Draft

10.6Examples 181

2. ComputethefactoredloadmomentMu. Fora simplysupportedbeamcarrying

uniformlydistributedload,

Mu=wuL

2

=8 = (1:52)(20)

2

=8 = 76k.ft

Assumingcompactsection,sincea vastmajority of rolledsectionssatisfypfor

boththe
angeandtheweb. ThedesignstrengthbMnis

bMn=bMp=bZxFy

Thedesignrequirement is

bMn=Mu

or,combingthosetwo equationswe have:

bZxFy=Mu

3. RequiredZxis

Zx=

Mu

bFy

=

76(12)

0 :90(36)

= 28 : 1 in

3

FromthenotesonStructuralMaterials,we selecta W12X22sectionwhich hasa

Zx= 29: 3 in

3

NotethatZxis approximatedby

wd

9

=

(22)(12)

9

= 29:3.

4. Check compactsectionlimitspforthe
   angesfromthetable

=

bf

2 tf

= 4 : 7

p =

65

p

Fy

=

65

p

36

= 10: 8 > 

p

andfortheweb:

=

hc

tw

= 41 : 8

p =

640

p

Fy

=

640

p

36

= 107

p

5. Check theStrengthby correctingthefactoredmomentMuto includetheselfweight.

Selfweight of thebeamW12X22is 22 lb./ft.or 0.022kip/ft

wD = 0 :2 + 0: 022 = 0: 222 k/ft

wu = 1 :2(0:222)+ 1:6(0:8) = 1: 55 k/ft

Mu = (1:55)(20)

2

=8 = 77: 3 k.ft

Mn = Mp=ZxFy=

(29:3)in

3

(36)ksi

(12)in/ft

= 87: 9 k.ft

bMn = 0 :90(87:9) = 79: 1 k.ft> Mu

p

Thereforeuse W12X22 section.

6. We nallycheck forthemaximumdistancebetweensupports.

ry =

s

Iy

A

=

r

5

6 : 5

= 0: 88 in (10.16-a)

Lp =

300

p

Fy

ry (10.16-b)

=

300

p

36

0 :88 = 43 ft (10.16-c)