V. CSA S16-14 - 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 Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Canada\CSA S16-14 - Beam Shear Capacity.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 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 2014
FYLD 350000 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD Output
STAAD.PRO CODE CHECKING - S16-14 (v1.0) ******************************************* ALL UNITS ARE - KN MET (UNLESS OTHERWISE Noted) -------------------- START OF DESIGN OUTPUT OF MEMBER 1 -------------------- *MEMBER NO: 1 CRITICAL RATIO: 1.803(FAIL) LOAD: 1 LOCATION : 0.00 CONDITION: Cl. 13.8 SECTION: ST W530X82 (CANADIAN SECTIONS) UNIT: KN MET STRENGTH CHECKS: CRITICAL RATIO: 1.803(FAIL) LOAD CASE: 1 LOCATION : 0.00 CONDITION: Cl. 13.8 DESIGN FORCES: Fx: 0.00(T) Fy: 254.22 Fz: 0.00 Mx: 0.00E+00 My: 0.00E+00 Mz: 5.40E+02 UNIT: CM SECTION PROPERTIES: AZZ: 55.594 AYY: 50.160 CW: 1340255.500 SZZ: 1806.818 SYY: 194.258 IZZ: 47700.008 IYY: 2030.000 UNIT: NEW MM MATERIAL PROPERTIES: FYLD (N MM): 350.000 FU (N MM): 450.000 ACTUAL MEMBER LENGTH (MET ): 11.000 PARAMETERS: KZ: 1.000 KY: 1.000 NSF: 1.000 SLF: 1.000 SLENDERNESS: ACTUAL SLENDERNESS RATIO: 250.172 LOAD: 1 LOC.: 0.000 ALLOWABLE SLENDERNESS RATIO: 300.000 SECTION CLASS: COMPRESSION: Class 4 FLEXURE MAJOR MINOR SECTION: Class 2 Class 2 FLANGE: Class 2 Class 2 WEB: Class 1 UNIT: KN MET TENSION: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET ): YIELDING: 0.000 3307.500 0.000 Cl. 13.2 1 0.000 RUPTURE: 0.000 3543.750 0.000 Cl. 13.2 1 0.000 STAAD SPACE -- PAGE NO. 6 STAAD.PRO CODE CHECKING - ( S16-14) v1.0 ******************************************** ALL UNITS ARE - KN MET (UNLESS OTHERWISE Noted) COMPRESSION: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION: MAJOR: 0.000 2253.274 0.000 Cl. 13.3.5(a) 1 0.000 MINOR: 0.000 253.222 0.000 Cl. 13.3.5(a) 1 0.000 INTERMEDIATE: Ag(CM): KL/r: Fe(N MM): λ n: MAJOR: 89.688 51.609 759.622 0.679 1.340 MINOR: 89.688 250.172 32.328 3.290 1.340 FLEX TOR BUCK: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET ): 0.000 854.388 0.000 Cl. 13.3.5(a) 1 0.000 INTERMEDIATE: Fe(N MM): λ n: 125.187 1.672 1.340 SHEAR: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET ): MAJOR: -538.417 1042.826 0.516 Cl. 13.4.1.1 1 11.000 MINOR: 0.000 1050.727 0.000 AISC G2-1 1 0.000 INTERMEDIATE: Aw(CM): Kv: Ka: Fcri(N MM): Fcre(N MM): Fs(N MM): MAJOR: 50.160 5.349 0.048 237.748 345.654 231.000 MINOR: 55.594 UNIT: KN MET YIELDING: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET ): MAJOR: -5.40E+02 6.49E+02 0.832 Cl. 13.5(a) 1 0.000 MINOR: 0.00E+00 9.54E+01 0.000 Cl. 13.5(a) 1 0.000 INTERMEDIATE: Mp: Se: My: MAJOR: 7.21E+02 0.00E+00 0.00E+00 MINOR: 1.06E+02 0.00E+00 0.00E+00 UNIT: KN MET LAT TOR BUCK: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET ): MAJOR: -5.40E+02 2.99E+02 1.803 Cl. 13.6(a)(ii 1 0.000 INTERMEDIATE: Iyc(CM): w 2: w 3: b x: Mu: rt: Myr: Lu: Lyr: MAJOR: 0.00E+00 2.29 0.00 0.00 3.33E+02 0.00 0.00E+00 0.00 0.00 UNIT: KN MET INTERACTION: RATIO: CRITERIA: LOAD CASE: LOCATION: FLEXURE AND AXIAL TENSION: C/S STRENGTH: 0.832 Cl. 13.9.1 1 0.000 MEMBER STRENGTH: 1.803 Cl. 13.9.2 1 0.000 FLEXURE AND AXIAL COMPRESSION: C/S STRENGTH: 0.707 Cl. 13.8.2 1 0.000 MEMBER STRENGTH: 0.707 Cl. 13.8.2 1 0.000 LTB STRENGTH: 1.533 Cl. 13.8.2 1 0.000 FLEX AND SHEAR: 1.422 Cl. 14.6(a) 1 0.000 BIAXIAL FLEX: 1.803 Cl. 13.8 1 0.000 STAAD SPACE -- PAGE NO. 7 INTERMEDIATE: FLEXURE AND AXIAL TENSION: C/S STRENGTH: Tf: 0.00E+00 Tr: 3.31E+03 Mfz: -5.40E+02 Mrz: 6.49E+02 FLEXURE AND AXIAL COMPRESSION: Cf: Mfz: Mfy: Cr: Mrz: Mry: b : Cez: Cey: w 1z: w 1y: U1z: U1y: C/S STR: 0.00E+00 -5.40E+02 0.00E+00 2.83E+03 6.49E+02 9.54E+01 0.85 7.98E+03 3.39E+02 0.74 0.60 1.00 1.00 MEM STR: 0.00E+00 -5.40E+02 0.00E+00 2.25E+03 6.49E+02 9.54E+01 0.85 7.98E+03 3.39E+02 0.60 0.74 1.00 1.00 LTB STR: 0.00E+00 -5.40E+02 0.00E+00 2.53E+02 2.99E+02 9.54E+01 0.85 7.98E+03 3.39E+02 0.74 0.60 1.00 1.00 FLEX SHEAR: Mfz: -5.40E+02 Mrz: 2.99E+02 Vfy: 2.54E+02 Vry: 1.04E+03 BIAX FLEX: Mfz: -5.40E+02 Mrz: 2.99E+02 Mfy: 0.00E+00 Mry: 9.54E+01 -------------------- END OF DESIGN OUTPUT OF MEMBER 1 -------------------- ***NOTE:OMEGA1 AND OMEGA2 ARE CALCULATED USING C/S MOMENT OF ANALYTICAL MEMBERS