V. CSA S16-14 - Wide Flange Capacity Combined Stresses
Check the capacity of a wide-flange column under combined stresses.
Reference
Kulak, G.L. and G.Y. Grondin. 2010. Limit States Design in Structural Steel. 9th Edition. Markham, ON:CISC. Example 8.5
Problem
The W250x73 column has the following concentrated loads applied at the top of the column:
Cf = 900 kN
Mfx = 180 kN·m
The material used is G40.21 350W steel (Fy = 350 MPa) (FYLD). The column is assumed to be braced laterally against lateral-torsional buckling (LAT 1).
L = 3.6 m
Axial Capacity
Determine the buckling load of the column, assuming that weak axis bucking will not control due to bracing:
The largest slenderness ratio controls:
Moment Modifier
κ = -0/180 = 0
ω1 = 0.6 - 0.4κ = 0.6 ≤ 1.0
Calculate the elastic buckling load for the bending axis:
Comparison
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\Canada\CSA S16-14 - Wide Flange Capacity Combined Stresses.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 17-Sep-13
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 3.6 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 ENFORCED BUT MX MY MZ
1 PINNED
2 ENFORCED BUT FY MX MZ
*2 ENFORCED BUT FX FZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
JOINT LOAD
1 FY 900
*1 MZ 180
2 FY -900 MZ 180
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PRINT SUPPORT REACTION ALL
PARAMETER 1
CODE CANADIAN 2014
FYLD 350000 ALL
LAT 1 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD Output
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: 0.896(PASS) LOAD: 1 LOCATION : 3.60 CONDITION: Cl. 13.8.2 SECTION: ST W250X73 (CANADIAN SECTIONS) UNIT: KN MET STRENGTH CHECKS: CRITICAL RATIO: 0.896(PASS) LOAD CASE: 1 LOCATION : 3.60 CONDITION: Cl. 13.8.2 DESIGN FORCES: Fx: 900.00(C) Fy: 50.00 Fz: 0.00 Mx: 0.00E+00 My: 0.00E+00 Mz: -1.80E+02 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 ): 3.600 PARAMETERS: KZ: 1.000 KY: 1.000 NSF: 1.000 SLF: 1.000 SLENDERNESS: ACTUAL SLENDERNESS RATIO: 55.675 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: 900.000 2715.935 0.331 Cl. 13.3 1 0.000 MINOR: 900.000 2233.940 0.403 Cl. 13.3 1 0.000 INTERMEDIATE: Ag(CM): KL/r: Fe(N MM): λ n: MAJOR: 92.800 32.624 1900.987 0.429 1.340 MINOR: 92.800 55.675 652.728 0.732 1.340 SHEAR: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET ): MAJOR: 50.000 452.349 0.111 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 5.360 0.070 480.943 1414.474 231.000 MINOR: 72.136 UNIT: KN MET YIELDING: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET ): MAJOR: 1.80E+02 3.10E+02 0.580 Cl. 13.5(a) 1 3.600 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 INTERACTION: RATIO: CRITERIA: LOAD CASE: LOCATION: FLEXURE AND AXIAL TENSION: C/S STRENGTH: 0.580 Cl. 13.9.1 1 3.600 FLEXURE AND AXIAL COMPRESSION: C/S STRENGTH: 0.801 Cl. 13.8.2 1 3.600 MEMBER STRENGTH: 0.896 Cl. 13.8.2 1 0.000 FLEX AND SHEAR: 0.472 Cl. 14.6(a) 1 3.600 BIAXIAL FLEX: 0.580 Cl. 13.8 1 3.600 INTERMEDIATE: FLEXURE AND AXIAL TENSION: C/S STRENGTH: Tf: 0.00E+00 Tr: 2.92E+03 Mfz: 1.80E+02 Mrz: 3.10E+02 FLEXURE AND AXIAL COMPRESSION: Cf: Mfz: Mfy: Cr: Mrz: Mry: b : Cez: Cey: w 1z: w 1y: U1z: U1y: C/S STR: 9.00E+02 1.80E+02 0.00E+00 2.92E+03 3.10E+02 1.46E+02 0.85 1.76E+04 6.06E+03 0.60 0.60 1.00 1.00 MEM STR: 9.00E+02 1.80E+02 0.00E+00 2.23E+03 3.10E+02 1.46E+02 0.85 1.76E+04 6.06E+03 0.60 0.60 1.00 1.00 FLEX SHEAR: Mfz: 1.80E+02 Mrz: 3.10E+02 Vfy: 5.00E+01 Vry: 4.52E+02 STAAD SPACE -- PAGE NO. 7 BIAX FLEX: Mfz: 1.80E+02 Mrz: 3.10E+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 46. FINISH