Problem 6.31

 

Given

 

rafter connection:  2x10 rafter at 6/12, 2x4 stud wall with double top plate
P_D = 140 lb
P_S = 560 lb
No. 1 S-P-F (South)
C_M = 1
C_t = 1

 

 

Actual Bearing Stress in Top Plate and Rafter

 

f_c = 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)

 

l_b = 1.5 in. (measured parallel to grain) < 6"  ✓
C_b = (l_b + 0.375)/l_b = 1.25

 

NDS Supplement table 4A Cr = 1 CM = 1 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	875	1.15	1	1	1	1.5	1	1		1			--
tension stress parallel to grain	Ft	400	1.15	1	1		1.5				1			-- --
shear stress parallel to grain	Fv	135	1.15	1	1						1			--
compression stress perpendicular to grain	Fc⊥	335		1	1						1		1.25	419
compression stress parallel to grain	Fc	1,050	1.15	1	1		1.15			1	1			--
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		--

 

F'_c⊥ = 419 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 = 1 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	875	1.15	1	1	1	1.1	1	1		1			--
tension stress parallel to grain	Ft	400	1.15	1	1		1.1				1			-- --
shear stress parallel to grain	Fv	135	1.15	1	1						1			--
compression stress perpendicular to grain	Fc⊥	335		1	1						1		1.25	419
compression stress parallel to grain	Fc	1,050	1.15	1	1		1			1	1			1,208
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		--

 

F^*_c = adjusted compression design value parallel to grain multiplied by all applicable adjustment factors except the column stability factor = 1,208 psi  (Appendix J)
F'_c⊥ = 419 psi
θ = arctan(12/6) = 63.43°
F'_θ = F^*_cF'_c⊥ / (F^*_csin²θ + F'_c⊥cos²θ) = 482.0 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