# V. CSA S16-19 - Short Column Compression

Determine the capacity of a short column per the CSA S16-19 code.

## Problem

A Canadian W250x73 section is used for a pedestal with a height of 1.1 m. The axial load is 1,000 kN in compression. The steel is grade 350W.

Section Properties

• D = 253 mm
• B = 254 mm
• tw = 8.6 mm
• tf = 14.2 mm
• Ag = 9,280 mm2
• Ix = 113×106 mm4
• Iy = 38.8×106 mm4
• J = 575,000 mm4
• Cw = 553×109 mm6

Material Properties

• Fy = 350 MPa
• Fu = 450 MPa
• E = 205,000 MPa
• G = 76,920 MPa

## Calculations

Section Classification

bel = B / 2 = 83.5 mm

h = D - 2×tf = 291.6 mm

Compression section classification per Table 1

• Flange classification:
$b el t = 127 14.2 = 8.94 < 200 F y = 10.69$
• Web classification about major axis:
$h w = 235.8 8.6 = 27.4 < 670 F y = 35.8$

Therefore, the section is Class 1 for compression.

Column Capacity

Assume K = 1.0,

$K L r x = 1.0 × 1,100 110.3 = 9.97$
$K L r y = 1.0 × 1,100 64.7 = 17.0$

Elastic buckling stress:

$λ x = F y F ex = 350 20,360 = 0.131$
$λ y = F y F ey = 350 6,991 = 0.224$

Per Cl. 13.3.1, n = 1.34 (Group 2 W shape):

Flexural Torsional Buckling

$F ez = π 2 E C w K z L z 2 + G J 1 A × r o 2$

Take the minimum of Fex, Fey, and Fez as FFTB:

FFTB = Fez = 6,382 MPa

$λ FTB = F y F e = 350 6,382 = 0.234$

Ratio = 1,000 / 2,879 = 0.347

## Comparison

Table 1. Comparison of results
λx 0.131 0.131 none
Fex (MPa) 20,360 20,360.98 negligible
Crx (kN) 2,914 2,910 negligible
λy 0.224 0.224 none
Fey (MPa) 6,991 6,991,204 negligible
Cry (kN) 2,884 2,880 negligible
λFTB 0.234 0.234 none
FFTB (MPa) 6,382 6,381.727 negligible
CFTB (kN) 2,879 2,880 negligible
Critical ratio 0.347 0.347 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Canada\CSA S16-19 - Short Column Compression.STD is typically installed with the program.

