V. CSA S16-01 - Beam Shear Capacity
Reference
Kulak, G.L. and G.Y. Grondin. 2010. Limit States Design in Structural Steel. 9th Edition. Markham, ON:CISC. Example 5.3
Problem
The W530x82 beam has a maximum shear force, v = 540 kN due to factored loads.
L = 11.0 m
The material used is G40.21 350W steel (Fy = 350 MPa) (FYLD)
Evaluate the slenderness effects of the beam web:
Therefore the shear capacity is calculated as:
Vr = ϕ×Aw×Fy = 0.9×528×9.5×350 = 1,043 kN
Calculate Equivalent Concentrated Load
The given end moments and assumed distributed loads (which was determined to given an equivalent mid-span moment of the given example) do not result in a shear force of 540 kN. Therefore, an additional concentrated load is added near the first support.
P = 540 kN - 253.2 kN = 287 kN
The STAAD.Pro will have this load applied at 1 mm away from the left support.
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 - Beam Shear Capacity.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 25-June-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 11 0 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 W530X82
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 ENFORCED BUT FX MY MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
JOINT LOAD
1 MZ 540
2 MZ -185
MEMBER LOAD
1 UNI GY -40.033
1 CON GY -352.27 10.945
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PRINT SUPPORT REACTION ALL
PARAMETER 1
CODE CANADIAN 2001
FYLD 350000 ALL
FU 450000 ALL
SHE 1 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
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 W530X82 (CANADIAN SECTIONS) FAIL CSA-13.8.2+ 4.092 1 0.00 C 0.00 540.00 0.00 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 = 1.05E+02 MEMBER LENGTH = 1.10E+03 IZ = 4.77E+04 SZ = 1.81E+03 PZ = 2.06E+03 IY = 2.03E+03 SY = 1.94E+02 PY = 3.03E+02 IX = 5.18E+01 CW = 1.34E+06 MATERIAL PROPERTIES (UNIT = MPA) -------------------------------- FYLD = 350.0 FU = 450.0 E = 2.05E+05 G = 7.88E+04 SECTION CAPACITIES (UNIT - KN,M) --------------------------------- CR1 = 3.308E+03 CR2 = 2.965E+02 SECTION CLASS 2 CRZ = 2.638E+03 CTORFLX = 2.965E+02 TENSILE CAPACITY = 3.308E+03 COMPRESSIVE CAPACITY = 2.965E+02 FACTORED MOMENT RESISTANCE : MRY = 9.545E+01 MRZ = 1.319E+02 MU = 1.466E+02 FACTORED SHEAR RESISTANCE : VRY = 1.043E+03 VRZ = 7.705E+02 MISCELLANEOUS INFORMATION -------------------------- NET SECTION FACTOR FOR TENSION = 1.000 KL/RY = 250.172 KL/RZ = 51.609 ALLOWABLE KL/R = 300.000 UNSUPPORTED LENGTH OF THE COMPRESSION FLANGE (M) = 11.000 OMEGA-1 (Y-AXIS) = 1.00 OMEGA-1 (Z-AXIS) = 1.00 OMEGA-2 = 1.00 SHEAR FORCE (KNS) : Y AXIS = 2.542E+02 Z AXIS = 0.000E+00 SLENDERNESS RATIO OF WEB (H/W) = 5.28E+01