V. CSA S16-14 - 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)
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.
Comparison
| Criteria | Reference | STAAD.Pro | Difference |
|---|---|---|---|
| Mr (kN·m) | 265 | 265 | none |
| wf (kN/m) | 39.8 | 39.76* | negligible |
Note: (*) STAAD.Pro does calculate the allowable uniform load on the beam. Instead, this
is done by applying a uniform load incrementally until the critical ratio is ≈
1.0. The, this uniform load is divided by the resulting critical ratio to normalize the
distributed load capacity of the beam. Thus, 39.8/1.001 = 39.67
kN/m
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Canada\CSA S16-14 - Beam Bending.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 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 2014
LAT 1 ALL
FYLD 350000 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD Output
STEEL DESIGN STAAD SPACE -- PAGE NO. 5 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: 1.001(FAIL) LOAD: 1 LOCATION : 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 : 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: 24.168 CW: 237980.875 SZZ: 748.428 SYY: 123.353 IZZ: 11900.002 IYY: 1030.000 UNIT: NEW MM MATERIAL PROPERTIES: FYLD (N MM): 350.000 FU (N MM): 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.: 0.000 ALLOWABLE SLENDERNESS RATIO: 300.000 SECTION CLASS: COMPRESSION: Class 4 FLEXURE MAJOR MINOR SECTION: Class 1 Class 1 FLANGE: Class 1 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 - ( S16-14) v1.0 ******************************************** ALL UNITS ARE - KN MET (UNLESS OTHERWISE Noted) COMPRESSION: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION: 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: 24.168 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: 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 - ( S16-14) v1.0 ******************************************** 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