Problem 7.32

 

Given

 

Member size 2X6 exterior stud wall 16" OC
Load axial compression + bending from wind about strong axis
D = 800 lb/ft
L = 800 lb/ft
Lr = 400 lb/ft
W = 15 psf
Stress grade and species No. 1 DF-L
Unbraced length lu = 14 ft for strong axis
lu = 0 for weak axis (sheathing)
Adjustment factors CM = 1
Ct = 1
Ci = 1

 

 

Load Combinations

 

ASCE 7 IBC ASD Load Combination Summary Load (lb/ft, psf) Load (lb, lb/ft) Shortest-Duration Load
1 16-8 D + F D 800 1,067 D
2 16-9 D + H + F + L + T D + L 1,600 2,133 L
3 16-10 D + H + F + (Lr or S or R) D + Lr 1,200 1,600 Lr
4 16-11 D + H + F + 0.75(L + T) + 0.75(Lr or S or R) D + 0.75(L+Lr) 1,700 2,267 Lr
5 16-12 D + H + F + (W or 0.7E) D + W 800, 15 1,067, 20 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+L+Lr) 1,700, 11.25 2,267, 15 W
7 16-14 0.6D + W + H --     --
8 16-15 0.6D + 0.7E + H --     --

PD, L, Lr = (w x 1 ft/12 in.)(16 in.)
wW = W x (16 in. x 1 ft/12 in.)

(D)max = 1,067 lb
(D+L)max = 2,133 lb
(D+Lr)max = 1,600 lb  (D+L+Lr is larger and has the same CD)
(D+L+Lr)max = 2,267 lb
(D+W)max = 1,067 lb, 20 lb/ft
(D+L+Lr+W)max = 2,267 lb, 15 lb/ft

 

 

Size (NDS Supplement table 1B)

 

A = 8.25 in.2
Sxx = 7.563 in.3
Syy = 2.063 in.3
Ixx = 20.80 in.4
Iyy = 1.547 in.4

 

 

Adjusted Design Values

 

NDS Supplement table 4A

Cr = 1.15 (16 in. OC)
CM = 1 (given)
CF =  1.5 for Fb, 1.5 for Ft, 1.15 for Fc 
Cfu = 1 (bending about strong axis)

NDS Supplement section 2.3

CD = 0.9 (D), 1 (L), 1.25 (Lr), 1.6 (W)
Ct = 1 (given)

NDS Supplement section 3.3

CL = 1 (sheathing)

NDS Supplement section 3.7

Ke = 1  (assumed)
le = Ke l
le1/d1 =  Ke lu1 / 5.5 in. = 168 in. / 5.5 in. = 30.55 (strong) 
le2/d2 =  Ke lu2 / 1.5 in. = 0 / 1.5 in. = 0 (weak)
 le1/d1 >  le2/d2  (strong axis governs)
 FcE = 0.822 E'min / (le/d)2 = 546.2 psi
F*c = F'c without CP = 1,485 (D), 1,650 (L), 2,063 (Lr), or 2,640 (W) psi
c = 0.8
CP = (1+FcE/F*c)/2c - sqrt{[(1+FcE/F*c) / 2c]2 - (FcE/F*c)/c}
      = 0.3342 (D), 0.3044 (L), 0.2483 (Lr), or 0.1972 (W)

NDS Supplement section 3.10

Cb = 1 (not enough info given)

NDS Supplement section 4.3

Ci = 1 (given)

NDS Supplement section 4.4

CT = 1 (not a truss)

 

