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 Fc

NDS Supplement section 2.3

CD = 1.15 (S)
Ct = 1

NDS 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 Fc

NDS Supplement section 2.3

CD = 1.15 (S)
Ct = 1

NDS 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'ccos2θ) = 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