V. CSA S16-14 - 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 Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\Verification Models\09 Steel Design\Canada\CSA S16-14 - Shear 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 2.00e+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
SSY 1 ALL
SSZ 1 ALL
FYLD 350000 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD Output
STAAD.PRO CODE CHECKING - CSA S16-19 (v1.0) *********************************************** ALL UNITS ARE IN KN MET UNLESS OTHERWISE Noted |--------------------------------------------------------------------------| | MEMBER NO.: 1 SECTION: ST W250X73 (CANADIAN SECTIONS)| | STATUS: PASS CRITICAL RATIO: 0.926 LOADCASE 1 | | LOCATION: 0.00 CRITICAL CONDITION: Cl. 13.8.2 | |--------------------------------------------------------------------------| | STRENGTH CHECK SUMMARY | | CRITICAL RATIO: 0.926(PASS) LOAD CASE: 1 | | LOCATION : 0.00 CONDITION: Cl. 13.8.2 | |--------------------------------------------------------------------------| | DESIGN FORCES LC: 1 LOC: 0.00 | | FX: 900.00(C) FY: 0.00 FZ: 0.00 | | MX: 0.000E+00 MY: 0.000E+00 MZ: 1.800E+02 | |--------------------------------------------------------------------------| | SECTION PROPERTIES (LOC: 0.00) UNIT: CM | | AXX: 92.800 AZZ: 72.136 AYY: 21.758 | | IXX: 57.500 IZZ: 11300.001 IYY: 3880.000 | | PZZ: 985.000 PYY: 463.000 | | SZZ: 893.281 SYY: 305.512 CW : 552900.312 | |--------------------------------------------------------------------------| | MATERIAL PROPERTIES UNIT: N MM | | FYLD: 350.000 FU: 450.000 E: 199999.984 G: 76920.000 | |--------------------------------------------------------------------------| | DESIGN PARAMETERS | | ACTUAL MEMBER LENGTH: 3.600 LZ: 3.600 LY: 3.600 | | KZ: 1.000 KY: 1.000 NSF: 1.000 SLF: 1.000 | |--------------------------------------------------------------------------| | SECTION CLASS | | COMPRESSION : Class 1 | | FLEXURE MAJOR MINOR | | SECTION : Class 2 Class 2 | | FLANGE : Class 2 Class 2 | | WEB (CRITICAL) : Class 1 | |==========================================================================| | SLENDERNESS | | ACTUAL SLENDERNESS RATIO : 55.675 LC : 1 | | ALLOWABLE SLENDERNESS RATIO: 200.000 LOC : 0.00 | |--------------------------------------------------------------------------| STAAD SPACE -- PAGE NO. 6 STAAD.PRO CODE CHECKING - CSA S16-19 (v1.0) *********************************************** ALL UNITS ARE IN KN MET UNLESS OTHERWISE Noted Member : 1 Contd. |--------------------------------------------------------------------------| | CHECKS FOR AXIAL TENSION | |--------------------------------------------------------------------------| | YIELDING | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | 0.00E+00 2.92E+03 0.000 Cl. 13.2 1 0.000 | | RUPTURE | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | 0.00E+00 3.13E+03 0.000 Cl. 13.2 1 0.000 | |--------------------------------------------------------------------------| | CHECKS FOR AXIAL COMPRESSION | |--------------------------------------------------------------------------| | FLEX BUCKLING | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | MAJOR: 9.00E+02 2.71E+03 0.332 Cl. 13.3 1 0.000 | | MINOR: 9.00E+02 2.22E+03 0.406 Cl. 13.3 1 0.000 | | INTERMEDIATE RESULTS: | | Ag:(CM) Fe:(N MM) λ: n: KL/r: | | MAJOR: 92.800 1854.621 0.434 1.34 32.624 | | MINOR: 92.800 636.808 0.741 1.34 55.675 | |--------------------------------------------------------------------------| | FLEXURAL TORSIONAL BUCKLING | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | 9.00E+02 2.22E+03 0.406 Cl. 13.3 1 0.000 | | INTERMEDIATE RESULTS: | | Ag:(CM) 92.800 Fe:(N MM) 636.808 λ: 0.741 n: 1.34 | |--------------------------------------------------------------------------| | CHECKS FOR SHEAR | |--------------------------------------------------------------------------| | SHEAR ALONG Y AXIS | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | 0.00E+00 4.52E+02 0.000 Cl. 13.4.1.1 1 0.000 | | INTERMEDIATE RESULTS: | | Aw:(CM) Kv: Ka: Fcri:(N MM) Fcre:(N MM) Fs:(N MM) | | 21.758 5.360 0.070 480.943 1414.474 231.000 | |--------------------------------------------------------------------------| | SHEAR ALONG Z AXIS | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | 0.00E+00 1.36E+03 0.000 AISC G2-1 1 0.000 | | INTERMEDIATE RESULTS: | | Aw:(CM) | | 72.136 | |--------------------------------------------------------------------------| STAAD SPACE -- PAGE NO. 7 STAAD.PRO CODE CHECKING - CSA S16-19 (v1.0) *********************************************** ALL UNITS ARE IN KN MET UNLESS OTHERWISE Noted Member : 1 Contd. |--------------------------------------------------------------------------| | CHECKS FOR BENDING | |--------------------------------------------------------------------------| | YIELDING ALONG MAJOR AXIS | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | -1.80E+02 3.103E+02 0.580 Cl. 13.5(a) 1 0.000 | | INTERMEDIATE RESULTS: Mp: 3.45E+02 Se(CM): 0.00E+00 My: 0.00E+00| |--------------------------------------------------------------------------| | YIELDING ALONG MINOR AXIS | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | 0.00E+00 1.458E+02 0.000 Cl. 13.5(a) 1 0.000 | | INTERMEDIATE RESULTS: Mp: 1.62E+02 Se(CM): 0.00E+00 My: 0.00E+00| |--------------------------------------------------------------------------| | LATERAL TORSIONAL BUCKLING (MAJOR AXIS) | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | -1.80E+02 3.103E+02 0.580 Cl. 13.6(a)(i) 1 0.000 | | INTERMEDIATE RESULTS: | | Iyc(CM): w 2: w 3: b x(CM): Mu: rt: Myr: Lu: Lyr: | | 0.00E+00 1.00 0.00 0.00 8.712E+02 0.00 0.00E+00 0.00 0.00 | |--------------------------------------------------------------------------| | CHECKS FOR INTERACTION | |--------------------------------------------------------------------------| | FLEXURE AND AXIAL TENSION | | RATIO: CRITERIA: LC: LOC: Tf: Tr: | | C/S STRENGTH : 0.493 Cl. 13.9.2 1 0.00 0.00E+00 2.92E+03 | | MEMBER STRENGTH: 0.580 Cl. 13.9.3 1 0.00 | | Mfz: Mfy: Mrz: Mry: | | C/S STRENGTH : -1.80E+02 0.00E+00 3.10E+02 1.46E+02 | |--------------------------------------------------------------------------| | FLEXURE AND AXIAL COMPRESSION | | RATIO: CRITERIA: LC: LOC: Cf: Cr: | | C/S STRENGTH : 0.828 Cl. 13.8.2 1 0.000 9.00E+02 2.92E+03 | | MEMBER STRENGTH: 0.852 Cl. 13.8.2 1 0.000 9.00E+02 2.71E+03 | | LTB STRENGTH : 0.926 Cl. 13.8.2 1 0.000 9.00E+02 2.22E+03 | | Mfz: Mfy: Mrz: Mry: w 1z: w 1y: | | C/S STRENGTH : -1.80E+02 0.00E+00 3.10E+02 1.46E+02 1.00 0.60 | | MEMBER STRENGTH: -1.80E+02 0.00E+00 3.10E+02 1.46E+02 0.60 1.00 | | LTB STRENGTH : -1.80E+02 0.00E+00 3.10E+02 1.46E+02 1.00 0.60 | | b : Cez: Cey: U1z: U1y: | | C/S STRENGTH : 0.60 1.72E+04 5.91E+03 1.06 1.00 | | MEMBER STRENGTH: 0.85 1.72E+04 5.91E+03 1.06 0.71 | | LTB STRENGTH : 0.85 1.72E+04 5.91E+03 1.06 0.71 | |--------------------------------------------------------------------------| | SHEAR CAPACITY MODIFICATION ( SHEAR AND FLEX ) | | FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: | | 0.00E+00 4.523E+02 0.000 Cl. 14.6 1 0.000 | |--------------------------------------------------------------------------| | BIAXIAL FLEXURE | | RATIO: CRITERIA: LC: LOC: Mfz: Mrz: Mfy: Mry: | | 0.580 Cl. 13.8 1 0.00 -1.80E+02 3.10E+02 0.00E+00 1.46E+02 | |==========================================================================| ***NOTE:OMEGA1 AND OMEGA2 ARE CALCULATED USING C/S MOMENT OF ANALYTICAL MEMBERS