An 18-foot-tall 6 × 8 Southern Pine column supports a roof load (dead load plus a seven-day live load) equal to 16 k. The weak axis of buckling is braced at a point nine feet, six inches from the bottom support. Determine the adequacy of the column.

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Accepted Answer

[latex]6 imes 8 ext { S4S Southern Pine Post: }\left(A=41.25 in.^{2} ;F_{ c }=975 psi ; E=1.6 imes 10^{6} psi ight)[/latex]

Check the slenderness ratio about the weak axis:

[latex]\frac{\ell_{ e }}{d}=\frac{\left(9.5^{\prime} imes 12 in . / ft . ight)}{5.5^{\prime \prime}}=20.7[/latex]

The slenderness ratio about the strong axis is

[latex]\frac{\ell_{ e }}{d}=\frac{\left(18^{\prime} imes 12 in . / ft . ight)}{7.5^{\prime \prime}}=28.8[/latex]

This value governs.

[latex]F_{ cE }=\frac{0.3 E}{\left(\ell_{ e } / d ight)^{2}}=\frac{0.3\left(1.6 imes 10^{6} psi ight)}{(28.8)^{2}}=579 psi[/latex]

[latex]F_{ c }^{*} \cong F_{ c } C_{ D }[/latex]

where

[latex]C_{ D }[/latex]=1.25 for 7-day-duration load

[latex] herefore F_{ c }^{*}=975 psi imes 1.25=1,219 psi[/latex]

[latex]\frac{F_{ cE }}{F_{ c }^{*}}=\frac{579 psi }{1,219 psi }=0.47[/latex]

From Table 9.3, [latex]C_{ p }=0.412[/latex]

[latex] herefore F_{c}^{\prime}=F_{c}^{*} C_{p}=1,219 ext { psi } imes 0.412=502 ext { psi }[/latex]

[latex]P_{ a }=F_{ c }^{\prime} imes A=(502 psi ) imes\left(41.25 in .^{2} ight)=20,700 \#[/latex]

[latex]P_{ a }=20.7 k >P_{ ext {actual }}=16 ext { kips }[/latex]

[latex] herefore O K[/latex]

