aisc lrfd-99 example 002
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PROGRAM NAME: SAP2000
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AISC LRFD-99 Example 002 - 1
AISC LRFD-99 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 ft tall and loaded with an axial load, 1400u
P kips and bending,ux uy
M , M =
200k-ft and 70k-ft, respectively. It is assumed that there is reverse-curvature bending with equalend 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 3 rd Edition, LRFD Manual of SteelConstruction, pages 6-6 to 6-8.
GEOMETRY, PROPERTIES AND LOADING
TECHNICAL FEATURES TESTED
Section Compactness Check (Compression & Bending) Member Compression Capacity
Member Bending Capacity Demand/Capacity Ratio, D/C
Member Properties
W14X176
E = 29000 ksi
Fy = 50 ksi
Loading
Pu = 1,400 kips
Mux = 200 kip-ft
Muy = 70 kip-ft
Geometry
H = 14.0 ft
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AISC LRFD-99 Example 002 - 2
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 to6-8.
Output Parameter SAP2000 IndependentPercent
Difference
Compactness Compact Compact 0.00%
c n P (kips) 1937.844 1937.839 0.00%
b nx M (k-ft) 1200 1200 0.00%
b ny M (k-ft) 600.478 600.478 0.00%
D/C 0.974 0.974 0.00%
COMPUTER
FILE
: AISC-LRFD99
E
X002
CONCLUSION
The results show an acceptable comparison with the independent results.
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AISC LRFD-99 Example 002 - 3
HAND CALCULATION
Properties:
Material: ASTM A992 Grade 50 Steel F y = 50 ksi, E = 29,000 ksi
Section: W14x176 A = 51.8 in2,
b f = 15.7 in, t f = 1.31 in, d = 15.2 in, t w = 0.83 in
2 15.2 2 1.31 12.58c f h d t in
I x = 2,140 in4
, I y = 838 in4
, r x = 6.4275 in, r y = 4.0221 inS x = 281.579 in3, S y = 106.7516 in3, Z x = 320.0 in3, Z y = 163.0 in3.
Member:
K x = K y = 1.0 L = Lb = 14 ft
Other
0.85c
0.9b
Loadings:
P u = 1400 kips
M ux = 200 k-ft M uy = 70 k-ft
Section Compactness:
Localized Buckling for Flange:
/ 2 15.7 / 25.99
1.31
f
f
b
t
290000.38 0.38 9.15
50 p
y
E
F
p , No localized flange buckling
Flange is Compact.
Localized Buckling for Web:
12.5815.16
0.83
c
w
h
t
0.9 51.8 50 2331b y b g y P A F kips
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AISC LRFD-99 Example 002 - 4
14000.601
2331
u
b y
P
P
Since 0.601 0.125u
b y
P
P
1.12 2.33 1.49u
p
y b y y
P E E
F P F
29000 29000
1.12 2.33 0.601 46.647 1.49 35.884
50 50
p
p , No localized web buckling
Web is Compact.
Section is Compact.
Member Compression Capacity:
For braced frames, K = 1.0 and K x L x = K y L y = 14.0 ft, From AISC Table 4-2,
kips P nc 1940
Or by hand,
1.0 14 12 500.552
4.022 29000
y y
c
y
K L F
r E
Since 1.5,c
2 2
0.5520.658 50 0.658 44.012c
cr y F F ksi
0.85 44.012 51.8c n c cr g
P F A
1937.84c n P kips
From LRFD Specification Section H1.2,
14000.722 0.2
1937.84
u
c n
P
P
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AISC LRFD-99 Example 002 - 5
Therefore, LRFD Specification Equation H1-1a governs.
Section Bending Capacity
50 3101333.333
12 px y x M F Z k ft
py y y M F Z
However,163
1.527 1.5,106.7516
y
y
Z
S
So 31.5 1.5 106.7516 160.1274 y y Z S in
50 160.1274667.198
12 py M k ft
Member Bending Capacity
From LRFD Specification Equation F1-4,
yf
y p F
E r L 76.1
2900011.76 4.02 14.2 14
1250 p b L ft L ft
b nx b px M M
0.9 1333.333b nx M
1200b nx M k ft
b ny b py M M
0.9 667.198b ny M
600.478b ny M k ft
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AISC LRFD-99 Example 002 - 6
I nteraction Capacity: Compression & Bending
From LRFD Specification section C1.2, for a braced frame, M lt = 0.
,1 ntx xux M B M where 200
ntx M kip-ft; and
,1 nty yuy M B M where 70nty M kip-ft
1
11
1
e
u
m
P
P
C B
For reverse curvature bending and equal end moments:
0.1
2
1
M
M
2
14.06.0 M
M C
m
2.00.14.06.0 m
C
2
1 2e
EI p
KL
2
1 2
29000 214021,702
14.0 12e x p kips
2
1 2
29000 8388,498
14.0 12
e y p
1
1
1
1
xe
u
mx
x
P
P
C B
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AISC LRFD-99 Example 002 - 7
1
0.20.214 1
14001
21702
x B
11
x B
1
1
1
1
ye
u
my
y
P
P
C B
1
0.20.239 1
14001
8498
y B
11
y B
2002000.1 ux
M kip-ft;
and
70700.1 uy M kip-ft
From LRFD Specification Equation H1-1a,
1400 8 200 700.974 1.0
1940 9 1200 600.478
, OK
0.974 D
C