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/ft
Stress 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

CD = 0.9 (D), 1.15 (S), 1.6 (W)
Ct = 1 (given)

NDS Supplement section 3.3

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

Cb = 1 (not enough info given)

NDS Supplement section 4.3

Ci = 1 (no information given)

NDS Supplement section 4.4

CT = 1 (not a truss)

 

Property Reference Design
Values (psi)
(Table 4D)
beam & stringer		 Adjustment 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
1.6		 1 1 1 1 1 1   1     1,440
1,840
2,560
tension stress parallel to grain Ft 950 0.9
1.15
1.6		 1 1   1       1     --
--
--
shear stress parallel to grain Fv 170 0.9
1.15
1.6		 1 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
1.6		 1 1   1     0.7446
0.6625
0.5379		 1     737.2
838.1
946.7
modulus 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  ✓