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

Answer:

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

Explanation:

$\to D.L = 50 \ \frac{ lbs}{ft} \\\\\to L.L = 60\ \frac{ lbs}{ft}$

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

                           $= 1.2 \times 50 +1.6\times 60\\\\= 60 +96\\\\=156 \ \frac{ lbs}{ft}\\\\= 131 \frac{ lbs}{in}$

$A= bd= 2\times 10 = 20 \ in^2\\\\Z= \frac{bd^2}{6} =\frac{2\times10^2}{6}= 33.33 \ in^3 \\\\L= 15 \ ft = 180 \ inch$

bending strength$= f_b =925 \ psi$

shear strength$= f_v = 120 \ psi$

movment strength $m_h= z \times f_b$

                                   $= 33.33 \times 925\\\\ = 20830.25 \ lb-in \\\\ = 30.83 \ kip-in$