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 (F_y = 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:

\frac{h}{w} = \frac{225}{8.6} = 26.2 < \frac{670}{\sqrt{350}} = 35.8

Evaluate the slenderness effects of the column flanges:

\frac{b}{2 t} = \frac{254}{2 \times 14.2} = 8.9 < \frac{200}{\sqrt{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,

\frac{L}{r_{x}} = \frac{1, 100}{110} = 10

\frac{L}{r_{y}} = \frac{1, 100}{64.6} = 17.03

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

F_{e} = \frac{π^{2} E}{k L / r_{y}} = \frac{π^{2} 205 \times 10^{3}}{1 \times 17.03} = 6, 978 kN

λ = \sqrt{\frac{F_{y}}{F_{e}}} = \sqrt{\frac{350}{6, 978}} = 0.224

When n = 1.34 (Group 2 W shape),

C_{r} = ϕ A F_{y} {(1 + λ^{2 n})}^{- 1 / n} = 0.90 \times 9, 280 \times 350 {[1 + {0.224}^{(2 \times 1.34)}]}^{- 1 / 1.34} = 2.884 \times {(10)}^{6} N = 2, 884 kN

Comparison

Table 1. Comparison of results
Criteria	Reference	STAAD.Pro	Difference
KL/r, major	10	9.968	negligible
KL/r, minor	17.03	17.012	negligible
C_r (kN)	2,884	2,884	none

STAAD.Pro Input File

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
MEMBER PROPERTY CANADIAN
1 TABLE ST W250X73
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
JOINT LOAD
2 FY -1
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PRINT SUPPORT REACTION ALL
PARAMETER 1
CODE CANADIAN 2001
FYLD 350000 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD.Pro Output

                       STAAD.PRO CODE CHECKING - (CAN/CSA-S16-01  ) V2.1           
                       ********************************************
 ALL UNITS ARE - KNS  MET  (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
       1 ST   W250X73                  (CANADIAN SECTIONS)
                           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)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          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