Question

PROBLEM #1 (CET 4450 and EVE 4450) Find: A 4 x 6 carries an axial compressive force caused by dead, live, and roof live loads. Lumber is No. 1 DF-L. CM = 1.0, C=1.0, and C = 1.0. The maximum column load for each LRFD load combination if the unbraced length of the member is a.) 3 ft b.) 6 ft c.) 9 ft d.)12 ft For a, b, c, and d please find le=Kelu : leldy, assuming Ke-1 Fon* (ksi) Fc (ksi) CP Fen' (ksi) Pn' = Fon'

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Given that A uxu carries an Mai compressive force caused live and roof live loads. dead, by 11 CM =1, et = 1 and (i=1, Cf al, CD =1 HI - 3++ 3X12.536" Hy =oft - 6x12 • 72", H3=qft - 9X123 108" Hu 12ft - 12*12 = 144 tb=1000 Ft-675, fy=180 -> Fc (Ferpendicular to grain] =625, - fc [ parallel to graio] E = 1970,00,000 psi, Emin - 620000psi EXCm & (+*C; 1998100psi = Emincm &C ; * 4 * CG 6.28 lofpsi d = 3.5" A = 3.5x3.5 = 12-25802 = 1350 € Em columes height #1 =3&t

column height +1-347 Le = Kel = 1,6XH, = 1.0+36 36" Assuming those both ends are pioned. Le T - 10-285 3.5 [Needs to be less than so :: NOS 3.7113] column stability factor: Fe = 0.8228 elamin 0-822 %62X105 (10.28592 ICE a 4817-19 psi F - FCX Co X con & 4 x C4 X Ci Ft 1350 * 1*1*1*1 * = 1350psi Csioan od it FCE it FCE fc •ECE JC FA Cswan a csuan Cswan

4819-19 1350 141-19 1330 4819.19 1350 **0.8 X08 (cp=0.9337 Anial Capauty : FC = FAX CF X Cmin X ( X CF X G X Cp Fcla 135000 9534 FC = 1260.62 psi Py = tc'x Area 1260 62 x 15.25 P = 15u42.65 16 b) for H2-6 72 3.5 le = 1(6X12)=92, be 320.57 [reeds to be less than ro) column stability factor : 0822x6.2 X10 ICE 0.822x t'min (20.572 Le - 12 04:3 PS)

@ wat 1+0.892 110.8912 10.89 0.892 2X0.8 280.8 FCE 1204.3 -0-892 1350 Tcp=0.65 Axial capacity tc' - 135080.650 877.67Psi {fc' = F C X CH & cm X 49 Cf x G xCp] P2 - & cxArea 10751.55db = 873.67 x 12.25 For H3-9ft: le. 1x [9x12] -108, 30-859 le d [leeds to be less than so] Column stability factor ? 0.822762x105 (30.85.12 FCE

ICE $35-49 psi From O 525-49 -0.2966 FE FC& 13.50 CPF T+0.39.66 (140.39.66 6.2966 08 = 0.3568 ICP Axial capacity tc' - 135080.3568 Tusi opsi Fcxar Area 481.8 x 12.25 5902.11b d) For Hy = 12ft. le = 1X (12x12] : luu, luu 41.14 d 3.5 Column stability factor: = 0.822x 6.28105 (ul.14272 ICE 301.08 psi

FCE 301.08 ICA ২ _0 0.2230 from O 1+0.2230 140.2231 opt 0.22% 2% 6.8 ২ X - ৪ cp = 0.2172 Axial capacity to - 135080.2172 293.22 psi Pu • Fc'* Area 293.22% 12.25 3591.90db