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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