Problem 6.16

 

Given

 

Load	wD = 200 lb/ft wS = 300 lb/ft
Load combination	D+S (ASD) 1.2D+1.6S (LRFD)
Span	L = 20 ft
Member size	5 x 19-1/4
Glulam bending stress class	24F-1.7E SP
Unbraced length	lu = L/2 = 10 ft
Moisture content	MC < 16%
Live load deflection limit	Allow. ΔS ≤ L/360 = 0.6667 in. Allow. ΔD+S ≤ L/240 = 1.000 in.
Dry-service conditions
Normal temperatures
Bending about strong axis

 

 

Size  (NDS Supplement table 1D)

 

A = 96.25 in.²
I_x = 2,972 in.⁴
S_x = 308.8 in.³

 

 

Reference Design Values  (most conservative of 24F SP/SP beams in NDS Supplement table 5A Expanded)

 

F⁺_bx = 2,400 psi
F_vx = 210 psi
E_x = 1,700,000 psi
Ey = 1,300,000 psi

 

 

Adjusted ASD Values: F'_b, F'_v , E'_x, E'_y

 

NDS Supplement table 5A CV = (21/L)1/x (12/d)1/x (5.125/b)1/x        = (21/20)1/20 (12/19.25)1/20 (5.125/5)1/20 = 0.9802 ≤ 1.0 Cfu = 1 CM = 1 NDS section 2.3 CD = 1.15 (S) Ct = 1

NDS section 3.3 lu/d = 6.23 < 7 le = 2.06 lu = 247.2" RB = sqrt(led/b2) = 13.80 F*B = 2760 psi E'y-min = 670,000 psi FbE = 1.20 E'y-min / RB2 = 4221 psi CL = 0.9283 NDS section 3.7 CP = 1 (not a column)

NDS section 3.10.4 Cb = 1 (not enough info) NDS section 5.3 Cc = 1 (not curved)

 C_L < C_V so use C_L  (C_V and C_L are not to be used together)

Property		Reference Design Values (psi) (Table 5A)	Adjustment Factors (Table 5.3.1)									Adjusted Design Values (psi)
			CD	CM	Ct	CL	CV	Cfu	Cc	CP	Cb
bending stress	F+bx F-bx	2,400 1,450	1.15	1	1	0.9283	1	1	1			2,562 --
tension stress parallel to grain	Ft	875	1.15	1	1							--
shear stress parallel to grain	Fvx	210	1.15	1	1							242
compression stress perpendicular to grain	Fc⊥x	740 650		1	1						1	--
compression stress parallel to grain	Fc	1,000	1.15	1	1					1		--
radial tension	Frt	--	1.15	1	1							--
modulus of elasticity (or MOE)	Ex	1,700,000		1	1							1,700,000
modulus of elasticity for stability calculations	Ex min	880,000		1	1							--
modulus of elasticity (or MOE)	Ey	1,300,000		1	1							1,300,000
modulus of elasticity for stability calculations	Ey min	670,000		1	1							670,000

 

 

Actual Stresses (ASD) and Deflection

 

vertical ground reactions:  wL/2
V_max = +/- wL/2
M_max = wL²/8

f_b = M/S = (500 lb/ft x 1 ft/12 in.)(20 ft x 12 in/ft)² / (8)(308.8) = 971.5 psi

f_v = 1.5V/A = 1.5 (500 lb/ft x 1 ft/12 in.)(20 ft x 12 in/ft) / 2(96.25 in.²) = 77.92 psi

Δ_S = 5(300 lb/ft x 1 ft/12 in.)(20 ft x 12 in./ft)⁴ / 384(1,700,000 psi)(2972 in.⁴) = 0.2138 in.

Δ_D+S = 5((200/2+300 lb/ft) x 1 ft/12 in.)(20 ft x 12 in./ft)⁴ / 384(1,700,000 psi)(2972 in.⁴) = 0.2850 in.  (dead load may be reduce by 1/2 if MC < 16% when installed and kept dry, IBC table 1604.3 footnote d)

 

Is Member Adequate? (ASD)

 

bending:  2,562 psi > 971.5 psi  ✓

shear:  242 psi > 77.92 psi  ✓

deflection_S:  0.6667 in. > 0.2138 in.  ✓

deflection_D+S:  1.000 in. > 0.2850 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)