Question

Given a 2x6 select structural DF-L top truss chord member loaded axially with 2800

lbs (dead plus live), determine if the given section is adequate. The chord is 8-ft long and is

laterally braced at mid-length about the weak axis. Assume the ends are pinned and that the

moisture content exceeds 19%.

Answer 1

Ans) Given,

Load = 2800 lb

Length = 8 ft

Moisture = 19%

Design Moment = WL²/8

W = Load / length

= 2800 / 8

= 350 lb/ft

M = 350 x 8²/ 8

M = 2800 lb-ft or 33600 lb-in

Nominal dimension for 2 x 6 DF-L are,

b = 1.5 in

d = 5.5 in

I = bd³/12

= 178 in⁴

y = d / 2

Section Modulus(Z) = I / y

= bd²/6

= 1.5 x 5.5²/6  

31.64 in³

Bending Stress = M / Z

= 33600 / 31.64

= 1061.90 psi

Bending stress value (F_b) for 2 x 6 DF-L = 1350 psi  

Allowable stress(F'b) = Fb x Cd x C_L x Cr x Cm x Ct x Cf

where , C_d = load duration factor (0.9)

C_L = beam stability factor (1)

Cr = repetative member factor (1.15)

C_m = wet service factor (1)

C_t = temperature factor (1)

C_f = size factor (1)

F'b = 1350 x 0.9 x 1.15 x 1 x 1 x 1 x1

= 1397.25 psi > 1062 psi ,

Hence OK

Check deflection :

E = 1700000 psi x Cm x Ct

= 1700000 psi

Deflection = 5 WL⁴ / (384EI)

= 5 x (350/12) x (8 x 12)⁴ /(384 x 1700000 x 178)

Deflection = 0.106 in < L/ 240

Hence OK

Check shear stress:

V = WL/2

= 350 x 8 /2

V = 1400 lb

Shear stress = V/bd

= 1400/(1.5 x 5.5)

= 169.70 psi

Allowable shear stress = Fv x Cd x Cm x Ct x Ch

= 180 x 1 x 1 x 1 x1

= 180 psi > 169.7 psi

Hence Ok