V. CSA S16-09 - Beam Bending
Determine the uniformly factored load that the member can resist.
Reference
Kulak, G.L. and G.Y. Grondin. 2010. Limit States Design in Structural Steel. 9th Edition. Markham, ON:CISC. Example 5.1
Problem
A W310x52 beam spans 7.3 m. Both ends of the beam are supported by columns connected standard web angle connections.
The material used is G40.21 350W steel (Fy = 350
MPa) (FYLD
)
Calculations
The nominal yield strength is used for the actual yield strength for a Group 2 section, per Table 3 and Table 4 of Appendix A of the reference.
Section Classification
Evaluate the slenderness effects of the beam flanges:
Evaluate the slenderness effects of the beam web:
Both the beam flanges and web are less than the local buckling limit, so the capacity of the column is evaluated using Eq. 5.7.
Bending Capacity
Factored moment resistance is:
Equate this to the bending moment due to a uniformly distributed load and solve for the load:
Comparison
Criteria | Reference | STAAD.Pro | Difference |
---|---|---|---|
Mr (kN·m) | 265 | 265 | none |
wf (kN/m) | 39.8 | 39.76* | negligible |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples Verification Models\09 Steel Design\Canada\S16 2009\CSA S16-09 - Beam Bending.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 17-Mar-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 7.3 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 W310X52
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MY MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GY -39.8
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PRINT SUPPORT REACTION ALL
PARAMETER 1
CODE CANADIAN 2009
LAT 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: 1.001(FAIL) LOAD: 1
LOCATION (MET): 3.65 CONDITION: Cl. 13.8
SECTION: ST W310X52 (CANADIAN SECTIONS)
UNIT: KN MET
STRENGTH CHECKS:
CRITICAL RATIO: 1.001(FAIL) LOAD CASE: 1 LOCATION (MET): 3.65 CONDITION: Cl. 13.8
DESIGN FORCES: Fx: 0.00(T) Fy: 0.00 Fz: 0.00
Mx: 0.00E+00 My: 0.00E+00 Mz: -2.65E+02
UNIT: CM
SECTION PROPERTIES: AZZ: 44.088 AYY: 23.165 CW: 237980.875
SZZ: 748.428 SYY: 123.353
IZZ: 11900.002 IYY: 1030.000
UNIT: NEW MM
MATERIAL PROPERTIES: FYLD: 350.000 FU: 450.000
ACTUAL MEMBER LENGTH(MET): 7.300
PARAMETERS: KZ: 1.000 KY: 1.000 NSF: 1.000 SLF: 1.000
SLENDERNESS: ACTUAL SLENDERNESS RATIO: 185.766 LOAD: 1 LOC.(MET): 0.000
ALLOWABLE SLENDERNESS RATIO: 300.000
SECTION CLASS:
COMPRESSION: Class 4
FLEXURE: Class 1
FLANGE: Class 1
WEB: Class 1
UNIT: KN MET
TENSION: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET):
YIELDING: 0.000 2101.050 0.000 Cl. 13.2 1 0.000
RUPTURE: 0.000 2251.125 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: 0.000 1587.513 0.000 Cl. 13.3.5(a) 1 0.000
MINOR: 0.000 322.454 0.000 Cl. 13.3.5(a) 1 0.000
INTERMEDIATE: Ag:(CM) KL/r: Fe:(N MM) λ n:
MAJOR: 65.224 54.653 677.375 0.719 1.340
MINOR: 65.224 185.766 58.630 2.443 1.340
FLEX TOR BUCK: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET):
0.000 1023.539 0.000 Cl. 13.3.5(a) 1 0.000
INTERMEDIATE: Fe:(N MM) λ n:
253.108 1.176 1.340
SHEAR: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET):
MAJOR: -145.270 502.453 0.289 Cl. 13.4.1.1 1 7.300
MINOR: 0.000 833.263 0.000 AISC G2-1 1 0.000
INTERMEDIATE: Aw:(CM) Kv: Ka: Fcri:(N MM) Fcre:(N MM) Fs:(N MM)
MAJOR: 23.165 5.348 0.044 326.992 653.857 231.000
MINOR: 44.088
UNIT: KN MET
YIELDING: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET):
MAJOR: 2.65E+02 2.65E+02 1.001 Cl. 13.5(a) 1 3.650
MINOR: 0.00E+00 5.95E+01 0.000 Cl. 13.5(a) 1 0.000
INTERMEDIATE: Mp: Se: My:
MAJOR: 2.94E+02 0.00E+00 0.00E+00
MINOR: 6.62E+01 0.00E+00 0.00E+00
UNIT: KN MET
INTERACTION: RATIO: CRITERIA: LOAD CASE: LOCATION(MET):
FLEXURE AND AXIAL TENSION:
C/S STRENGTH: 1.001 Cl. 13.9.1 1 3.650
FLEXURE AND AXIAL COMPRESSION:
C/S STRENGTH: 0.851 Cl. 13.8.2 1 3.650
MEMBER STRENGTH: 0.851 Cl. 13.8.2 1 0.000
FLEX AND SHEAR: 0.729 Cl. 14.6(a) 1 3.042
BIAXIAL FLEX: 1.001 Cl. 13.8 1 3.650
INTERMEDIATE:
FLEXURE AND AXIAL TENSION:
C/S STRENGTH: Tf: 0.00E+00 Tr: 2.10E+03 Mfz: 2.65E+02 Mrz: 2.65E+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: 0.00E+00 2.65E+02 0.00E+00 2.05E+03 2.65E+02 5.95E+01 0.85 4.52E+03 3.91E+02 0.60 0.60 1.00 1.00
MEM STR: 0.00E+00 2.65E+02 0.00E+00 3.22E+02 2.65E+02 5.95E+01 0.85 4.52E+03 3.91E+02 0.60 0.60 1.00 1.00
FLEX SHEAR: Mfz: 2.58E+02 Mrz: 2.65E+02 Vfy: 2.42E+01 Vry: 5.02E+02
BIAX FLEX: Mfz: 2.65E+02 Mrz: 2.65E+02 Mfy: 0.00E+00 Mry: 5.95E+01
-------------------- END OF DESIGN OUTPUT OF MEMBER 1 --------------------
***NOTE:OMEGA1 AND OMEGA2 ARE CALCULATED USING C/S MOMENT OF ANALYTICAL MEMBERS