V. CSA S16-14 - 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 | 170.118 | negligible |
λ, critical | 2.26 | 2.237 | 1.0% |
Cr (kN) | 529 | 538.161 | 1.7% |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\Canada\CSA S16-14 - Slender Column Compression.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 22-Apr-14
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 -0.001
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PRINT SUPPORT REACTION ALL
PARAMETER 1
CODE CANADIAN 2014
FYLD 350000 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD Output
STEEL DESIGN
STAAD SPACE -- PAGE NO. 5
STAAD.PRO CODE CHECKING - S16-14 (v1.0)
*******************************************
ALL UNITS ARE - KN MET (UNLESS OTHERWISE Noted)
-------------------- START OF DESIGN OUTPUT OF MEMBER 1 --------------------
MEMBER NO: 1 CRITICAL RATIO: 0.000(PASS) LOAD: 1
LOCATION : 0.00 CONDITION: Cl. 13.8.2
SECTION: ST W250X73 (CANADIAN SECTIONS)
UNIT: KN MET
STRENGTH CHECKS:
CRITICAL RATIO: 0.000(PASS) LOAD CASE: 1 LOCATION : 0.00 CONDITION: Cl. 13.8.2
DESIGN FORCES: Fx: 0.00(C) Fy: 0.00 Fz: 0.00
Mx: 0.00E+00 My: 0.00E+00 Mz: 0.00E+00
UNIT: CM
SECTION PROPERTIES: AZZ: 72.136 AYY: 21.758 CW: 552900.312
SZZ: 893.281 SYY: 305.512
IZZ: 11300.001 IYY: 3880.000
UNIT: NEW MM
MATERIAL PROPERTIES: FYLD (N MM): 350.000 FU (N MM): 450.000
ACTUAL MEMBER LENGTH (MET ): 11.000
PARAMETERS: KZ: 1.000 KY: 1.000 NSF: 1.000 SLF: 1.000
SLENDERNESS: ACTUAL SLENDERNESS RATIO: 170.118 LOAD: 1 LOC.: 0.000
ALLOWABLE SLENDERNESS RATIO: 200.000
SECTION CLASS:
COMPRESSION: Class 1
FLEXURE MAJOR MINOR
SECTION: Class 2 Class 2
FLANGE: Class 2 Class 2
WEB: Class 1
UNIT: KN MET
TENSION: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET ):
YIELDING: 0.000 2923.200 0.000 Cl. 13.2 1 0.000
RUPTURE: 0.000 3132.000 0.000 Cl. 13.2 1 0.000
STAAD SPACE -- PAGE NO. 6
STAAD.PRO CODE CHECKING - ( S16-14) v1.0
********************************************
ALL UNITS ARE - KN MET (UNLESS OTHERWISE Noted)
COMPRESSION: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION:
MAJOR: 0.001 1266.716 0.000 Cl. 13.3 1 0.000
MINOR: 0.001 538.161 0.000 Cl. 13.3 1 0.000
INTERMEDIATE: Ag(CM): KL/r: Fe(N MM): λ n:
MAJOR: 92.800 99.684 203.610 1.311 1.340
MINOR: 92.800 170.118 69.912 2.237 1.340
SHEAR: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET ):
MAJOR: 0.000 452.349 0.000 Cl. 13.4.1.1 1 0.000
MINOR: -0.000 1363.370 0.000 AISC G2-1 1 0.000
INTERMEDIATE: Aw(CM): Kv: Ka: Fcri(N MM): Fcre(N MM): Fs(N MM):
MAJOR: 21.758 5.342 0.023 480.151 1409.819 231.000
MINOR: 72.136
UNIT: KN MET
YIELDING: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET ):
MAJOR: -0.00E+00 3.10E+02 0.000 Cl. 13.5(a) 1 0.000
MINOR: 0.00E+00 1.46E+02 0.000 Cl. 13.5(a) 1 0.000
INTERMEDIATE: Mp: Se: My:
MAJOR: 3.45E+02 0.00E+00 0.00E+00
MINOR: 1.62E+02 0.00E+00 0.00E+00
UNIT: KN MET
LAT TOR BUCK: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET ):
MAJOR: -0.00E+00 2.83E+02 0.000 Cl. 13.6(a)(i) 1 0.000
INTERMEDIATE: Iyc(CM): w 2: w 3: b x: Mu: rt: Myr: Lu: Lyr:
MAJOR: 0.00E+00 2.50 0.00 0.00 4.66E+02 0.00 0.00E+00 0.00 0.00
UNIT: KN MET
INTERACTION: RATIO: CRITERIA: LOAD CASE: LOCATION:
FLEXURE AND AXIAL TENSION:
C/S STRENGTH: 0.000 Cl. 13.9.1 1 0.000
FLEXURE AND AXIAL COMPRESSION:
C/S STRENGTH: 0.000 Cl. 13.8.2 1 0.000
MEMBER STRENGTH: 0.000 Cl. 13.8.2 1 0.000
LTB STRENGTH: 0.000 Cl. 13.8.2 1 0.000
FLEX AND SHEAR: 0.000 Cl. 14.6(a) 1 0.000
BIAXIAL FLEX: 0.000 Cl. 13.8 1 0.000
INTERMEDIATE:
FLEXURE AND AXIAL TENSION:
C/S STRENGTH: Tf: 0.00E+00 Tr: 2.92E+03 Mfz: -0.00E+00 Mrz: 3.10E+02
STAAD SPACE -- PAGE NO. 7
STAAD.PRO CODE CHECKING - ( S16-14) v1.0
********************************************
ALL UNITS ARE - KN MET (UNLESS OTHERWISE Noted)
FLEXURE AND AXIAL COMPRESSION:
Cf: Mfz: Mfy: Cr: Mrz: Mry: b : Cez: Cey: w 1z: w 1y: U1z: U1y:
C/S STR: 1.00E-03 -0.00E+00 0.00E+00 2.92E+03 3.10E+02 1.46E+02 0.85 1.89E+03 6.49E+02 0.60 0.60 1.00 1.00
MEM STR: 1.00E-03 -0.00E+00 0.00E+00 5.38E+02 3.10E+02 1.46E+02 0.85 1.89E+03 6.49E+02 0.60 0.60 1.00 1.00
LTB STR: 1.00E-03 -0.00E+00 0.00E+00 5.38E+02 2.83E+02 1.46E+02 0.85 1.89E+03 6.49E+02 0.60 0.60 1.00 1.00
FLEX SHEAR: Mfz: -0.00E+00 Mrz: 2.83E+02 Vfy: 0.00E+00 Vry: 4.52E+02
BIAX FLEX: Mfz: -0.00E+00 Mrz: 2.83E+02 Mfy: 0.00E+00 Mry: 1.46E+02
-------------------- END OF DESIGN OUTPUT OF MEMBER 1 --------------------
***NOTE:OMEGA1 AND OMEGA2 ARE CALCULATED USING C/S MOMENT OF ANALYTICAL MEMBERS