Contents AISC LRFD 93 Example 002

User Manual: AISC LRFD-93 Example 002

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Software Verification
PROGRAM NAME:
SAP2000
REVISION NO.:
0
AISC LRFD-93 Example 002
WIDE FLANGE MEMBER UNDER COMBINED COMPRESSION & BIAXIAL BENDING
EXAMPLE DESCRIPTION
A check of the column adequacy is checked for combined axial compression and
flexural loads. The column is 14 feet tall and loaded with an axial load,
1400
u
P=
kips and bending,
ux uy
M ,M
= 200k-ft and 70k-ft, respectively. It is
assumed that there is reverse-curvature bending with equal end moments about
both axes and no loads along the member. The column demand/capacity ratio is
checked against the results of Example 6.2 in the 3rd Edition, LRFD Manual of
Steel Construction, pages 6-6 to 6-8.
GEOMETRY, PROPERTIES AND LOADING
TECHNICAL FEATURES TESTED
Section compactness check (compression)
Member compression capacity
Member bending capacity
Demand/capacity ratio, D/C
Member Properties
W14X176
E = 29000 ksi
Fy = 50 ksi
Loading
P
u
= 1,400 kips
Mux = 200 kip-ft
Muy = 70 kip-ft
Geometry
H = 14.0 ft
AISC LRFD-93 Example 002 - 1
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RESULTS COMPARISON
Independent results are hand calculated and compared with the results from
Example 6.2 in the 3rd Edition, LRFD Manual of Steel Construction, pages 6-6 to
6-8.
Output Parameter SAP2000 Independent Percent
Difference
Compactness Compact Compact 0.00%
(kips) 1937.84 1937.84 0.00%
b nx
M
φ
(k-ft) 1200 1200 0.00%
b ny
M
φ
(k-ft) 600.478 600.478 0.00%
D/C 0.974 0.974 0.00%
COMPUTER FILE: AISC LRFD-93 EX002
CONCLUSION
The results show an exact comparison with the independent results.
AISC LRFD-93 Example 002 - 2
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HAND CALCULATION
Properties:
Material: ASTM A992 Grade 50 Steel
Fy = 50 ksi, E = 29,000 ksi
Section: W14x176
A = 51.8 in2,
bf = 15.7 in, tf = 1.31 in, d = 15.2 in, tw = 0.83 in
2 15.2 2 1.31 12.58
cf
h d t in= − = −• =
Ix = 2,140 in4, Iy = 838 in4, rx = 6.4275 in, ry = 4.0221 in
Sx = 281.579 in3, Sy = 106.7516 in3, Zx = 320.0 in3, Zy = 163.0 in3.
Member:
Kx = Ky = 1.0
L = Lb = 14 ft
Other
0.85φ=
c
0.9φ=
b
Loadings:
Pu = 1400 kips
Mux = 200 k-ft
Muy = 70 k-ft
Section Compactness:
Localized Buckling for Flange:
( )
( )
/2 15.7 / 2 5.99
1.31
λ= = =
f
f
b
t
65 65 9.19
50
λ= = =
p
y
F
λ<λ
p
, No localized flange buckling
Flange is Compact.
AISC LRFD-93 Example 002 - 3
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Localized Buckling for Web:
12.58 15.16
0.83
λ= = =
c
w
h
t
0.9 51.8 50 2331 kipsφ =φ = •=
by b g y
P AF
1400 0.601
2331
= =
φ
u
by
P
P
Since
0.601 0.125= >
φ
u
by
P
P
191 253
2.33

λ= − ≥


φ

u
p
by
yy
P
P
FF
( )
191 253
2.33 0.601 46.714 35.780
50 50
λ= = ≥ =
p
λ<λ
p
, No localized web buckling
Web is Compact.
Section is Compact.
Member Compression Capacity:
For braced frames, K = 1.0 and KxLx = KyLy = 14.0 ft, From AISC Table 4-2,
1940 kipsφ=
cn
P
Or by hand,
1.0 14 12 50 0.552
4.022 29000
••
λ= = =
π •π
yy
c
y
KL F
rE
Since
1.5,λ<
c
( )
22
0.552
0.658 50 0.658 44.012ksi= =•=
λ
c
cr y
FF
0.85 44.012 51.8φ=φ = •
c n c cr g
P FA
1937.84 kipsφ=
cn
P
AISC LRFD-93 Example 002 - 4
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From LRFD Specification Section H1.2,
1400 0.722 0.2
1937.84
= = >
φ
u
cn
P
P
Therefore, LRFD Specification Equation H1-1a governs.
Section Bending Capacity
50 310 1333.333 k-ft
12
= = =
px y x
M FZ
py y y
M FZ=
However,
163 1.527 1.5,
106.7516
y
y
Z
S= = >
So
3
1.5 1.5 106.7516 160.1274in==•=
yy
ZS
50 160.1274 667.198k-ft
12
= =
py
M
Member Bending Capacity
From LRFD Specification Equation F1-4,
yf
y
pF
E
r
L76
.1
=
29000 1
1.764.02 • 14.2ft 14ft
12
50
= = >=
pb
LL
φ=φ
b nx b px
MM
0.9 1333.333φ=
b nx
M
1200k-ftφ=
b nx
M
φ=φ
b ny b py
MM
0.9667.198φ=
b ny
M
600.478 k-ft
φ=
b ny
M
AISC LRFD-93 Example 002 - 5
Software Verification
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Interaction Capacity: Compression & Bending
From LRFD Specification section C1.2, for a braced frame, Mlt = 0.
,
1ntxxux
MBM =
where
200=
ntx
M
kip-ft; and
,
1ntyyuy MBM =
where
70=
nty
M
kip-ft
1
1
1
1
=
e
u
m
P
P
C
B
For reverse curvature bending and equal end moments:
0.1
2
1+=
M
M
=
2
1
4.0
6.0 M
M
Cm
( )
2.00.14.06.0 ==
m
C
( )
2
12
π
=
e
EI
pKL
( )
2
12
29000 2140 21,702
14.0 12
π• •
= =
ex
p kips
( )
2
12
29000 838 8,498
14.0 12
π• •
= =
ey
p
1
1
1
1
=
xe
u
mx
x
P
P
C
B
1
0.2 0.214 1
1400
121702
x
B= = ≥



AISC LRFD-93 Example 002 - 6
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0
1
1=
x
B
1
1
1
1
=
ye
u
my
y
P
P
C
B
1
0.2 0.239 1
1400
18498
y
B= = ≥



1
1
=
y
B
200
2000
.
1=
=
ux
M
kip-ft;
and
70
700
.1 =
=
uy
M
kip-ft
From LRFD Specification Equation H1-1a,
1400 8 200 70 0.974 1.0
1940 9 1200 600.478

++ =<


, OK
0.974
D
C=
AISC LRFD-93 Example 002 - 7

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