Given:
L=15 ft
P=20 kips
wdl=1.5 klf
wLL=2.0 klf
Step 1:
Calculate B.M for point load and UDL separately
Pu=1.2(D.L)=1.2(20)=24 kips
M=PL/4=24x15/4=90 ft-kips (For point load)
Wu=1.2(D.L)+1.6(L.L)
Wu=1.2(1.5)+1.6(2)
Wu=5 klf
M=5x152/8=140.625 ft-kips
Total B.M=140.625+90=230.625 ft-kips
Step 2:
Fy=50 ksi
Calculate the Zx value
Zx=M/Fy
Zx=230.625x12/(0.9x50)
Zx=61.5 in3
Step 3:
Select a W section having Zx>61.5 in3
Since we have W14X38 having Zx exactly equal to 61.5 in3, it is better to prefer next higher section
Select W16X36
From the Zx tables, Moment capacity=240 kips
Step 4:
Calculate shear
V=wuL/2+W/2
V=5x15/2+20/2
V=47.5 kips
Shear capacity=340 kips from Zx tables
Step 5:
Check live load deflection:
=5wL4/384EI
=5x(2/12)x(15x12)4/384x29000x448
=0.175 in
Permissible deflection=L/240=5*12/240=0.75 in
So W16X36 can be used in bending, shear and deflection safely
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