V. CSA S16-19 - Short Column Compression
Determine the capacity of a short column per the CSA S16-19 code.
Problem
A Canadian W250x73 section is used for a pedestal with a height of 1.1 m. The axial load is 1,000 kN in compression. The steel is grade 350W.
Section Properties
- D = 253 mm
- B = 254 mm
- tw = 8.6 mm
- tf = 14.2 mm
- Ag = 9,280 mm2
- Ix = 113×106 mm4
- Iy = 38.8×106 mm4
- J = 575,000 mm4
- Cw = 553×109 mm6
Material Properties
- Fy = 350 MPa
- Fu = 450 MPa
- E = 205,000 MPa
- G = 76,920 MPa
Calculations
Section Classification
bel = B / 2 = 83.5 mm
h = D - 2×tf = 291.6 mm
Compression section classification per Table 1
- Flange classification:
- Web classification about major axis:
Therefore, the section is Class 1 for compression.
Column Capacity
Assume K = 1.0,
Elastic buckling stress:
Per Cl. 13.3.1, n = 1.34 (Group 2 W shape):
Flexural Torsional Buckling
Take the minimum of Fex, Fey, and Fez as FFTB:
FFTB = Fez = 6,382 MPa
Ratio = 1,000 / 2,879 = 0.347
Comparison
Criteria | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
λx | 0.131 | 0.131 | none | |
Fex (MPa) | 20,360 | 20,360.98 | negligible | |
Crx (kN) | 2,914 | 2,910 | negligible | |
λy | 0.224 | 0.224 | none | |
Fey (MPa) | 6,991 | 6,991,204 | negligible | |
Cry (kN) | 2,884 | 2,880 | negligible | |
λFTB | 0.234 | 0.234 | none | |
FFTB (MPa) | 6,382 | 6,381.727 | negligible | |
CFTB (kN) | 2,879 | 2,880 | negligible | |
Critical ratio | 0.347 | 0.347 | none |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\Canada\CSA S16-19 - Short Column Compression.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 20-Sep-21
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 -1000
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PRINT SUPPORT REACTION ALL
PARAMETER 1
CODE CANADIAN 2019
FYLD 350000 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD Output
STAAD.PRO CODE CHECKING - CSA S16-19 (v1.0) *********************************************** ALL UNITS ARE IN KN MET UNLESS OTHERWISE Noted |--------------------------------------------------------------------------| | MEMBER NO.: 1 SECTION: ST W250X73 (CANADIAN SECTIONS)| | STATUS: PASS CRITICAL RATIO: 0.347 LOADCASE 1 | | LOCATION: 0.00 CRITICAL CONDITION: Cl. 13.8.2 | |--------------------------------------------------------------------------| | STRENGTH CHECK SUMMARY | | CRITICAL RATIO: 0.347(PASS) LOAD CASE: 1 | | LOCATION : 0.00 CONDITION: Cl. 13.8.2 | |--------------------------------------------------------------------------| | DESIGN FORCES LC: 1 LOC: 0.00 | | FX: 1000.00(C) 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: 92.800 AZZ: 72.136 AYY: 21.758 | | IXX: 57.500 IZZ: 11300.001 IYY: 3880.000 | | PZZ: 985.000 PYY: 463.000 | | SZZ: 893.281 SYY: 305.512 CW : 552900.312 | |--------------------------------------------------------------------------| | MATERIAL PROPERTIES UNIT: N MM | | FYLD: 350.000 FU: 450.000 E: 204999.984 G: 76920.000 | |--------------------------------------------------------------------------| | DESIGN PARAMETERS | | ACTUAL MEMBER LENGTH: 1.100 LZ: 1.100 LY: 1.100 | | KZ: 1.000 KY: 1.000 NSF: 1.000 SLF: 1.000 | |--------------------------------------------------------------------------| | SECTION CLASS | | COMPRESSION : Class 1 | | FLEXURE MAJOR MINOR | | SECTION : Class 2 Class 2 | | FLANGE : Class 2 Class 2 | | WEB (CRITICAL) : Class 1 | |==========================================================================| | SLENDERNESS | | ACTUAL SLENDERNESS RATIO : 17.012 LC : 1 | | ALLOWABLE SLENDERNESS RATIO: 200.000 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: | | 0.00E+00 2.92E+03 0.000 Cl. 13.2 