V. CSA S16-01 - 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.
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Canada\CSA S16-01 - Shear Capacity Combined Stresses.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 26-June-20
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
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 ENFORCED BUT FY MX MZ
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 2001
SSY 1 ALL
SSZ 1 ALL
FYLD 350000 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
STAAD SPACE -- PAGE NO. 5 STAAD.PRO CODE CHECKING - (CAN/CSA-S16-01 ) V2.1 ******************************************** ALL UNITS ARE - KNS MET (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= 1 ST W250X73 (CANADIAN SECTIONS) PASS CSA-13.8.2C 0.926 1 900.00 C 0.00 180.00 3.60 STAAD SPACE -- PAGE NO. 6 ALL UNITS ARE - KNS MET (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= MEMBER PROPERTIES (UNIT = CM) ----------------------------- CROSS SECTION AREA = 9.28E+01 MEMBER LENGTH = 3.60E+02 IZ = 1.13E+04 SZ = 8.93E+02 PZ = 9.85E+02 IY = 3.88E+03 SY = 3.06E+02 PY = 4.63E+02 IX = 5.75E+01 CW = 5.53E+05 MATERIAL PROPERTIES (UNIT = MPA) -------------------------------- FYLD = 350.0 FU = 450.0 E = 2.00E+05 G = 7.69E+04 SECTION CAPACITIES (UNIT - KN,M) --------------------------------- CR1 = 2.923E+03 CR2 = 2.217E+03 SECTION CLASS 2 CRZ = 2.710E+03 CTORFLX = 2.217E+03 TENSILE CAPACITY = 2.923E+03 COMPRESSIVE CAPACITY = 2.217E+03 FACTORED MOMENT RESISTANCE : MRY = 1.458E+02 MRZ = 3.103E+02 MU = 8.714E+02 FACTORED SHEAR RESISTANCE : VRY = 4.523E+02 VRZ = 1.001E+03 MISCELLANEOUS INFORMATION -------------------------- NET SECTION FACTOR FOR TENSION = 1.000 KL/RY = 55.675 KL/RZ = 32.624 ALLOWABLE KL/R = 200.000 UNSUPPORTED LENGTH OF THE COMPRESSION FLANGE (M) = 3.600 OMEGA-1 (Y-AXIS) = 1.00 OMEGA-1 (Z-AXIS) = 1.00 OMEGA-2 = 1.00 SHEAR FORCE (KNS) : Y AXIS = 0.000E+00 Z AXIS = 0.000E+00 SLENDERNESS RATIO OF WEB (H/W) = 2.61E+01