START JOB INFORMATION
ENGINEER DATE 20-Sep-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 1.1 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.92
ALPHA 1.2e-05
DAMP 0.03
TYPE STEEL
*STRENGTH FY 350000 FU 450000 RY 1.5 RT 1.2
G 7.692e+07
END DEFINE MATERIAL
1 TABLE ST W250X73
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
2 FY -1000
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PRINT SUPPORT REACTION ALL
PARAMETER 1
FYLD 350000 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD.PRO CODE CHECKING - CSA S16-19 (v1.0)
***********************************************
ALL UNITS ARE IN KN   MET   UNLESS OTHERWISE Noted
|--------------------------------------------------------------------------|
|   MEMBER NO.:      1      SECTION: ST  W250X73          (CANADIAN SECTIONS)|
|  STATUS:        PASS    CRITICAL RATIO:  0.347         LOADCASE    1     |
|  LOCATION:      0.00    CRITICAL CONDITION:            Cl. 13.8.2        |
|--------------------------------------------------------------------------|
|  STRENGTH CHECK SUMMARY                                                  |
|   CRITICAL RATIO:  0.347(PASS)            LOAD CASE:     1               |
|   LOCATION      :   0.00                  CONDITION: Cl. 13.8.2          |
|--------------------------------------------------------------------------|
|  DESIGN FORCES              LC:       1      LOC:      0.00              |
|         FX:   1000.00(C)    FY:     0.00      FZ:      0.00              |
|         MX:  0.000E+00      MY: 0.000E+00     MZ:  0.000E+00             |
|--------------------------------------------------------------------------|
|  SECTION PROPERTIES (LOC:   0.00)             UNIT:      CM              |
|   AXX:      92.800     AZZ:      72.136      AYY:         20.537         |
|   IXX:      57.500     IZZ:   11300.001      IYY:       3880.000         |
|   PZZ:     985.000     PYY:     463.000                                  |
|   SZZ:     893.281     SYY:     305.512      CW :     552900.312         |
|--------------------------------------------------------------------------|
|  MATERIAL PROPERTIES                          UNIT:      N MM            |
|   FYLD:     350.000     FU:   450.000      E: 204999.984  G:  76920.000  |
|--------------------------------------------------------------------------|
|  DESIGN PARAMETERS                                                       |
|   ACTUAL MEMBER LENGTH:     1.100        LZ:    1.100    LY:    1.100    |
|   KZ:  1.000        KY:  1.000      NSF:  1.000      SLF:  1.000         |
|--------------------------------------------------------------------------|
|  SECTION CLASS                                                           |
|   COMPRESSION    :            Class 1                                    |
|   FLEXURE           MAJOR               MINOR                            |
|   SECTION        : Class 2             Class 2                           |
|   FLANGE         : Class 2             Class 2                           |
|   WEB (CRITICAL) :            Class 1                                    |
|==========================================================================|
|  SLENDERNESS                                                             |
|   ACTUAL SLENDERNESS RATIO   :      17.012          LC   :        1      |
|   ALLOWABLE SLENDERNESS RATIO:     200.000          LOC  :      0.00     |
|--------------------------------------------------------------------------|
STAAD SPACE                                              -- PAGE NO.    6
STAAD.PRO CODE CHECKING - CSA S16-19 (v1.0)
***********************************************
ALL UNITS ARE IN KN   MET   UNLESS OTHERWISE Noted
Member :     1       Contd.
|--------------------------------------------------------------------------|
|                         CHECKS FOR AXIAL TENSION                         |
|--------------------------------------------------------------------------|
|  YIELDING                                                                |
|   FORCE:      CAPACITY:     RATIO:     CRITERIA:      LC:     LOC:       |
|    0.00E+00   2.92E+03       0.000      Cl. 13.2          1     0.000    |
|  RUPTURE                                                                 |
|   FORCE:      CAPACITY:     RATIO:     CRITERIA:      LC:     LOC:       |
|    0.00E+00   3.13E+03       0.000      Cl. 13.2          1     0.000    |
|--------------------------------------------------------------------------|
|                       CHECKS FOR AXIAL COMPRESSION                       |
|--------------------------------------------------------------------------|
|  FLEX BUCKLING                                                           |
|            FORCE:    CAPACITY:   RATIO:    CRITERIA:      LC:    LOC:    |
|   MAJOR:   1.00E+03   2.91E+03     0.343  Cl. 13.3            1    0.000 |
|   MINOR:   1.00E+03   2.88E+03     0.347  Cl. 13.3            1    0.000 |
|  INTERMEDIATE RESULTS:                                                   |
|               Ag:(CM)     Fe:(N MM)       λ:        n:      KL/r:        |
|   MAJOR:      92.800     20360.980      0.131     1.34       9.968       |
|   MINOR:      92.800      6991.204      0.224     1.34      17.012       |
|--------------------------------------------------------------------------|
|  FLEXURAL TORSIONAL BUCKLING                                             |
|   FORCE:      CAPACITY:     RATIO:     CRITERIA:      LC:     LOC:       |