1 0.000 | | RUPTURE | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | 0.00E+00 3.13E+03 0.000 Cl. 13.2 1 0.000 | |--------------------------------------------------------------------------| | CHECKS FOR AXIAL COMPRESSION | |--------------------------------------------------------------------------| | FLEX BUCKLING | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | MAJOR: 1.00E+03 2.91E+03 0.343 Cl. 13.3 1 0.000 | | MINOR: 1.00E+03 2.88E+03 0.347 Cl. 13.3 1 0.000 | | INTERMEDIATE RESULTS: | | Ag:(CM) Fe:(N MM) λ: n: KL/r: | | MAJOR: 92.800 20360.980 0.131 1.34 9.968 | | MINOR: 92.800 6991.204 0.224 1.34 17.012 | |--------------------------------------------------------------------------| | FLEXURAL TORSIONAL BUCKLING | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | 1.00E+03 2.88E+03 0.347 Cl. 13.3 1 0.000 | | INTERMEDIATE RESULTS: | | Ag:(CM) 92.800 Fe:(N MM) 6381.727 λ: 0.234 n: 1.34 | |--------------------------------------------------------------------------| | CHECKS FOR SHEAR | |--------------------------------------------------------------------------| | SHEAR ALONG Y AXIS | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | 0.00E+00 4.52E+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) | | 21.758 5.552 0.224 489.474 1465.103 231.000 | |--------------------------------------------------------------------------| | SHEAR ALONG Z AXIS | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | -0.00E+00 1.36E+03 0.000 AISC G2-1 1 0.000 | | INTERMEDIATE RESULTS: | | Aw:(CM) | | 72.136 | |--------------------------------------------------------------------------| 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 3.103E+02 0.000 Cl. 13.5(a) 1 0.000 | | INTERMEDIATE RESULTS: Mp: 3.45E+02 Se(CM): 0.00E+00 My: 0.00E+00| |--------------------------------------------------------------------------| | YIELDING ALONG MINOR AXIS | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | 0.00E+00 1.458E+02 0.000 Cl. 13.5(a) 1 0.000 | | INTERMEDIATE RESULTS: Mp: 1.62E+02 Se(CM): 0.00E+00 My: 0.00E+00| |--------------------------------------------------------------------------| | LATERAL TORSIONAL BUCKLING (MAJOR AXIS) | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | -0.00E+00 3.103E+02 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 1.982E+04 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 : 0.000 Cl. 13.9.2 1 0.00 0.00E+00 2.92E+03 | | Mfz: Mfy: Mrz: Mry: | | C/S STRENGTH : -0.00E+00 0.00E+00 3.10E+02 1.46E+02 | |--------------------------------------------------------------------------| | FLEXURE AND AXIAL COMPRESSION | | RATIO: CRITERIA: LC: LOC: Cf: Cr: | | C/S STRENGTH : 0.342 Cl. 13.8.2 1 0.000 1.00E+03 2.92E+03 | | MEMBER STRENGTH: 0.347 Cl. 13.8.2 1 0.000 1.00E+03 2.88E+03 | | LTB STRENGTH : 0.347 Cl. 13.8.2 1 0.000 1.00E+03 2.88E+03 | | Mfz: Mfy: Mrz: Mry: w 1z: w 1y: | | C/S STRENGTH : -0.00E+00 0.00E+00 3.10E+02 1.46E+02 0.60 0.60 | | MEMBER STRENGTH: -0.00E+00 0.00E+00 3.10E+02 1.46E+02 0.60 0.60 | | LTB STRENGTH : -0.00E+00 0.00E+00 3.10E+02 1.46E+02 0.60 0.60 | | b : Cez: Cey: U1z: U1y: | | C/S STRENGTH : 0.69 1.89E+05 6.49E+04 1.00 1.00 | | MEMBER STRENGTH: 0.69 1.89E+05 6.49E+04 1.00 1.00 | | LTB STRENGTH : 0.69 1.89E+05 6.49E+04 1.00 1.00 | |--------------------------------------------------------------------------| | SHEAR CAPACITY MODIFICATION ( SHEAR AND FLEX ) | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | 0.00E+00 4.523E+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 3.10E+02 0.00E+00 1.46E+02 | |==========================================================================| STAAD SPACE -- PAGE NO. 8