Problem 7.23

 

Given

 

Member size 8x12  Note that this size is considered a beam-and-stringer but is being used as a column/post.
Load axial compression for D and D+L
Stress grade and species No. 1 S-P-F(S)
Unbraced length lu = 16 ft for strong axis
lu = 8 ft for weak axis
Adjustment factors CM = 1
Ct = 1

 

 

Load Combinations

 

ASCE 7 IBC ASD Load Combination Summary Shortest-Duration Load
1 16-8 D + F D D
2 16-9 D + H + F + L + T D + L L
3 16-10 D + H + F + (Lr or S or R) D D
4 16-11 D + H + F + 0.75(L + T) + 0.75(Lr or S or R) D + 0.75L L
5 16-12 D + H + F + (W or 0.7E) D D
6 16-13 D + H + F + 0.75(W or 0.7E) + 0.75L + 0.75(Lr or S or R) D + 0.75L L
7 16-14 0.6D + W + H -- --
8 16-15 0.6D + 0.7E + H -- --

 

 

Size (NDS Supplement table 1B)

 

A = 86.25 in.2
Sxx = 165.3 in.3
Syy = 107.8 in.3
Ixx = 950.5 in.4
Iyy = 404.3 in.4

 

 

Adjusted Design Values

 

NDS Supplement table 4D

Cr = 1 (column)
 CM = 1 (given)
CF =  1 (not greater than 12")
Cfu = 1 (not a beam)

NDS Supplement section 2.3

CD = 0.9 (D), 1 (L)
Ct = 1 (given)

NDS Supplement section 3.3

CL = 1 (no flexure)

NDS Supplement section 3.7

Ke = 1  (assumed)
Let l = lu  (full length not given)
le = Ke l
le1/d1 =  Ke lu1 / 11.5 in. (NDS Supplement table 1B) = 192 in. / 11.5 in. = 16.69 (strong)
le2/d2 =  Ke lu2 / 7.5 in. (NDS Supplement table 1B) = 96 in. / 7.5 in. = 12.80 (weak)
 le1/d1 >  le2/d2  (strong axis governs)
FcE = 0.822 E'min / (le/d)2 = 1,298 (strong) or 2,208 (weak) psi
F*c = F'c without CP = 495 (D) or 550 (L) psi
c = 0.8
CP = (1+FcE/F*c)/2c - sqrt{[(1+FcE/F*c) / 2c]2 - (FcE/F*c)/c} = 0.9047 (D, strong), 0.8917 (L, strong), 0.9487 (D, weak), or 0.9422 (L, weak) 
(I calculated all four values to prove to myself that the strong axis governs.)

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 900 0.9
1		 1 1 1 1 1 1   1     --
--
--
tension stress parallel to grain Ft 450 0.9
1		 1 1   1       1     --
--
--
shear stress parallel to grain Fv 125 0.9
1		 1 1           1     --
--
--
compression stress perpendicular to grain Fc⊥ 335   1 1           1   1 --
compression stress parallel to grain Fc 550 0.9
1		 1 1   1     0.9047
0.8917		 1     447.8
490.4
modulus of elasticity (or MOE) E 1,200,000   1 1           1     --
modulus of elasticity for stability calculations Emin 440,000   1 1           1 1   440,000

 

 

Actual Stress (ASD)

 

fc = P/A ≤ F'c

Pmax = F'cA = 38,620 (D) or 42,300 lb (D+L)