Problem 6.5
Given
Load PD = 400 lb
PLr = 1,600 lbLoad combination D+Lr (ASD)
1.2D+1.6Lr (LRFD)Span L = 8 ft Member size 4x8 Stress grade and species No. 1 DF-L Unbraced length lu = L = 8 ft Moisture content MC ≤ 19% Live load deflection limit Allow. Δ ≤ L/360 = 0.2667 in. Dry-service conditions Normal temperatures Bending about strong axis
Size Category (NDS Supplement tables 1A and 1B)
dimension lumber
dressed size: 3.5" x 7.25"
A = 25.38 in.2
Sxx = 30.66 in.3
Ixx = 111.1 in.4
Reference Design Values (NDS Supplement table 4A)
Fb = 1,000 psi
Fv = 180 psi
E = 1,700,000 psi
Adjusted ASD Values: F'b, F'v , E'
NDS Supplement table 4A Cr = 1
CM = 1
CF = 1.3 for Fb, 1.2 for Ft, 1.05 for Fc
Cfu = 1NDS Supplement section 2.3
CD = 1.25 (Lr)
Ct = 1NDS Supplement section 3.3 lu/d = 13.24 ≥ 7
le = 1.37 lu + 3d = 153.27 in.
RB = sqrt(led/b2) = sqrt(153.27" x 7.25" / (3.5")2) = 9.524
F*b = 1,625 psi
FbE = 1.20 E'min / RB2 = 8,202 psi
CL = 0.9880NDS Supplement section 3.7
CP = 1 (not a column)
NDS Supplement section 3.10
Cb = 1 (not enough info given)
NDS Supplement section 4.3 Ci = 1
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 1.25 1 1 0.9880 1.3 1 1 1 1,606 tension stress parallel to grain Ft 675 1.25 1 1 1.2 1 -- shear stress parallel to grain Fv 180 1.25 1 1 1 225 compression stress perpendicular to grain Fc⊥ 625 1 1 1 1 -- compression stress parallel to grain Fc 1,500 1.25 1 1 1.05 1 1 -- modulus of elasticity (or MOE) E 1,700,000 1 1 1 1,700,000 modulus of elasticity for stability calculations Emin 620,000 1 1 1 1 620,000
Actual Stresses (ASD) and Deflection
fb = M/S = (4 kip-ft x 1000 lb/kip x 12 in/ft) / 30.66 in.3 = 1,566 psi
fv = 1.5V/A = 1.5 (1000 lb) / 25.38 in.2 = 59.10 psi
ΔL = (1600 lb)(96 in.)3 / 48(1,700,000 psi)(111.1 in.4) = 0.1561 in.
Is Member Adequate? (ASD)
bending: 1,606 psi > 1,566 psi ✓
shear: 225 psi > 59.10 psi ✓
deflection: 0.2667 in. > 0.1561 in. ✓
Nominal LRFD Values
Fbn, Fvn, E
Adjusted LRFD Values
F'bn, F'vn, E'
Adjusted LRFD Moment and Shear Resistances
M'n, V'n
Factored Moment and Shear (LRFD) and Actual Deflection
Mu, Vn, Δ
Is Member Adequate? (LRFD)