|    1.00E+03   2.88E+03       0.347      Cl. 13.3          1     0.000    |
|  INTERMEDIATE RESULTS:                                                   |
|   Ag:(CM)    92.800   Fe:(N MM)     6381.727  &#955;:     0.234  n: 1.34      |
|--------------------------------------------------------------------------|
|                             CHECKS FOR SHEAR                             |
|--------------------------------------------------------------------------|
|  SHEAR ALONG Y AXIS                                                      |
|   FORCE:      CAPACITY:     RATIO:     CRITERIA:      LC:     LOC:       |
|    0.00E+00   4.52E+02       0.000    Cl. 13.4.1.1        1     0.000    |
|  INTERMEDIATE RESULTS:                                                   |
|   Aw:(CM)      Kv:       Ka:     Fcri:(N MM)  Fcre:(N MM)  Fs:(N MM)     |
|     21.758    5.552     0.224       489.474      1465.103    231.000     |
|--------------------------------------------------------------------------|
|  SHEAR ALONG Z AXIS                                                      |
|   FORCE:      CAPACITY:     RATIO:     CRITERIA:      LC:     LOC:       |
|    0.00E+00   1.36E+03       0.000    AISC G2-1           1     0.000    |
|  INTERMEDIATE RESULTS:                                                   |
|   Aw:(CM)                                                                |
|     72.136                                                               |
|--------------------------------------------------------------------------|
STAAD SPACE                                              -- PAGE NO.    7
STAAD.PRO CODE CHECKING - CSA S16-19 (v1.0)
***********************************************
ALL UNITS ARE IN KN   MET   UNLESS OTHERWISE Noted
Member :     1       Contd.
|--------------------------------------------------------------------------|
|                            CHECKS FOR BENDING                            |
|--------------------------------------------------------------------------|
|  YIELDING ALONG MAJOR AXIS                                               |
|   FORCE:      CAPACITY:     RATIO:     CRITERIA:      LC:     LOC:       |
|     0.00E+00  3.103E+02      0.000    Cl. 13.5(a)         1     0.000    |
|  INTERMEDIATE RESULTS: Mp:  3.45E+02   Se(CM):  0.00E+00    My:  0.00E+00|
|--------------------------------------------------------------------------|
|  YIELDING ALONG MINOR AXIS                                               |
|   FORCE:      CAPACITY:     RATIO:     CRITERIA:      LC:     LOC:       |
|    0.00E+00  1.458E+02      0.000    Cl. 13.5(a)         1     0.000     |
|  INTERMEDIATE RESULTS: Mp:  1.62E+02   Se(CM):  0.00E+00    My:  0.00E+00|
|--------------------------------------------------------------------------|
|  LATERAL TORSIONAL BUCKLING (MAJOR AXIS)                                 |
|   FORCE:      CAPACITY:     RATIO:     CRITERIA:      LC:     LOC:       |
|    0.00E+00  3.103E+02      0.000   Cl. 13.6(a)(i)       1     0.000     |
|  INTERMEDIATE RESULTS:                                                   |
|   Iyc(CM):    w 2:    w 3:    b x(CM):  Mu:       rt:   Myr:     Lu:       Lyr:  |
|  0.00E+00   2.50  0.00     0.00  1.982E+04  0.00  0.00E+00  0.00   0.00  |
|--------------------------------------------------------------------------|
|                          CHECKS FOR INTERACTION                          |
|--------------------------------------------------------------------------|
|  FLEXURE AND AXIAL TENSION                                               |
|                    RATIO:   CRITERIA:   LC:   LOC:     Tf:        Tr:    |
|   C/S STRENGTH   : 0.000  Cl. 13.9.2      1   0.00   0.00E+00  2.92E+03  |
|                        Mfz:         Mfy:          Mrz:         Mry:      |
|   C/S STRENGTH   :    0.00E+00      0.00E+00     3.10E+02      1.46E+02  |
|--------------------------------------------------------------------------|
|  FLEXURE AND AXIAL COMPRESSION                                           |
|                    RATIO:   CRITERIA:   LC:   LOC:     Cf:        Cr:    |
|   C/S STRENGTH   : 0.342  Cl. 13.8.2      1   0.000 1.00E+03  2.92E+03   |
|   MEMBER STRENGTH: 0.347  Cl. 13.8.2      1   0.000 1.00E+03  2.88E+03   |
|   LTB STRENGTH   : 0.347  Cl. 13.8.2      1   0.000 1.00E+03  2.88E+03   |
|                        Mfz:      Mfy:      Mrz:      Mry:    w 1z:    w 1y:    |
|   C/S STRENGTH   :  0.00E+00  0.00E+00  3.10E+02  1.46E+02  0.60   0.60  |
|   MEMBER STRENGTH:  0.00E+00  0.00E+00  3.10E+02  1.46E+02  0.60   0.60  |
|   LTB STRENGTH   :  0.00E+00  0.00E+00  3.10E+02  1.46E+02  0.60   0.60  |
|                        b :         Cez:     Cey:         U1z:     U1y:     |
|   C/S STRENGTH   :    0.69     1.89E+05  6.49E+04     1.00     1.00      |
|   MEMBER STRENGTH:    0.69     1.89E+05  6.49E+04     1.00     1.00      |
|   LTB STRENGTH   :    0.69     1.89E+05  6.49E+04     1.00     1.00      |
|--------------------------------------------------------------------------|
|  SHEAR CAPACITY MODIFICATION  ( SHEAR AND FLEX )                         |
|   FORCE:      CAPACITY:     RATIO:     CRITERIA:      LC:     LOC:       |
|     0.00E+00  4.523E+02      0.000    Cl. 14.6            1     0.000    |
|--------------------------------------------------------------------------|
|  BIAXIAL FLEXURE                                                         |
|   RATIO:  CRITERIA:  LC:   LOC:     Mfz:      Mrz:       Mfy:      Mry:  |
|   0.000  Cl. 13.8     1    0.00   0.00E+00  3.10E+02  0.00E+00  1.46E+02 |