56	165	5.49
6	29.58	46	24.96	86	17.79	126	9.41	166	5.42
7	29.50	47	24.81	87	17.58	127	9.26	167	5.35
8	29.42	48	24.66	88	17.37	128	9.11	168	5.29
9	29.34	49	24.51	89	17.15	129	8.97	169	5.23
10	29.26	50	24.35	90	16.94	130	8.84	170	5.17
11	29.17	51	24.19	91	16.72	131	8.70	171	5.11
12	29.08	52	24.04	92	16.50	132	8.57	172	5.05
13	28.99	53	23.88	93	16.29	133	8.44	173	4.99
14	28.90	54	23.72	94	16.06	134	8.32	174	4.93
15	28.80	55	23.55	95	15.84	135	8.19	175	4.88
16	28.71	56	23.39	96	15.62	136	8.07	176	4.82
17	28.61	57	23.22	97	15.39	137	7.96	177	4.77
18	28.51	58	23.06	98	15.17	138	7.84	178	4.71
19	28.40	59	22.89	99	14.94	139	7.73	179	4.66
20	28.30	60	22.72	100	14.71	140	7.62	180	4.61
21	28.19	61	22.55	101	14.47	141	7.51	181	4.56
22	28.08	62	22.37	102	14.24	142	7.41	182	4.51
23	27.97	63	22.20	103	14.00	143	7.30	183	4.46
24	27.86	64	22.02	104	13.77	144	7.20	184	4.41
25	27.75	65	21.85	105	13.53	145	7.10	185	4.36
26	27.63	66	21.67	106	13.29	146	7.01	186	4.32
27	27.52	67	21.49	107	13.04	147	6.91	187	4.27
28	27.40	68	21.31	108	12.80	148	6.82	188	4.23
29	27.28	69	21.12	109	12.57	149	6.73	189	4.18
30	27.15	70	20.94	110	12.34	150	6.64	190	4.14
31	27.03	71	20.75	111	12.12	151	6.55	191	4.09
32	26.90	72	20.56	112	11.90	152	6.46	192	4.05
33	26.77	73	20.38	113	11.69	153	6.38	193	4.01
34	26.64	74	20.10	114	11.49	154	6.30	194	3.97
35	26.51	75	19.99	115	11.29	155	6.22	195	3.93
36	26.38	76	19.80	116	11.10	156	6.14	196	3.89
37	26.25	77	19.61	117	10.91	157	6.06	197	3.85
38	26.11	78	19.41	118	10.72	158	5.98	198	3.81
39	25.97	79	19.21	119	10.55	159	5.91	199	3.77
40	25.83	80	19.01	120	10.37	160	5.83	200	3.73
[latex]^ { a }[/latex] [latex] ext { When element width-to-thickness ratio exceeds noncompact section limits of Sect. B5.1. }[/latex] [latex] ext { see Appendix B5. }[/latex] [latex] ext { Note: } C _{ c }=126.1[/latex]

Question 9.8: A 24-foot-tall steel column (W14 × 82) with Fy = 50 ksi has ...

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