Property Reference Design
Values (psi)
(Table 4A)		 Adjustment Factors (Table 4.3.1) Adjusted Design
Values (psi)
CD CM Ct CL CF Cfu Cr CP Ci CT Cb
bending stress Fb 1,000 0.9
1
1.25
1.6		 1 1 1 1.3 1 1.15   1     1,346
1,495
1,869
2,392
tension stress parallel to grain Ft 675 0.9
1
1.25
1.6		 1 1   1.3       1     --
--
--
--
shear stress parallel to grain Fv 180 0.9
1
1.25
1.6		 1 1           1     --
--
--
--
compression stress perpendicular to grain Fc⊥ 625   1 1           1   1 --
compression stress parallel to grain Fc 1,500 0.9
1
1.25
1.6		 1 1   1.1     0.3342
0.3044
0.2483
0.1972		 1     496.3
502.3
512.1
520.6
modulus of elasticity (or MOE) E 1,700,000   1 1           1     --
modulus of elasticity for stability calculations Emin 620,000   1 1           1 1   620,000

 

 

Actual Stresses for (D) Load Combination (ASD)

 

(D)max = 1,067 lb

Axial compression...

fc = P/A = 1,067 lb / 8.25 in.2 = 129.3 psi ≤ 496.3 psi  ✓

Bending stress...

wD = 0 lb/ft
Vmax = 0 lb/ft x 14 ft / 2 = 0 lb
Mmax = 0.5 x 7 ft x 0 lb = 0 lb-ft x 12 in./ft = 0 lb-in.

fb = M/S = 0 lb-in. / 7.563 in.3 = 0 psi ≤ 1,346 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+L) Load Combination (ASD)

 

(D+L)max = 2,133 lb

Axial compression...

fc = P/A = 2,133 lb / 8.25 in.2 = 258.5 psi ≤ 502.3 psi  ✓

Bending stress...

wD = 0 lb/ft
Vmax = 0 lb/ft x 14 ft / 2 = 0 lb
Mmax = 0.5 x 7 ft x 0 lb = 0 lb-ft x 12 in./ft = 0 lb-in.

fb = M/S = 0 lb-in. / 7.563 in.3 = 0 psi ≤ 1,495 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+L+Lr) Load Combination (ASD)

 

(D+L+Lr)max = 2,267 lb

Axial compression...

fc = P/A = 2,267 lb / 8.25 in.2 = 274.8 psi ≤ 512.1 psi  ✓

Bending stress...

wD = 0 lb/ft
Vmax = 0 lb/ft x 14 ft / 2 = 0 lb
Mmax = 0.5 x 7 ft x 0 lb = 0 lb-ft x 12 in./ft = 0 lb-in.

fb = M/S = 0 lb-in. / 7.563 in.3 = 0 psi ≤ 1,869 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 = 1,067 lb, 20 lb/ft

Axial compression...

fc = P/A = 1,067 lb / 8.25 in.2 = 129.3 psi ≤ 520.6 psi  ✓

Bending stress...

wD = 20 lb/ft
Vmax = 20 lb/ft x 14 ft / 2 = 140 lb
Mmax = 0.5 x 7 ft x 140 lb = 490 lb-ft x 12 in./ft = 5,880 lb-in.

fb = M/S = 5,880 lb-in. / 7.563 in.3 = 777.5 psi ≤ 2,392 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

(129.3/520.6)2 + 777.5/{2,392[1-(129.3/546.2)]} + 0 = 0.4875 ≤ 1.0  ✓

 

 

Actual Stresses for (D+L+Lr+W) Load Combination (ASD)

 

(D+L+Lr+W)max = 2,267 lb, 15 lb/ft

Axial compression...

fc = P/A = 2,267 lb / 8.25 in.2 = 274.8 psi ≤ 520.6 psi  ✓

Bending stress...

wD = 15 lb/ft
Vmax = 15 lb/ft x 14 ft / 2 = 105 lb
Mmax = 0.5 x 7 ft x 105 lb = 367.5 lb-ft x 12 in./ft = 4,410 lb-in.

fb = M/S = 4,410 lb-in. / 7.563 in.3 = 583.1 psi ≤ 2,392 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

(274.8/520.6)2 + 583.1/{2,392[1-(274.8/546.2)]} + 0 = 0.7692 ≤ 1.0  ✓