Determine the required section modulus for 2 X 8 nominal Dou

Determine the required section modulus, for 2” X 8” (nominal) Douglas Fir-Larch No. 1 grade roof rafters that are 14 feet long and are spaced at 16 inches on center. Assume that the wet service factor and the temperature factor are 1.0. Dressed (actual) size of the members is 1.5” X 7.25”. The dead load is 14 psf and the roof live load is 20 psf.

Solution

given data:

nominal size of the Douglas Fir-larch(DF) no.1 grade = 2\'\'*8\'\'

dressed size of DF = 1.5\'\'*7.25\'\'

dead load DL = 14psf

live load LL = 20 psf

from sectional properties tables of DF no.1 grade ,the sectional properties are

cross sectional area A_xx = 10.875 in²(b=1.5\'\'* d=7.25\'\')

moment of inertia I_xx = 47.635 in⁴ ( b*d³/12 = 1.5\'\'*7.25\'\'³/12)

section modulus S_xx = 13.14 in³ (I_xx /c=47.635/(7.25\'\'/2))

adjustment factors:

moisture content factor C_m = 1.0

temperature factor C_t = 1.0

the wood contains moisture content which will exceeded 19%with the time so the design values should be multiplied by the adjustment factors

therefore the required section modulus S_xx =  C_m*C_t*S_xx

= 1.0*1.0*13.14

= 13.14 in³