V. CSA S16-14 - Slender Column Compression (2024)

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 (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:

$\frac{b}{2 t} = \frac{254}{2 \times 14.2} = 8.9 < \frac{200}{\sqrt{350}} = 10.7$

Column Capacity

Assume K = 1.0,

$\frac{L}{r_{x}} = \frac{11, 000}{110} = 100$

$\frac{L}{r_{y}} = \frac{11, 000}{64.6} = 170$

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

$F_{e} = \frac{π^{2} \times 200, 000}{{(1.0 \times 170)}^{2}} = 68.3 kN$

$λ = \sqrt{\frac{F_{y}}{F_{e}}} = \sqrt{\frac{350}{68.3}} = 2.26$

When n = 1.34 (Group 2 W shape),

$C_{r} = ϕ A F_{y} {(1 + λ^{2 n})}^{- 1 / n} = 0.90 \times 9, 280 \times 350 {[1 + {2.26}^{(2 \times 1.34)}]}^{- 1 / 1.34} = 0.529 \times {(10)}^{6} N = 529 kN$

Comparison

Table 1. Comparison of results
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%
C_r (kN)	529	538.161	1.7%

STAAD Input

The file C:\Users\Public\PublicDocuments\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Canada\CSA S16-14 - Slender Column Compression.STD is typically installed with the program.

STAAD SPACESTART JOB INFORMATIONENGINEER DATE 22-Apr-14END JOB INFORMATIONINPUT WIDTH 79UNIT METER KNJOINT COORDINATES1 0 0 0; 2 0 11 0;MEMBER INCIDENCES1 1 2;DEFINE MATERIAL STARTISOTROPIC STEELE 2.05e+08POISSON 0.3DENSITY 76.92ALPHA 1.2e-05DAMP 0.03TYPE STEEL*STRENGTH FY 350000 FU 450000 RY 1.5 RT 1.2G 7.692e+07END DEFINE MATERIALMEMBER PROPERTY CANADIAN1 TABLE ST W250X73CONSTANTSMATERIAL STEEL ALLSUPPORTS1 FIXEDLOAD 1 LOADTYPE None TITLE LOAD CASE 1JOINT LOAD2 FY -0.001PERFORM ANALYSISPRINT MEMBER PROPERTIES ALLPRINT SUPPORT REACTION ALLPARAMETER 1CODE CANADIAN 2014FYLD 350000 ALLFU 450000 ALLTRACK 2 ALLCHECK CODE ALLFINISH

STAAD Output

 WARNING: The current units are in KN METE. All the design results are in KN MET (unless otherwise noted). 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: 20.537 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: 20.537 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 --------------------