Problem 7.28
Given
Member size 6x10 exterior column Load axial compression + bending from wind about strong axis
D = 5 kip
S = 15 kip
W = 200 lb/ftStress grade and species Select Structural DF-L Unbraced length lu = 16 ft for strong axis
lu = 0 for weak axis (wall framing)Adjustment factors CM = 1
Ct = 1
Load Combinations
ASCE 7 IBC ASD Load Combination Summary Load (kip, lb/ft) Shortest-Duration Load 1 16-8 D + F D 5 D 2 16-9 D + H + F + L + T D 5 D 3 16-10 D + H + F + (Lr or S or R) D + S 20 S 4 16-11 D + H + F + 0.75(L + T) + 0.75(Lr or S or R) D + 0.75S 16.25 S 5 16-12 D + H + F + (W or 0.7E) D + W 5, 200 W 6 16-13 D + H + F + 0.75(W or 0.7E) + 0.75L + 0.75(Lr or S or R) D + 0.75(W+S) 16.25, 150 W 7 16-14 0.6D + W + H -- -- -- 8 16-15 0.6D + 0.7E + H -- -- -- (D)max = 5 kip
(D+S)max = 20 kip
(D+W)max = 5 kip, 200 lb/ft
(D+S+W)max = 16.25 kip, 150 lb/ft
Size (NDS Supplement table 1B)
A = 52.25 in.2
Sxx = 82.73 in.3
Syy = 47.90 in.3
Ixx = 393.0 in.4
Iyy = 131.7 in.4
Adjusted Design Values
NDS Supplement table 4D Cr = 1 (column)
CM = 1 (given)
CF = 1 (does not exceed 12 in.)
Cfu = 1 (not a beam)NDS Supplement section 2.3
NDS Supplement section 3.3CD = 0.9 (D), 1.15 (S), 1.6 (W)
Ct = 1 (given)CL = 1 (no flexure)
NDS Supplement section 3.7
Ke = 1 (assumed)
le = Ke l
le1/d1 = Ke lu1 / 9.5 in. = 192 in. / 9.5 in. = 20.21 (strong)
le2/d2 = Ke lu2 / 5.5 in. = 0 / 5.5 in. = 0 (weak)
le1/d1 > le2/d2 (strong axis governs)
FcE = 0.822 E'min / (le/d)2 = 1,167 psi
F*c = F'c without CP = 990 (D), 1,265 (S), or 1,760 (W) psi
c = 0.8
CP = (1+FcE/F*c)/2c - sqrt{[(1+FcE/F*c) / 2c]2 - (FcE/F*c)/c}
= 0.7446 (D), 0.6625 (S), or 0.5379 (W)NDS Supplement section 3.10
NDS Supplement section 4.3Cb = 1 (not enough info given)
Ci = 1 (no information given)
NDS Supplement section 4.4
CT = 1 (not a truss)
Property Reference Design
Values (psi)
(Table 4D)
beam & stringerAdjustment Factors (Table 4.3.1) Adjusted Design
Values (psi)CD CM Ct CL CF Cfu Cr CP Ci CT Cb bending stress Fb 1,600 0.9
1.15
1.61 1 1 1 1 1 1 1,440
1,840
2,560tension stress parallel to grain Ft 950 0.9
1.15
1.61 1 1 1 --
--
--shear stress parallel to grain Fv 170 0.9
1.15
1.61 1 1 --
--
--compression stress perpendicular to grain Fc⊥ 625 1 1 1 1 -- compression stress parallel to grain Fc 1,100 0.9
1.15
1.61 1 1 0.7446
0.6625
0.53791 737.2
838.1
946.7modulus of elasticity (or MOE) E 1,600,000 1 1 1 -- modulus of elasticity for stability calculations Emin 580,000 1 1 1 1 580,000
Actual Stresses for (D) Load Combination (ASD)
(D)max = 5 kip
Axial compression...
fc = P/A = 5,000 lb / 52.25 in.2 = 95.69 psi ≤ 737.2 psi ✓
Bending stress...
wD = 0 lb/ft
Vmax = 0 lb/ft x 16 ft / 2 = 0 lb
Mmax = 0.5 x 8 ft x 0 lb = 0 lb-ft x 12 in./ft = 0 lb-in.fb = M/S = 0 lb-in. / 82.73 in.3 = 0 psi ≤ 1,440 psi ✓
Check formula in NDS section 3.9.2 for combined axial compression and bending...
(fc/F'c)2 + fb1/{F'b1[1-(fc/FcE1)]} + fb2/{F'b2[1-(fc/FcE2)-(fb1/FbE)2]} ≤ 1.0
Actual Stresses for (D+S) Load Combination (ASD)
(D+S)max = 20 kip
Axial compression...
fc = P/A = 20,000 lb / 52.25 in.2 = 382.8 psi ≤ 838.1 psi ✓
Bending stress...
wD = 0 lb/ft
Vmax = 0 lb/ft x 16 ft / 2 = 0 lb
Mmax = 0.5 x 8 ft x 0 lb = 0 lb-ft x 12 in./ft = 0 lb-in.fb = M/S = 0 lb-in. / 82.73 in.3 = 0 psi ≤ 1,840 psi ✓
Check formula in NDS section 3.9.2 for combined axial compression and bending...
(fc/F'c)2 + fb1/{F'b1[1-(fc/FcE1)]} + fb2/{F'b2[1-(fc/FcE2)-(fb1/FbE)2]} ≤ 1.0
Actual Stresses for (D+W) Load Combination (ASD)
(D+W)max = 5 kip, 200 lb/ft
Axial compression...
fc = P/A = 5,000 lb / 52.25 in.2 = 95.69 psi ≤ 946.7 psi ✓
Bending stress...
wD = 200 lb/ft
Vmax = 200 lb/ft x 16 ft / 2 = 1,600 lb
Mmax = 0.5 x 8 ft x 1,600 lb = 6400 lb-ft x 12 in./ft = 76,800 lb-in.fb = M/S = 76,800 lb-in. / 82.73 in.3 = 928.3 psi ≤ 2,560 psi ✓
Check formula in NDS section 3.9.2 for combined axial compression and bending...
(fc/F'c)2 + fb1/{F'b1[1-(fc/FcE1)]} + fb2/{F'b2[1-(fc/FcE2)-(fb1/FbE)2]} ≤ 1.0
(95.69/946.7)2 + 928.3/{2,560[1-(95.69/1,167)]} + 0 = 0.4052 ≤ 1.0 ✓
Actual Stresses for (D+S+W) Load Combination (ASD)
(D+S+W)max = 16.25 kip, 150 lb/ft
Axial compression...
fc = P/A = 16,250 lb / 52.25 in.2 = 311.0 psi ≤ 946.7 psi ✓
Bending stress...
wD = 150 lb/ft
Vmax = 150 lb/ft x 16 ft / 2 = 1,200 lb
Mmax = 0.5 x 8 ft x 1,200 lb = 4,800 lb-ft x 12 in./ft = 57,600 lb-in.fb = M/S = 57,600 lb-in. / 82.73 in.3 = 696.4 psi ≤ 2,560 psi ✓
Check formula in NDS section 3.9.2 for combined axial compression and bending...
(fc/F'c)2 + fb1/{F'b1[1-(fc/FcE1)]} + fb2/{F'b2[1-(fc/FcE2)-(fb1/FbE)2]} ≤ 1.0
(311.0/946.7)2 + 696.4/{2,560[1-(311.0/1,167)]} + 0 = 0.4788 ≤ 1.0 ✓