Question

8. Using the LRFD Method (ry-min & Zx-min Cat 1 assumption), select an economical W16 wide flange steel beam for a simple beam that spans 24 feet (braced at 1/5 points) and will carry a dead load of 1 kip/ft. and a live load of 2 kip/ft. Fy = 50 ksi ; E = 29,000 ksi; No checks necessary. Provide beam selection and corresponding Zx and ry (10 points) in. in3 ry: Zx: Beam Selection:

Answer 1

LRFD solution:

Step 1:

Wu=1.2(D.L)+1.6(L.L)

Wu=1.2(1)+1.6(2)

Wu=4.4 kips/ft

M=WuL2/8

Mu=4.4x24x24/8

Mu=316.8 ft-kips

Step 2:

Zx=Mu/(0.9Fy)

Zx=316.8x12/(0.9x50)

Zx=85 in3 is the required section modulus

Check with W16X50 and consider for self weight also

Self weight=0.05 ft/kips

Wu=1.2(1.05)+1.6(2)

Wu=4.46

Mu=4.46x24x24/8

Mu=321.12 ft-kips

Zx=321.12x12/(0.9x50)

Zx=85.6 in3

Provided is 92 in3

Step 3:

Finding the minimum radius of gyration:

Iy=37.2 in4

A=14.7 in2

ry=(Iy/A)0.5

ry=(37.2/14.7)0.5

ry=1.59 in