Question

A 2x10 wood beam is to support a service dead load (including beam self-weight) of 50 lbs/ft and a service live load of 60 lbs/ft (note that the loads given are per foot and not per square ft). The beam is part of a series of adjacent parallel beams spaced 16 inches apart. Span length is 15 ft. Assume that lateral buckling is prevented. Wood species/grade is "Red Maple", No.1. Moisture content is less than 19% (dry). This member’s service temperature is not elevated. What is the design moment strength (M'n) in kip-in?

Answer 1

The answer is "
`30.83 \ kip-in`"

Step-by-step explanation:

`\to D.L = 50 \ ( lbs)/(ft) \\\\\to L.L = 60\ ( lbs)/(ft)\\\\`

Factered load
`w_u= 1.2 D.L+1.6 \ D.L`

`= 1.2 * 50 +1.6* 60\\\\= 60 +96\\\\=156 \ ( lbs)/(ft)\\\\= 131 ( lbs)/(in)\\\\`

`A= bd= 2* 10 = 20 \ in^2\\\\Z= (bd^2)/(6) =(2*10^2)/(6)= 33.33 \ in^3 \\\\L= 15 \ ft = 180 \ inch`

bending strength
`= f_b =925 \ psi`

shear strength
`= f_v = 120 \ psi`

movment strength
`m_h= z * f_b`

`= 33.33 * 925\\\\ = 20830.25 \ lb-in \\\\ = 30.83 \ kip-in`