A 6 × 8 Douglas fir No. 1 post supports a roof load of 20 k. Check the adequacy of the column assuming pin support conditions at the top and bottom. From Table 5.2, use Fc = 1,000 psi and E = 1.6 × 10^6 psi.

Question

A 6 × 8 Douglas fir No. 1 post supports a roof load of 20 k. Check the adequacy of the column assuming pin support conditions at the top and bottom. From Table 5.2, use [latex]F_{ c } [/latex] = 1,000 psi and E = 1.6 × [latex]10^{6} [/latex] psi.

Accepted Answer

6 × 8 S4S Douglas fir No. 1 (A = 41.25 in.² )

[latex]\frac{\ell_{ e }}{d}=\frac{12^{\prime} imes 12 in . / ft .}{5.5^{\prime \prime}}=26.2[/latex]

[latex]F_{ cE }=\frac{0.3 E }{\left(\ell_{ e } / d ight)^{2}}=\frac{0.3\left(1.6 imes 10^{6} ight)}{(26.2)^{2}}=699 psi[/latex]

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

Load duration factor for snow is [latex]C_{ D }=1.15[/latex]

(15% increase in stress above “normal” condition)

[latex] herefore F_{c}^{*}=(1,000 psi )(1.15)=1,150 psi[/latex]

The column stability factor [latex]C_{ p }[/latex] can be obtained from Table 9.3 by entering the ratio

[latex]\frac{F_{ cE }}{F_{ c }^{*}}=\frac{699 psi }{1,150 psi }=0.61[/latex]

[latex] herefore C_{ p }=0.506[/latex]

[latex]F_{c}^{\prime}=F_{c}^{*} C_{p}=(1,150 psi ) imes(.506)=582 psi[/latex]

Then,

[latex]P_{ ext {allowable }}=P_{ a }=F_{ c }^{\prime} imes A=(582 psi ) imes\left(41.25 in .^{2} ight)[/latex]

= 24,000 #

[latex]P_{ a }=24 k >P_{ ext {actual }}=20 k[/latex]

The column is adequate.

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

Table 5.2 Allowable stresses for selected engineering materials.
Materials	Unit Weight (density) [latex]\gamma[/latex](pfc)	Modules of Elasticity E (ksi)	Allowable Tension Stress [latex]F_{ t }[/latex]	Allowable Axial Compress [latex]F_{ c }[/latex]	Allowable Compress Bearing [latex]F_{ c \perp}[/latex]	Allowable Bending Stress [latex]F_{ b }[/latex]	Allowable Shear Stress [latex]F_{ v}[/latex]
Metals:
A36 Steel [latex]F_{y}[/latex] =36 ksi	490	29,000	22 ksi	22 ksi		22 ksi	14.5 ksi
A572 Grade 50/A992	490	30,000	30 ksi	30 ksi		30 ksi	20 ksi
A572 Steel [latex]F_{y}[/latex] =65 ksi	490	30,000	39 ksi	39 ksi		39 ksi	26 ksi
Aluminum	165	10,000	16 ksi	16 ksi		16 ksi	10 ksi
Iron (cast)	450	15,000	5 ksi	20 ksi		5 ksi	7.5 ksi
Brittle Materials:
Concrete	150	3,000	100 psi	1,350 psi			100 psi
Stone Masonry	165	1,000	10 psi	100 psi			10 psi
Brick Masonry	120	1,500	20 psi	300 psi			30 psi
Wood:
Doug-Fir Larch North*
• Joist & Rafters (No. 2)	35	1,700	650 psi	1,050 psi	625 psi	1,450 psi	95 psi
• Beams & Posts (No. 1) Southern Pine*	35	1,600	700 psi	1,000 psi	625 psi	1,300 psi	85 psi
• Joists & Rafters (No. 2)	35	1,600	625 psi	1,000 psi	565 psi	1,400 psi	90 psi
• Beams & Posts (D-No. 1) Hem-Fir*	35	1,600	1,050 psi	975 psi	440 psi	1,550 psi	110 psi
• Joists & Rafters (No. 2)	30	1,400	800 psi	1,050 psi	405 psi	1,150 psi	75 psi
• Beams & Posts (No. 1)	30	1,300	600 psi	850 psi	405 psi	1,000 psi	70 psi
Wood Products:
Glu-Lam Beams	35	1,800	1,100 psi	1,650 psi	650 psi	2,400 psi	165 psi
Micro-Lam Beams	37	1,800	1,850 psi	2,460 psi	750 psi	2,600 psi	285 psi
Parallam Beams	45	2,000	2,000 psi	2,900 psi	650 psi	2,900 psi	290 psi

*Averaged stress values for design.

Question 9.13: A 6 × 8 Douglas fir No. 1 post supports a roof load of 20 k....

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