Question

Determine the lightest W14 section to carry LRFD factored compression load of 900 kips and LRFD factored strong axis moment of 600 foot-kips.

Answer 1

LRFD solution:

Step 1:

Pu=900 Kips

Mux=600 ft-kips

Muy=0

Step 2:

Assume a length of 16 ft for the column as it is not given

Start with a W14 sectionwith Pu/Pn>0.2 and less than 1, try with a W14x99 Section

Pu/Pn=900/1080=0.833

p=1/1080=9.25x10-4

bx=8/9Mcx

bx=8/9(646 ft-kips)

bx=0.001357

Step 3:

Check for stability

pPu+bxMux+byMuy

=9.25x10-4x900+0.001357x600+0

=0.833+0.81=1.643>1, so this section will not be adequate, Try for another section

Step 4:

Try with a W14X120 section

p=1/1309=7.63x10-4

Mx=8/9x795=0.0011

Check for stability

pPu+bxMux+byMuy

=7.63x10-4x900+0.0011x600=1.347>1

so this section will not be adequate, Try for another section

Step 5:

Select a W14X132 section

p=1446 Kips

pPu=900/1446=0.62

bx=0.001

pPu+bxMux+byMuy

=900/1446+0.001x600

=1.22>1, Not Good

Step 6:

Consider a W14X159 section

Pn=1777 Kips

p=1/1777=5.62x10-4

pPu=0.5

bx=8/9Mcx

bx=8/9x1080

bx=8.14x10-4

pPu+bxMux+byMuy

=0.5+8.14x10-4x600

=0.98<1

The lightest section which can carry the given load and moment is W14X159 section