V.CSA S16-09 - 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
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.
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.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Canada\S16 2009\CSA S16-09 - Wide Flange Capacity Combined Stresses.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 17-Mar-19
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 2009
FYLD 350000 ALL
LAT 1 ALL
SSZ 1 ALL
SSY 1 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
STAAD.PRO CODE CHECKING - S16-09 (v1.1) ******************************************* ALL UNITS ARE - KN MET (UNLESS OTHERWISE Noted) -------------------- START OF DESIGN OUTPUT OF MEMBER 1 -------------------- MEMBER NO: 1 CRITICAL RATIO: 0.801(PASS) LOAD: 1 LOCATION (MET): 3.60 CONDITION: Cl. 13.8.2 SECTION: ST W250X73 (CANADIAN SECTIONS) UNIT: KN MET STRENGTH CHECKS: CRITICAL RATIO: 0.801(PASS) LOAD CASE: 1 LOCATION (MET): 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: 20.537 CW: 552900.312 SZZ: 893.281 SYY: 305.512 IZZ: 11300.001 IYY: 3880.000 UNIT: NEW MM MATERIAL PROPERTIES: FYLD: 350.000 FU: 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.(MET): 0.000 ALLOWABLE SLENDERNESS RATIO: 200.000 SECTION CLASS: COMPRESSION: Class 1 FLEXURE: Class 2 FLANGE: 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 - ( S16-09) v1.1 ******************************************** ALL UNITS ARE - KN MET (UNLESS OTHERWISE Noted) COMPRESSION: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET): 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: 20.537 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(MET): 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: 0.715 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 0.60 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 0.63 0.70 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 --------------------