# V. CSA S16-19 - Axial Tension

Determine the capacity of a member subject to axial tension load per the CSA S16-19 code.

## Problem

A 4 m long member is subjected to a 630 kN tensile load. The section is a Canadian W100x19. The steel is grade 300W.

Section Properties

• Ag = 2,480 mm2

Material Properties

• Fy = 300 MPa
• Fu = 450 MPa

## Calculations

Assume the gross area for both yielding and rupture limit states. Therefore, Ane = Ag = 2,480 mm2.

So, the tensile capacity = 669.6 kN.

The critical stress ratio 630 / 669.6 = 0.941.

## Comparison

Table 1. Comparison of results
Yielding tension capacity, Tr (kN) 669.6 669.6 none
Rupture tension capacity, Tr (kN) 837 837 none
Critical Ratio 0.941 0.941 none

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

The following design parameters are used:
• The parameter SNUG 0 is used for welded or pre-tenstioned bolts (i.e., no reduction for bolt holes)
• The default value of NSF 1 is used for net section equal to the gross area.
• The default value of SLF 1 is used for a shear lag factor of 1 (i.e., no shear lag in connection)
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 16-Sep-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 4 0 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 W100x19
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MY MZ
2 FX 630
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PRINT SUPPORT REACTION ALL
PARAMETER 1
FYLD 300000 ALL
FU 450000 ALL
SNUG 0 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  W100X19          (CANADIAN SECTIONS)|
|  STATUS:        PASS    CRITICAL RATIO:  0.941         LOADCASE    1     |
|  LOCATION:      0.00    CRITICAL CONDITION:            Cl. 13.9.2        |
|--------------------------------------------------------------------------|
|  STRENGTH CHECK SUMMARY                                                  |
|   CRITICAL RATIO:  0.941(PASS)            LOAD CASE:     1               |
|   LOCATION      :   0.00                  CONDITION: Cl. 13.9.2          |
|--------------------------------------------------------------------------|
|  DESIGN FORCES              LC:       1      LOC:      0.00              |
|         FX:    630.00(T)    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:      24.800     AZZ:      18.128      AYY:          6.901         |
|   IXX:       6.360     IZZ:     477.000      IYY:        161.000         |
|   PZZ:     103.000     PYY:      48.000                                  |
|   SZZ:      90.000     SYY:      31.262      CW :       3785.434         |
|--------------------------------------------------------------------------|
|  MATERIAL PROPERTIES                          UNIT:      N MM            |
|   FYLD:     300.000     FU:   450.000      E: 204999.984  G:  76920.000  |
|--------------------------------------------------------------------------|
|  DESIGN PARAMETERS                                                       |
|   ACTUAL MEMBER LENGTH:     4.000        LZ:    4.000    LY:    4.000    |
|   KZ:  1.000        KY:  1.000      NSF:  1.000      SLF:  1.000         |
|--------------------------------------------------------------------------|
|  SECTION CLASS                                                           |
|   COMPRESSION    :            Class 1                                    |
|   FLEXURE           MAJOR               MINOR                            |
|   SECTION        : Class 1             Class 1                           |
|   FLANGE         : Class 1             Class 1                           |
|   WEB (CRITICAL) :            Class 1                                    |
|==========================================================================|
|  SLENDERNESS                                                             |
|   ACTUAL SLENDERNESS RATIO   :     156.990          LC   :        1      |
|   ALLOWABLE SLENDERNESS RATIO:     300.000          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:       |
|    6.30E+02   6.70E+02       0.941      Cl. 13.2          1     0.000    |
|  RUPTURE                                                                 |
|   FORCE:      CAPACITY:     RATIO:     CRITERIA:      LC:     LOC:       |
|    6.30E+02   8.37E+02       0.753      Cl. 13.2          1     0.000    |
|--------------------------------------------------------------------------|
|                       CHECKS FOR AXIAL COMPRESSION                       |
|--------------------------------------------------------------------------|
|  FLEX BUCKLING                                                           |
|            FORCE:    CAPACITY:   RATIO:    CRITERIA:      LC:    LOC:    |
