An 11-foot-tall Douglas fir glu-lam column is used to support a roof load (dead load plus snow) as shown. A partial-height wall braces the 5 1/8^" direction, and knee braces from the beam support the six inch face. Determine the capacity of the column.

Question

An 11-foot-tall Douglas fir glu-lam column is used to support a roof load (dead load plus snow) as shown. A partial-height wall braces the [latex]5 \frac{1}{8}^{ \prime \prime }[/latex] direction, and knee braces from the beam support the six inch face. Determine the capacity of the column.

Accepted Answer

[latex]5\frac{1}{8}^{\prime \prime} imes 6^{\prime \prime} ext { glu-lam post: }\left(A=30.8 in.^{2} ; F_{ c }=1650 psi ; E=1.8 imes 10^{6} psi ight)[/latex]

Buckling in the plane of the 6" dimension:

[latex]\frac{\ell_{ e }}{d}=\frac{8^{\prime} imes 12 in. / ft. }{6^{\prime \prime}}=16 \Longleftarrow[/latex] Governs

In the [latex]5 \frac{1}{8}^{ \prime \prime }[/latex] direction:

[latex]\frac{\ell_{ e }}{d}=\frac{8^{\prime} imes 12 in. / ft. }{6^{\prime \prime}}=16 \Longleftarrow[/latex] Governs

Comparing the buckling condition in both directions, the 6" direction is more critical and, therefore, governs.

[latex]F_{ cE }=\frac{0.418 E}{\left(\ell_{ e } / d ight)^{2}}=\frac{0.418 imes\left(1.8 imes 10^{6} psi ight)}{(16)^{2}}[/latex]

= 2,939 psi

[latex]F_{ c }{ }^{*} \cong F_{ c } C_{ D }=1,650 psi imes(1.15)=1,898 psi[/latex]

[latex]\frac{F_{ cE }}{F_{ c }}=\frac{2,939 psi }{1,898 psi }=1.55[/latex]

From Table 9.3, [latex]C_{ p }=0.883.[/latex]

[latex] herefore F_{c}^{\prime}=F_{c}^{*} C p=1,898 ext { psi } imes(0.883)=1,581 psi[/latex]

[latex]P_{ a }=F_{ c }^{\prime} imes A=1,581 psi imes\left(30.8 in .^{2} ight)=48,700 \#[/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 9.15: An 11-foot-tall Douglas fir glu-lam column is used to suppor...

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