# V. CSA S16-01 - Short Column Compression

Determine the factored compressive resistance of a short column.

## Reference

Kulak, G.L. and G.Y. Grondin. 2010. Limit States Design in Structural Steel. 9th Edition. Markham, ON:CISC. Example 4.1

## Problem

A W250x73 section is used for a pedestal with a height of 1.1 m.

The material used is G40.21 350W steel (Fy = 350 MPa) (FYLD)

## Calculations

The nominal yield strength is used for the actual yield strength for a Group 2 section, per Table 3 and Table 4 of Appendix A of the reference.

## Local Element Buckling

Evaluate the slenderness effects of the column web:

$h w = 225 8.6 = 26.2 ⁢ < 670 350 = 35.8$

Evaluate the slenderness effects of the column flanges:

$b 2 t = 254 2 × 14.2 = 8.9 < 200 350 = 10.7$

Both the column web and flanges are less than the local buckling limit, so the capacity of the column is evaluated using Eq. 4.21.

## Column Capacity

Assume K = 1.0,

$L r x = 1 , 100 110 = 10$
$Lry=1,10064.6=17.03$

The largest slenderness ration controls, thus the slenderness factor for buckling about the minor axis:

$λ=FyFe=3506,978=0.224$

When n = 1.34 (Group 2 W shape),

## Comparison

Table 1. Comparison of results
KL/r, major 10 9.968 negligible
KL/r, minor 17.03 17.012 negligible
Cr (kN) 2,884 2,884 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Canada\CSA S16-01 - Short Column Compression.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 26-June-20
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 -1
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 - (CAN/CSA-S16-01  ) V2.1
********************************************
ALL UNITS ARE - KNS  MET  (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
PASS     CSA-13.8.3C        0.000         1
1.00 C          0.00           0.00        1.10
STAAD SPACE                                              -- PAGE NO.    6
ALL UNITS ARE - KNS  MET  (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
MEMBER PROPERTIES (UNIT = CM)
-----------------------------
CROSS SECTION AREA =  9.28E+01   MEMBER LENGTH =  1.10E+02
IZ =  1.13E+04   SZ =  8.93E+02   PZ =  9.85E+02
IY =  3.88E+03   SY =  3.06E+02   PY =  4.63E+02
IX =  5.75E+01   CW =  5.53E+05
MATERIAL PROPERTIES (UNIT = MPA)
--------------------------------
FYLD = 350.0   FU = 450.0   E =  2.05E+05   G =  7.88E+04
SECTION CAPACITIES (UNIT - KN,M)
---------------------------------
CR1 =  2.884E+03   CR2 =  2.914E+03   SECTION CLASS 1
CRZ =  2.914E+03   CTORFLX =  2.884E+03
TENSILE CAPACITY     =  2.923E+03   COMPRESSIVE CAPACITY =  2.884E+03
FACTORED MOMENT RESISTANCE : MRY =  1.458E+02   MRZ =  3.103E+02
MU =  7.934E+03
FACTORED SHEAR RESISTANCE  : VRY =  4.523E+02   VRZ =  1.001E+03
MISCELLANEOUS INFORMATION
--------------------------
NET SECTION FACTOR FOR TENSION =  1.000
KL/RY =   17.012   KL/RZ =    9.968   ALLOWABLE KL/R =  200.000
UNSUPPORTED LENGTH OF THE COMPRESSION FLANGE (M) =  1.100
OMEGA-1 (Y-AXIS) = 0.00   OMEGA-1 (Z-AXIS) = 0.00   OMEGA-2 = 1.00
SHEAR FORCE (KNS) : Y AXIS =  0.000E+00   Z AXIS =  0.000E+00
SLENDERNESS RATIO OF WEB (H/W) =  2.61E+01