Question

A W shape is to be used for a uniformly loaded simple beam carrying a total dead load of 22 kips and a total live load of 50 kips on a 30-ft span. Select the lightest weight shape for unbraced lengths of (2) 10 ft, and (2) 15 ft.

Answer 1

(1)

Step 1:

D.L=22 kips/30=0.73 kip/ft

L.L=50 kips/30=1.66 kip/ft

Wu=1.2(0.73)+1.6(1.66)

Wu=3.532 kips/ft

Mu=3.532x30x30/8=397.35 ft-kips

Step 2:

Fy=50 ksi

Mu/Cb=397.35/1.45=274 ft-kips

Enter the Unbraced length vs Moment available table with Lb=10 ft

Consider W14x43 section

For Cb=1

Mn=261 ft-kips

For Cb=1.45

Mn=1.45x261=378 ft-kips> which is not possible (Not good)

Step 4:

Go for a higher section:

Consider a W10X60 section:

For Cb=1

Mn=280 ft-kips>274 ft-kips

For Lb=10 ft, consider W10X60 section

(2)

Lb=15 ft

Cb=1.3

Mu/Cb=397.35x/1.3=305.65 ft-kips

Now enter the table of Mu vs Lb with Lb=15 ft

Consider a W16X45 section for Cb=1

Mb=309 ft-kips

For Lb=15 ft, W16X45 section should be used