Problem 6.32
Given
rafter connection: 2x10 rafter at 12/12, 2x4 stud wall with double top plate
PD = 140 lb
PS = 560 lb
No. 2 DF-L
MC > 19%
Ct = 1
Actual Bearing Stress in Top Plate and Rafter
fc = P/A = (140 + 560 lb)/(1.5 in. x 3.5 in.) = 133.3 psi
Adjusted ASD Bearing Value F'c⊥ in 2x4 Top Plate (NDS section 3.10.4)
lb = 1.5 in. (measured parallel to grain) < 6" ✓
Cb = (lb + 0.375)/lb = 1.25
NDS Supplement table 4A Cr = 1
CM = 0.85 for Fb, 1 for Ft, 0.97 for Fv, 0.67 for Fc⊥, 0.8 for Fc, 0.9 for E and Emin
Cfu = 1
CF = 1.5 for Fb, 1.5 for Ft, 1.15 for FcNDS Supplement section 2.3
CD = 1.15 (S)
Ct = 1NDS Supplement section 3.3 CL = 1 (fully braced)
NDS 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 900 1.15 0.85 1 1 1.5 1 1 1 -- tension stress parallel to grain Ft 575 1.15 1 1 1.5 1 --
--shear stress parallel to grain Fv 180 1.15 0.97 1 1 -- compression stress perpendicular to grain Fc⊥ 625 0.67 1 1 1.25 523 compression stress parallel to grain Fc 1,350 1.15 0.8 1 1.15 1 1 -- modulus of elasticity (or MOE) E 1,600,000 0.9 1 1 -- modulus of elasticity for stability calculations Emin 580,000 0.9 1 1 1 --
F'c⊥ = 523 psi > 133.3 psi ✓
Adjusted ASD Bearing Value F'cθ in 2x10 Rafter (NDS section 3.10.3, Appendix J)
NDS Supplement table 4A Cr = 1
CM = 0.85 for Fb, 1 for Ft, 0.97 for Fv, 0.67 for Fc⊥⊥, 0.8 for Fc, 0.9 for E and Emin
Cfu = 1
CF = 1.1 for Fb, 1.1 for Ft, 1 for FcNDS Supplement section 2.3
CD = 1.15 (S)
Ct = 1NDS Supplement section 3.3 CL = 1 (fully braced)
NDS 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 900 1.15 0.85 1 1 1.1 1 1 1 -- tension stress parallel to grain Ft 575 1.15 1 1 1.1 1 --
--shear stress parallel to grain Fv 180 1.15 0.97 1 1 -- compression stress perpendicular to grain Fc⊥ 625 0.67 1 1 1.25 523 compression stress parallel to grain Fc 1,350 1.15 0.8 1 1 1 1 1,242 modulus of elasticity (or MOE) E 1,600,000 0.9 1 1 -- modulus of elasticity for stability calculations Emin 580,000 0.9 1 1 1 --
F*c = adjusted compression design value parallel to grain multiplied by all applicable adjustment factors except the column stability factor = 1,242 psi (Appendix J)
F'c⊥ = 523 psi
θ = arctan(12/12) = 45°
F'θ = F*cF'c⊥ / (F*csin2θ + F'c⊥cos2θ) = 736.1 psi > 133 psi ✓
Factored Bearing Load Pu in Top Plate and Rafter
Adjusted LRFD Bearing Resistance P'n⊥ in 2x4 Top Plate
Adjusted LRFD Bearing Resistance P'nθ in 2x10 Rafter