Page 300 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch06.qxd 9/29/05 5:15 PM Page 6.22

DESIGN OF BUILDING MEMBERS

6.22 CHAPTER SIX

5. PNA at the bottom of the top flange (∆A f = A f ).

∑ Q = 324 5 2 . × =
.
− ×1 675 50 157 0 . kips
n
a = 157 0 . = 0 68410 in
.
×
.
.
085 × 30 90
=
e = 13 7 . + 5 25 0 6841 11 758 in
.
.
− .
2

−
.
. )
.
+ . (
− .
.
M = 157 0 . ×11 758 0 5 324 5 157 0 13 7 0 335 2 324 5 . . −157 0 .  

×
n
×1 675 50
⋅
= 2965 kip in
=
ϕ M = 0 90 2965 222 4. × = . kip ⋅ft
n
6. Plastic neutral axis within the web: ∑Q n = 104 kips is the average of items 5 and 7. (See Table 6.3.):
∑ Q = 157 0 . + 81 1 . = 119 1 . kips
n
2
a = 119 1 . = 0 5187 in
.
×
.
.
085 × 30 90
e = 13 7 . + 5 25 0 5187 11 841 in
=
.
− .
.
2
 324 5 . −119 1 . 
−
− .
.
. )
+ . (
.
.
M = 119 1 . ×11 5187 0 5 324 5 119 1 13 7 0 335 2 ×1 675 50 

n
×
.
⋅
= 2775 kip in
ϕ M = 0.90 2775 208 1× = . kip ⋅ft
90
n
∑ Q = × =
7. n C = 025 3245 811 . kips
.
.
c
a = 81 1 . = 0 3535 in
.
×
085 × 30 90
.
.
.
C c ( d − 2 ) = 81 1
t
2 P yw f 2 × 0 23 50. ×
= 353. in = distance from PNA to the center of gravity of the beam
335
.
y = 0 335 × 5 0. × 13 7 2 3 53 0 335 2( . / + . − . / ) + 0 23 13 7 2 3 53 0. [( . / + . − .335 2)/ ] 2
+
−
×
0335 50 023 137 2) + 353 0335]
.
.
.
[
.
.
(
/
.
= 720 in = distance from centroid tensile portion of beam to the
.
center of gravity of the beam
.
.
+
+
.
.
.
e = 13 7 − 353 720 525− 0 3535
2 2
.
e = 15 60 in = distance from PNA to C c
.
+
+
y ′ = 13 7 . − 353 720 525− 0 335
.
.
.
2 2
.
C
y ′ = 10 36 in = distance from PNA to C flange
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