V. CSA S16-01 - Slender Column Compression
Determine the factored compressive resistance of a slender column.
Reference
Kulak, G.L. and G.Y. Grondin. 2010. Limit States Design in Structural Steel. 9th Edition. Markham, ON:CISC. Example 4.2
Problem
A W250x73 section is used for a pedestal with a height of 11.0 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:
Evaluate the slenderness effects of the column flanges:
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,
The largest slenderness ration controls, thus the slenderness factor for buckling about the minor axis:
When n = 1.34 (Group 2 W shape),
Comparison
Criteria | Reference | STAAD.Pro | Difference |
---|---|---|---|
KL/r, major | 100 | 99.684 | negligible |
KL/r, minor | 170.3 | 170.118 | negligible |
Cr (kN) | 537.3 | 538.2 | negligible |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\Canada\CSA S16-01 - Slender 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 11 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 0.002 1
1.00 C 0.00 0.00 11.00
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+03
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 = 5.382E+02 CR2 = 1.267E+03 SECTION CLASS 1
CRZ = 1.267E+03 CTORFLX = 5.382E+02
TENSILE CAPACITY = 2.923E+03 COMPRESSIVE CAPACITY = 1.267E+03
FACTORED MOMENT RESISTANCE : MRY = 1.458E+02 MRZ = 1.694E+02
MU = 1.882E+02
FACTORED SHEAR RESISTANCE : VRY = 4.523E+02 VRZ = 1.001E+03
MISCELLANEOUS INFORMATION
--------------------------
NET SECTION FACTOR FOR TENSION = 1.000
KL/RY = 170.118 KL/RZ = 99.684 ALLOWABLE KL/R = 200.000
UNSUPPORTED LENGTH OF THE COMPRESSION FLANGE (M) = 11.000
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