Problem 7.1

 

Given

 

Member size	3x8
Load	20 kip tension due to wind
Stress grade and species	Select Structural DF-L
Fasteners	single line of 7/8" bolts
Adjustment factors	CM = 1 Ct = 1 Ci = 1

 

 

Size (NDS Supplement table 1B)

 

A_g = 18.13 in.²
A_n = A_g - 2.5 in. x (7/8 in. + 1/16 in.) = 15.79 in.²  (NDS section 11.1.2.2 and appendix L table L1)

 

 

Adjusted Design Values

 

NDS Supplement table 4A Cr = 1 (diaphragm member) CM = 1 (given) CF = 1.2 for Fb, 1.2 for Ft, 1.05 for Fc Cfu = 1 (not a beam) NDS Supplement section 2.3 CD = 1.6 (W) Ct = 1 (given)

NDS Supplement section 3.3 CL = 1 (no compression) 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 (given) 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	1,500	1.6	1	1	1	1.2	1	1		1			--
tension stress parallel to grain	Ft	1,000	1.6	1	1		1.2				1			1,920
shear stress parallel to grain	Fv	180	1.6	1	1						1			--
compression stress perpendicular to grain	Fc⊥	625		1	1						1		1	--
compression stress parallel to grain	Fc	1,700	1.6	1	1		1.05			1	1			--
modulus of elasticity (or MOE)	E	1,900,000		1	1						1			--
modulus of elasticity for stability calculations	Emin	690,000		1	1						1	1		--

 

 

Actual Stress (ASD)

 

f_t = P/A_n = 20,000 lb / 15.79 in.² = 1,267 psi ≤ 1,920 psi  ✓

P_max = F'_tA_n = 1,920 psi x 15.79 in.² = 30,320 lb