CSA S16-09 Example 002

Software Verification PROGRAM NAME: REVISION NO.:

SAP2000 0

CSA S16-09 Example 002 WIDE FLANGE MEMBER UNDER COMPRESSION & BENDING EXAMPLE DESCRIPTION The frame object axial and moment strengths are tested in this example. A continuous column is subjected to factored loads and moments C  f = 2000 kN;  M  fx-top kN-m; M  fx-bottom  fx-top= 200 kN-m; M   fx-bottom= 300 kN-m. This example was tested using the CSA S16-09 steel frame design code. The design capacities are compared with Handbook of Steel Construction (9th Edition) results.

GEOMETRY, PROPERTIES AND LOADING 2000 kN  xf =

3.7 m

A

200 kN-m

A

W310x118  xf =

200,000 MPa 0.3 76,923.08 MPa

Section A-A

Loading

Design Properties

C  f  = 2000 kN  M  fx-top = 200 kN-m  fx-top  M  fx-bottom  fx-bottom = 300 kN-m

 f  y

Material Properties E= ν = G=

300 kN-m

= 345 MPa

TECHNICAL FEATURES TESTED   

Section compactness check (compression & bending) Member compression capacity Member bending capacity with no mid-span loading

CSA S16-09 Example 002 - 1

Software Verification PROGRAM NAME: REVISION NO.:

SAP2000 0

RESULTS COMPARISON Independent results are taken from Example 1 on page 4-114 of the Hand Book of Steel Construction to CSA S16-01 published by the Canadian Institute of Steel Construction.

SAP2000

Independent

Percent Difference

Compactness

Class 2

Class 2

0.00%

Axial Capacity, C r  (kN)

3849.5

3849.5

0.00%

Bending Capacity, M r3  3 (kN-m)

605.5

605.5

0.00%

Output Parameter

COMPUTER FILE: CSA S16-09 EX002 CONCLUSION The results show an exact comparison with the independent results.

CSA S16-09 Example 002 - 2

Software Verification PROGRAM NAME: REVISION NO.:

SAP2000 0

HAND CALCULATION Properties:

Material:  f  y = 345 MPa  E = 200,000 MPa G = 76923.08 MPa Section: W310x118  A g  = 15000 mm2 r 33 = 135.4006 mm, r 22 = 77.5457 mm  I 22 = 90,200,000 mm4  Z 33 = 1,950,000 mm3  J = 1,600,000 mm4

ro r 

2

1.966 10



xo

2

o

12



C w

2



yo

2

6

mm

 r22

2

 r33

2

  0  

2

0

2

 77.5457

2

 135.4006

2

2



24346.658 mm

Member: l  z = l e33 = l e22 = 3700 mm (unbraced length) k  z =k 33 = k 22 =1.0

  0.9

Loadings:

C   f  



2000 kN

 M a



M xf  ,top   200 kN-m

 M b



M xf  ,bottom   300 kN-m





CSA S16-09 Example 002 - 3

Software Verification PROGRAM NAME: REVISION NO.:

SAP2000 0

Section Compactness:

Localized Buckling for Flange: 145

Cl .1 

145

 F  y 170

Cl .2 







170

 F  y

b f   2t  f  

 9.15

345 307



 7.81

345

 8.21

2  18.7

Cl .1     Cl .2 ,  

Flange is Class 2.

Localized Buckling for Web: C y



f y Ag 

Cl .1  

h

345 15000 

1000



1100 

5175 kN

C  f    1  0.39  C  y   F  y 



t w

276.6

2000   1  0.39 5175   50.30 345  

1100

 23.24

11.9

   Cl .1 ,

Web is Class 1.

Section is Class 2

Member Compression Capacity:

Flexural Buckling n = 1.34 (wide flange section)

CSA S16-09 Example 002 - 4

Software Verification PROGRAM NAME: REVISION NO.:



max( 22 , 33 )   22

Cr  Ag F y C r 

1    2n





k22l 22

 f   y

r22 

E 



1.0  3700

345

77.5457

200000



1

n

 0.9 15000  345  1  0.6308

21.34





SAP2000 0

0.6308

1 1.34

3489.5kN



Torsional & Lateral-Torsional Buckling



 F ex

 F ey 

2 E   k33l 33     r 33 

2



2 E   k22l 22     r 22 

2



2 2 105  1 3700   135.4006   

2

2 2  105  1  3700   77.5457   

2

 2643MPa

 867MPa

   EC   1 w  Fez     GJ    k l     A g r o   z z    2  2 105  1.966  1012  1 6   76923.08  1.6  10  F    2   15000  24347 1 3700   2

2

2

ez 

 F eZ 

 Fe





1113.222MPa



min Fex , Fey , Fez

Cr  Ag F e

1    2n

C r   9674.5kN







F ey



867 MPa

1

n

 0.9  15000  867 

1 0.6308

21.34





1 1.34

(does not govern)

Section Bending Capacity:

 M p 33



Z33 F y



1,950,000 345 



672.75kN-m

CSA S16-09 Example 002 - 5

Software Verification SAP2000 0

PROGRAM NAME: REVISION NO.:

M ember B endi ng Capacity: 2

  M   M   2  1.75  1.05  a   0.3  a   2.5   M b   M b  2

 200   200  2  1.75  1.05    0.3   2.583  2.5  300   300  So

 M u

 M u

 M u



2

 



2.5

  E   GJ     l  

 2

EI 22

l22

2

I 22C w

22

2.5  

2  10

5

 9.02  10  76923.08  1.6  10 7

3700



6

     2  105     3700 

2

9.02  10

7

 1.966  1012

3163.117kN-m

Since  M u



0.67  M p 33

 M r 33

 M     1.15M p 1  0.28 p   M p  M u  

 M r 33

672.75    1.15  0.9  672.75 1  0.28   0.9  672.75 3163.117  

33

33

33

  654.830  605.475  M r 33   M r 33   605.5kN-m 

CSA S16-09 Example 002 - 6