Table 9.3

[latex] ext { Column S+A1:L53tability Factor } C_{p}[/latex]
[latex]{ }^{"} C _{ p }^{"}[/latex] [latex]F _{ C }^{\prime}= C _{ p } \cdot F _{ c }^{*} \quad F _{ CE }=\frac{30 E }{(l / d )^{2}} ext { for sawn posts } F _{ CF }=\frac{.418 E }{(l / d )^{2}} ext { for Glu-lam posts }[/latex]
[latex]\frac{F_{C E}}{F_{C}^{*}}[/latex]	Sawn [latex]C_{p}[/latex]	Glu-Lam [latex]C_{p}[/latex]	[latex]\frac{F_{C E}}{F_{C}^{*}}[/latex]	Sawn [latex]C_{p}[/latex]	Glu-Lam [latex]C_{p}[/latex]	[latex]\frac{F_{C E}}{F_{C}^{*}}[/latex]	Sawn [latex]C_{p}[/latex]	Glu-Lam [latex]C_{p}[/latex]	[latex]\frac{F_{C E}}{F_{C}^{*}}[/latex]	Sawn [latex]C_{p}[/latex]	Glu-Lam [latex]C_{p}[/latex]
0.00	0.000	0.000	0.60	0.500	0.538	1.20	0.750	0.822	2.40	0.894	0.940
0.01	0.010	0.010	0.61	0.506	0.545	1.22	0.755	0.826	2.45	0.897	0.941
0.02	0.020	0.020	0.62	0.512	0.552	1.24	0.760	0.831	2.50	0.899	0.943
0.03	0.030	0.030	0.63	0.518	0.559	1.26	0.764	0.836	2.55	0.901	0.944
0.04	0.040	0.040	0.64	0.524	0.566	1.28	0.769	0.840	2.60	0.904	0.946
0.05	0.049	0.050	0.65	0.530	0.573	1.30	0.773	0.844	2.65	0.906	0.947
0.06	0.059	0.060	0.66	0.536	0.580	1.32	0.777	0.848	2.70	0.908	0.949
0.07	0.069	0.069	0.67	0.542	0.587	1.34	0.781	0.852	2.75	0.910	0.950
0.08	0.079	0.079	0.68	0.548	0.593	1.36	0.785	0.855	2.80	0.912	0.951
0.09	0.088	0.089	0.69	0.553	0.600	1.38	0.789	0.859	2.85	0.914	0.952
0.10	0.098	0.099	0.70	0.559	0.607	1.40	0.793	0.862	2.90	0.916	0.953
0.11	0.107	0.109	0.71	0.564	0.613	1.42	0.796	0.865	2.95	0.917	0.954
0.12	0.117	0.118	0.72	0.569	0.619	1.44	0.800	0.868	3.00	0.919	0.955
0.13	0.126	0.128	0.73	0.575	0.626	1.46	0.803	0.871	3.05	0.920	0.956
0.14	0.136	0.138	0.74	0.580	0.632	1.48	0.807	0.874	3.10	0.922	0.957
0.15	0.145	0.147	0.75	0.585	0.638	1.50	0.810	0.877	3.15	0.923	0.958
0.16	0.154	0.157	0.76	0.590	0.644	1.52	0.813	0.879	3.20	0.925	0.959
0.17	0.164	0.167	0.77	0.595	0.650	1.54	0.816	0.882	3.25	0.926	0.960
0.18	0.173	0.176	0.78	0.600	0.655	1.56	0.819	0.884	3.30	0.927	0.961
0.19	0.182	0.186	0.79	0.605	0.661	1.58	0.822	0.887	3.35	0.929	0.961
0.20	0.191	0.195	0.80	0.610	0.667	1.60	0.825	0.889	3.40	0.930	0.962
0.21	0.200	0.205	0.81	0.614	0.672	1.62	0.827	0.891	3.45	0.931	0.963
0.22	0.209	0.214	0.82	0.619	0.678	1.64	0.830	0.893	3.50	0.932	0.963
0.23	0.218	0.224	0.83	0.623	0.683	1.66	0.832	0.895	3.55	0.933	0.964
0.24	0.227	0.233	0.84	0.628	0.688	1.68	0.835	0.897	3.60	0.934	0.965
0.25	0.235	0.242	0.85	0.632	0.693	1.70	0.837	0.899	3.65	0.936	0.965
0.26	0.244	0.252	0.86	0.637	0.698	1.72	0.840	0.901	3.70	0.937	0.966
0.27	0.253	0.261	0.87	0.641	0.703	1.74	0.842	0.903	3.75	0.938	0.966
0.28	0.261	0.270	0.88	0.645	0.708	1.76	0.844	0.904	3.80	0.938	0.967
0.29	0.270	0.279	0.89	0.649	0.713	1.78	0.846	0.906	3.85	0.939	0.968
0.30	0.278	0.288	0.90	0.653	0.718	1.80	0.849	0.908	3.90	0.940	0.968
0.31	0.287	0.297	0.91	0.658	0.722	1.82	0.851	0.909	3.95	0.941	0.969
0.32	0.295	0.306	0.92	0.661	0.727	1.84	0.853	0.911	4.00	0.942	0.969
0.33	0.304	0.315	0.93	0.665	0.731	1.86	0.855	0.912	4.05	0.943	0.969
0.34	0.312	0.324	0.94	0.669	0.735	1.88	0.857	0.914	4.10	0.944	0.970
0.35	0.320	0.333	0.95	0.673	0.740	1.90	0.858	0.915	4.15	0.944	0.970
0.36	0.328	0.342	0.96	0.677	0.744	1.92	0.860	0.916	4.20	0.945	0.971
0.37	0.336	0.351	0.97	0.680	0.748	1.94	0.862	0.918	4.25	0.946	0.971
0.38	0.344	0.360	0.98	0.684	0.752	1.96	0.864	0.919	4.30	0.947	0.972
0.39	0.352	0.368	0.99	0.688	0.756	1.98	0.866	0.920	4.35	0.947	0.972
0.40	0.360	0.377	1.00	0.691	0.760	2.00	0.867	0.921	4.40	0.948	0.972
0.41	0.367	0.386	1.01	0.694	0.764	2.02	0.869	0.922	4.45	0.949	0.973
0.42	0.375	0.394	1.02	0.698	0.767	2.04	0.870	0.924	4.50	0.949	0.973
0.43	0.383	0.403	1.03	0.701	0.771	2.06	0.872	0.925	4.55	0.950	0.974
0.44	0.390	0.411	1.04	0.704	0.774	2.08	0.874	0.926	4.60	0.950	0.974
0.45	0.398	0.420	1.05	0.708	0.778	2.10	0.875	0.927	4.65	0.951	0.974
0.46	0.405	0.428	1.06	0.711	0.781	2.12	0.876	0.928	4.70	0.952	0.975
0.47	0.412	0.436	1.07	0.714	0.784	2.14	0.878	0.929	4.75	0.952	0.975
0.48	0.419	0.444	1.08	0.717	0.788	2.16	0.879	0.930	4.80	0.953	0.975
0.49	0.427	0.453	1.09	0.720	0.791	2.18	0.881	0.931	4.85	0.953	0.975
0.50	0.434	0.461	1.10	0.723	0.794	2.20	0.882	0.932	4.90	0.954	0.976
0.51	0.441	0.469	1.11	0.726	0.797	2.22	0.883	0.932	5.00	0.955	0.976
0.52	0.448	0.477	1.12	0.729	0.800	2.24	0.885	0.933	6.00	0.963	0.981
0.53	0.454	0.484	1.13	0.731	0.803	2.26	0.886	0.934	8.00	0.973	0.986
0.54	0.461	0.492	1.14	0.734	0.806	2.28	0.887	0.935	10.00	0.979	0.989
0.55	0.468	0.500	1.15	0.737	0.809	2.30	0.888	0.936	20.00	0.990	0.995
0.56	0.474	0.508	1.16	0.740	0.811	2.32	0.889	0.937	40.00	0.995	0.997
0.57	0.481	0.515	1.17	0.742	0.814	2.34	0.891	0.937	60.00	0.997	0.998
0.58	0.487	0.523	1.18	0.745	0.817	2.36	0.892	0.938	100.00	0.998	0.999
0.59	0.494	0.530	1.19	0.747	0.819	2.38	0.893	0.939	200.00	0.999	0.999

Question 9.14: An 18-foot-tall 6 × 8 Southern Pine column supports a roof l...

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