|   MAJOR:   0.00E+00   3.57E+02     0.000  Cl. 13.3            1    0.000 |
|   MINOR:   0.00E+00   1.62E+02     0.000  Cl. 13.3            1    0.000 |
|  INTERMEDIATE RESULTS:                                                   |
|               Ag:(CM)     Fe:(N MM)       λ:        n:      KL/r:        |
|   MAJOR:      24.800       243.221      1.111     1.34      91.207       |
|   MINOR:      24.800        82.093      1.912     1.34     156.990       |
|--------------------------------------------------------------------------|
|  FLEXURAL TORSIONAL BUCKLING                                             |
|   FORCE:      CAPACITY:     RATIO:     CRITERIA:      LC:     LOC:       |
|    0.00E+00   1.62E+02       0.000      Cl. 13.3          1     0.000    |
|  INTERMEDIATE RESULTS:                                                   |
|   Ag:(CM)    24.800   Fe:(N MM)       82.093  λ:     1.912  n: 1.34      |
|--------------------------------------------------------------------------|
|                             CHECKS FOR SHEAR                             |
|--------------------------------------------------------------------------|
|  SHEAR ALONG Y AXIS                                                      |
|   FORCE:      CAPACITY:     RATIO:     CRITERIA:      LC:     LOC:       |
|    0.00E+00   1.34E+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)     |
|      7.526    5.343     0.026       932.501      6203.750    198.000     |
|--------------------------------------------------------------------------|
|  SHEAR ALONG Z AXIS                                                      |
|   FORCE:      CAPACITY:     RATIO:     CRITERIA:      LC:     LOC:       |
|    0.00E+00   2.94E+02       0.000    AISC G2-1           1     0.000    |
|  INTERMEDIATE RESULTS:                                                   |
|   Aw:(CM)                                                                |
|     18.128                                                               |
|--------------------------------------------------------------------------|
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  2.781E+01      0.000    Cl. 13.5(a)         1     0.000    |
|  INTERMEDIATE RESULTS: Mp:  3.09E+01   Se(CM):  0.00E+00    My:  0.00E+00|
|--------------------------------------------------------------------------|
|  YIELDING ALONG MINOR AXIS                                               |
|   FORCE:      CAPACITY:     RATIO:     CRITERIA:      LC:     LOC:       |
|    0.00E+00  1.296E+01      0.000    Cl. 13.5(a)         1     0.000     |
|  INTERMEDIATE RESULTS: Mp:  1.44E+01   Se(CM):  0.00E+00    My:  0.00E+00|
|--------------------------------------------------------------------------|
|  LATERAL TORSIONAL BUCKLING (MAJOR AXIS)                                 |
|   FORCE:      CAPACITY:     RATIO:     CRITERIA:      LC:     LOC:       |
|    0.00E+00  2.781E+01      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  8.267E+01  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   : 0.941  Cl. 13.9.2      1   0.00   6.30E+02  6.70E+02  |
|                        Mfz:         Mfy:          Mrz:         Mry:      |
|   C/S STRENGTH   :    0.00E+00      0.00E+00     2.78E+01      1.30E+01  |
|--------------------------------------------------------------------------|
|  FLEXURE AND AXIAL COMPRESSION                                           |
|                    RATIO:   CRITERIA:   LC:   LOC:     Cf:        Cr:    |
|   C/S STRENGTH   : 0.000  Cl. 13.8.2      1   0.000 0.00E+00  6.70E+02   |
|   MEMBER STRENGTH: 0.000  Cl. 13.8.2      1   0.000 0.00E+00  1.62E+02   |
|   LTB STRENGTH   : 0.000  Cl. 13.8.2      1   0.000 0.00E+00  1.62E+02   |
|                        Mfz:      Mfy:      Mrz:      Mry:    w 1z:    w 1y:    |
|   C/S STRENGTH   :  0.00E+00  0.00E+00  2.78E+01  1.30E+01  0.60   0.60  |
|   MEMBER STRENGTH:  0.00E+00  0.00E+00  2.78E+01  1.30E+01  0.60   0.60  |
|   LTB STRENGTH   :  0.00E+00  0.00E+00  2.78E+01  1.30E+01  0.60   0.60  |
|                        b :         Cez:     Cey:         U1z:     U1y:     |
|   C/S STRENGTH   :    0.85     6.03E+02  2.04E+02     1.00     1.00      |
|   MEMBER STRENGTH:    0.85     6.03E+02  2.04E+02     1.00     1.00      |
|   LTB STRENGTH   :    0.85     6.03E+02  2.04E+02     1.00     1.00      |
|--------------------------------------------------------------------------|
|  SHEAR CAPACITY MODIFICATION  ( SHEAR AND FLEX )                         |
|   FORCE:      CAPACITY:     RATIO:     CRITERIA:      LC:     LOC:       |
|     0.00E+00  1.341E+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  2.78E+01  0.00E+00  1.30E+01 |