Select the most economical W8 shape column, 16 feet long, with P = 180 k. Assume that lateral bracing is provided at midheight in the weak axis of buckling and that the top and bottom are pin connected. Fy = 36 ksi.

Question

Select the most economical W8 shape column, 16 feet long, with P = 180 k. Assume that lateral bracing is provided at midheight in the weak axis of buckling and that the top and bottom are pin connected. [latex]F_{y}[/latex] = 36 ksi.

Accepted Answer

Again, we need to begin by guessing at a size and then checking the adequacy of the selection.

Try W8 × 35.

[latex]W 8 imes 35\left(A=10.3 in .{ }^{2} ; r_{x}=3.51^{\prime \prime} ; r_{y}=2.03^{\prime \prime} ight)[/latex]

Determine the critical slenderness ratio:

[latex]\frac{K \ell}{r_{y}}=\frac{(0.80)\left(18^{\prime} imes 12 in . / ft . ight)}{3.09}=55.9[/latex]

[latex]\frac{K \ell}{r_{x}}=\frac{(0.80)\left(18^{\prime} imes 12 in . / ft . ight)}{5.44^{\prime \prime}}=31.8[/latex]

Buckling about the strong axis is more critical in this example because of the lateral bracing provided for the weak axis. Therefore, the [latex]F_{ a } [/latex] value is obtained from Table 9.1 based on [latex] K \ell / r=54.7[/latex]

[latex]F_{ a }=17.93 ksi[/latex]

[latex]P_{ ext {allowable }}=F_{ a } imes A=(17.93 ksi ) imes\left(10.3 in .^{2} ight)[/latex]

= 184.7 k

[latex]P_{ ext {allowable }}=184.7 k >P_{ ext {actual }}=180 k[/latex]

[latex]\% ext { stress }=\frac{180 k }{184.7 k } imes 100 \%=97.5 \%[/latex]

(very efficient selection)

Therefore, use W8 × 35.

Table 9.1

Table C-36 Allwoable Stress For compression Members of 36-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	21.56	41	19.11	81	15.24	121	10.14	161	5.76
2	21.52	42	19.03	82	15.13	122	9.99	162	5.69
3	21.48	43	18.95	83	15.02	123	9.85	163	5.62
4	21.44	44	18.86	84	14.90	124	9.70	164	5.55
5	21.39	45	18.78	85	14.79	125	9.55	165	5.49
6	21.35	46	18.70	86	14.67	126	9.41	166	5.42
7	21.30	47	18.61	87	14.56	127	9.26	167	5.35
8	21.25	48	18.53	88	14.44	128	9.11	168	5.29
9	21.21	49	18.44	89	14.32	129	8.97	169	5.23
10	21.16	50	18.35	90	14.20	130	8.84	170	5.17
11	21.10	51	18.26	91	14.09	131	8.70	171	5.11
12	21.05	52	18.17	92	13.97	132	8.57	172	5.05
13	21.00	53	18.08	93	13.84	133	8.44	173	4.99
14	20.95	54	17.99	94	13.72	134	8.32	174	4.93
15	20.89	55	17.90	95	13.60	135	8.19	175	4.88
16	20.83	56	17.81	96	13.48	136	8.07	176	4.82
17	20.78	57	17.71	97	13.35	137	7.96	177	4.77
18	20.72	58	17.62	98	13.23	138	7.84	178	4.71
19	20.66	59	17.53	99	13.10	139	7.73	179	4.66
20	20.60	60	17.43	100	12.98	140	7.62	180	4.61
21	20.54	61	17.33	101	12.85	141	7.51	181	4.56
22	20.48	62	17.24	102	12.72	142	7.41	182	4.51
23	20.41	63	17.14	103	12.59	143	7.30	183	4.46
24	20.35	64	17.04	104	12.47	144	7.20	184	4.41
25	20.28	65	16.94	105	12.33	145	7.10	185	4.36
26	20.22	66	16.84	106	12.20	146	7.01	186	4.32
27	20.15	67	16.74	107	12.07	147	6.91	187	4.27
28	20.08	68	16.64	108	11.94	148	6.82	188	4.23
29	20.01	69	16.53	109	11.81	149	6.73	189	4.18
30	19.94	70	16.43	110	11.67	150	6.64	190	4.14
31	19.87	71	16.33	111	11.54	151	6.55	191	4.09
32	19.80	72	16.22	112	11.40	152	6.46	192	4.05
33	19.73	73	16.12	113	11.26	153	6.38	193	4.01
34	19.65	74	16.01	114	11.13	154	6.30	194	3.97
35	19.58	75	15.90	115	10.99	155	6.22	195	3.93
36	19.50	76	15.79	116	10.85	156	6.14	196	3.89
37	19.42	77	15.69	117	10.71	157	6.06	197	3.85
38	19.35	78	15.58	118	10.57	158	5.98	198	3.81
39	19.27	79	15.47	119	10.43	159	5.91	199	3.77
40	19.19	80	15.36	120	10.28	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 9.11: Select the most economical W8 shape column, 16 feet long, wi...

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