V.CSA S16-09 - Shear Capacity Combined Stresses
Reference
Kulak, G.L. and G.Y. Grondin. 2010. Limit States Design in Structural Steel. 9th Edition. Markham, ON:CISC. Example 8.6
Problem
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)
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.
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 - Shear Capacity Combined Stresses.STD is typically installed with the program.
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
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: 0.926(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 --------------------