V. CSA S16-09 - Shear Capacity Combined Stresses
References
Kulak, G.L. and G.Y. Grondin. 2010. Limit States Design in Structural Steel. 9th Edition. Markham, ON:CISC. Example 8.6
Details
The W250x73 column has the following concentrated loads
Cf = 900 kN
And a uniform moment of:
Mfx = 180 kN·m
The material used is G40.21 350W steel (Fy = 350
MPa) (FYLD). The beam is braced against
lateral-torsional buckling only at the ends (LAT 0, default)
Calculations
Calculations
Axial Capacity
Determine the buckling load of the column:
The largest slenderness ratio controls:
Moment Modifier
Uniform moment:
ω1 = 1.0
Calculate the elastic buckling load for the bending axis:
Bending Capacity
ω2 = 1.0
EIyGJ =
200,000×38.8×76.92×575= 343.2×1021 MPa2·mm8
Plastic moment capacity:
Mp =
ZxFy = 985×103 × 350 = 345×106
N·mm = 345 kN·m
Mu = 871 kN·m >
0.67×Mp = 0.67×345 = 231 kN·m
Therefore, the moment capacity is calculated as:
Check the capacity based on the strength cross-section:
Mrx =
0.9×985×103 ×350 = 310 kN·m
This governs capacity.
Combined Stress Ratio
Results
| Criteria | Reference | STAAD.Pro | Difference |
|---|---|---|---|
| (KL/r)x | 33 | 32.624 | negligible |
| (KL/r)y | 56 | 55.675 | negligible |
| Cr (kN) | 2,216 | 2,220 | negligible |
| Ce (kN) | 17,211 | 17,200 | negligible |
| Stress Ratio | 0.929 | 0.926 | negligible |
Note: Both the reference and
hand calculations agree with the
STAAD.Pro results that the section is adequate.
The reference however neglects to account for section capacity checks, which
control in this case.
Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2026\Samples Verification Models\09 Steel Design\Canada\S16 2009\CSA S16-09 - Shear Capacity Combined Stresses.STD is typically installed with the program.
STAAD
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 21-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 2.00e+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
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 MZ 180
2 FY -900 MZ -180
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PRINT SUPPORT REACTION ALL
PARAMETER 1
CODE CANADIAN 2009
SSY 1 ALL
SSZ 1 ALL
FYLD 350000 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
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: 0.926(PASS) LOAD: 1
LOCATION (MET): 0.00 CONDITION: Cl. 13.8.2
SECTION: ST W250X73 (CANADIAN SECTIONS)
UNIT: KN MET
STRENGTH CHECKS:
CRITICAL RATIO: 0.926(PASS) LOAD CASE: 1 LOCATION (MET): 0.00 CONDITION: Cl. 13.8.2
DESIGN FORCES: Fx: 900.00(C) Fy: 0.00 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 2709.553 0.332 Cl. 13.3 1 0.000
MINOR: 900.000 2217.120 0.406 Cl. 13.3 1 0.000
INTERMEDIATE: Ag:(CM) KL/r: Fe:(N MM) λ n:
MAJOR: 92.800 32.624 1854.621 0.434 1.340
MINOR: 92.800 55.675 636.808 0.741 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 5.360 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 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: -1.80E+02 3.17E+02 0.567 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 1.00 0.00 0.00 8.71E+02 0.00 0.00E+00 0.00 0.00
UNIT: KN MET
INTERACTION: RATIO: CRITERIA: LOAD CASE: LOCATION(MET):
FLEXURE AND AXIAL TENSION:
C/S STRENGTH: 0.580 Cl. 13.9.1 1 0.000
MEMBER STRENGTH: 0.580 Cl. 13.9.2 1 0.000
FLEXURE AND AXIAL COMPRESSION:
C/S STRENGTH: 0.828 Cl. 13.8.2 1 0.000
MEMBER STRENGTH: 0.926 Cl. 13.8.2 1 0.000
LTB STRENGTH: 0.926 Cl. 13.8.2 1 0.000
FLEX AND SHEAR: 0.422 Cl. 14.6(a) 1 0.000
BIAXIAL FLEX: 0.580 Cl. 13.8 1 0.000
INTERMEDIATE:
FLEXURE AND AXIAL TENSION:
C/S STRENGTH: Tf: 0.00E+00 Tr: 2.92E+03 Mfz: -1.80E+02 Mrz: 3.10E+02
STAAD SPACE -- PAGE NO. 7
STAAD.PRO CODE CHECKING - ( S16-09) v1.1
********************************************
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: 9.00E+02 -1.80E+02 0.00E+00 2.92E+03 3.10E+02 1.46E+02 0.60 1.72E+04 5.91E+03 1.00 0.60 1.06 1.00
MEM STR: 9.00E+02 -1.80E+02 0.00E+00 2.22E+03 3.10E+02 1.46E+02 0.85 1.72E+04 5.91E+03 0.60 1.00 1.06 0.71
LTB STR: 9.00E+02 -1.80E+02 0.00E+00 2.22E+03 3.10E+02 1.46E+02 0.85 1.72E+04 5.91E+03 1.00 0.60 1.06 0.71
FLEX SHEAR: Mfz: -1.80E+02 Mrz: 3.10E+02 Vfy: 0.00E+00 Vry: 4.52E+02
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 --------------------