Page 299 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch06.qxd 9/29/05 5:15 PM Page 6.21

DESIGN OF BUILDING MEMBERS

DESIGN OF BUILDING MEMBERS 6.21

1. Full composite:
∑ Q = A F = 324 5 kips
.
s y
n
ϕ M = 277 2 kip ft
⋅
.
n
2. Plastic neutral axis ∆A f = A f /4 = 0.4188 in below the top of the top flange. From Table 6.3,
∑Q n = A s F y − 2∆A f F y .
∑ Q = 324 5 2 0 4188 50 = 282 6 . kips
×
.
− × .
n
a = 282 6 . = 1 2315 in
.
×
.
.
085 × 30 90
.
e = 13 7 . + 525 − 1 2315 = 11 484 in
.
.
2 2

−
.
.
. )
M = 282 6 . ×11 484 0 5 324 5 282 6 13 7 0 335 2 324 5 . . − 282 6 .  
+ . (
.
− .

n
×
×1 675 50
⋅
= 3531 kip in
ϕ M = 090 × 3531 = 264 8. kip ft
⋅
.
n n
12
3. PNA ∆A f = A f /2 = 0.8375 in below the top of the top flange.
∑ Q = 324 5 2 0 8375 50 = 240 8 . kips
×
.
− × .
n
a = 240 8 . = 1 0490 in
.
×
085 × 30 90
.
.
.
e = 13 7 . + 525 − 1 0490 = 11 575 in
.
.
2 2

−
.
+ . (
. )
− .
.
M = 240 8 . ×11 575 0 5 324 5 240 68 13 7 0 335 2 324 5 . . − 240 8 .  
.

×
n
×1 675 50
⋅
= 3353 kip in
⋅
ϕ M = 090 × 3353 = 251 5. kip ft
.
n n
12
4. PNA ∆A f = 3A f /4 = 1.2563 in below the top of the top flange.
∑ Q = 324 5 2 . × =
− ×1 2563 50 198 9 . kips
.
n
a = 198 9 . = 0 8665 in
.
×
.
085 × 30 90
.
e = 13 7 . + 5 25 0 8665 11 667 in
=
.
− .
.
2

−
.
+ . (
− .
M = 198 9 . ×11 667 0 5 324 5 198 9 13 7 0 335 324 5 . . −198 9 .  
. )
.
.

n
×
2
×1 675 50
⋅
= 3165 kip in
⋅
ϕ M = 090 × 3165 = 237 4. kip ft
= .
n
12
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