V. CSA S16-19 - Check for Bending and LTB
Determine the capacity of a laterally unbraced beam subject to bending moment per the CSA S16-19 code.
Problem
A 7.5 m long, simply supported beam is subjected to a distributed load of 12 kN/m. The section is a Canadian W310x52. The steel is grade 350W.Section Properties
- D = 318 mm
- B = 167 mm
- tw = 7.6 mm
- tf = 13.2 mm
- Zx = 841,000 mm3
- Zy = 189,000 mm3
- Iy = 10.3×106 mm4
- J = 308,000 mm4
- Cw = 238×109 mm6
Material Properties
- Fy = 350 MPa
- Fu = 450 MPa
- E = 205,000 MPa
- G = 76,920 MPa
Calculations
Section Classification
Flexure section classification per Table 2:
- Flange classification about major axis:
Class 1
- Flange classification about minor axis:
Class 1
- Web classification about major axis:
Class 1
- Web classification about minor axis:
Class 1
Therefore, the section is Class 1 for flexure.
Bending Capacity
For a Class 2, doubly symmetric section, the capacity is determined by Cl. 13.5a:
Major axis:
The ratio = 84.4 / 264.9 = 0.318
Minor axis:
Lateral Torsional Buckling
Check for lateral torsional buckling per Cl. 13.6:
Ratio = 84.4 / 98.38 = 0.858.
Comparison
Criteria | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Nominal flexure capacity about major axis, Mpx (kN·m) | 294.4 | 294 | negligible | |
Ultimate flexure capacity about major axis, Mrx (kN·m) | 264.9 | 264.9 | none | |
Nominal flexure capacity about minor axis, Mpy (kN·m) | 66.2 | 66.2 | none | |
Ultimate flexure capacity about minor axis, Mrx (kN·m) | 59.5 | 59.54 | negligible | |
Ratio | 0.318 | 0.318 | none | |
Nominal lateral torsional bending capacity, Mu (kN) | 109.3 | 109.3 | none | |
Ultimate lateral torsional bending capacity, Mr (kN) | 98.38 | 98.38 | none | |
Critical Ratio | 0.858 | 0.858 | none |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\Canada\CSA S16-19 - Check for Bending and LTB.STD is typically installed with the program.
- The laterally unsupported is designated by the parameter
LAT 0
. - The value of ω2
is specified as 1 using the parameter
CB 1
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 10-Oct-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 7.5 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 -12
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PRINT SUPPORT REACTION ALL
PARAMETER 1
CODE CANADIAN
LAT 0 ALL
CB 1 ALL
FYLD 350000 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD Output
STAAD.PRO CODE CHECKING - CSA S16-19 (v1.0)
***********************************************
ALL UNITS ARE IN KN MET UNLESS OTHERWISE Noted
|--------------------------------------------------------------------------|
| MEMBER NO.: 1 SECTION: ST W310X52 (CANADIAN SECTIONS)|
| STATUS: PASS CRITICAL RATIO: 0.858 LOADCASE 1 |
| LOCATION: 3.75 CRITICAL CONDITION: Cl. 13.8 |
|--------------------------------------------------------------------------|
| STRENGTH CHECK SUMMARY |
| CRITICAL RATIO: 0.858(PASS) LOAD CASE: 1 |
| LOCATION : 3.75 CONDITION: Cl. 13.8 |
|--------------------------------------------------------------------------|
| DESIGN FORCES LC: 1 LOC: 3.75 |
| FX: 0.00(T) FY: 0.00 FZ: 0.00 |
| MX: 0.000E+00 MY: 0.000E+00 MZ: -8.438E+01 |
|--------------------------------------------------------------------------|
| SECTION PROPERTIES (LOC: 3.75) UNIT: CM |
| AXX: 66.700 AZZ: 44.088 AYY: 24.168 |
| IXX: 30.800 IZZ: 11900.002 IYY: 1030.000 |
| PZZ: 841.000 PYY: 189.000 |
| SZZ: 748.428 SYY: 123.353 CW : 237980.875 |
|--------------------------------------------------------------------------|
| MATERIAL PROPERTIES UNIT: N MM |
| FYLD: 350.000 FU: 450.000 E: 204999.984 G: 76920.000 |
|--------------------------------------------------------------------------|
| DESIGN PARAMETERS |
| ACTUAL MEMBER LENGTH: 7.500 LZ: 7.500 LY: 7.500 |
| KZ: 1.000 KY: 1.000 NSF: 1.000 SLF: 1.000 |
|--------------------------------------------------------------------------|
| SECTION CLASS |
| COMPRESSION : Class 4 |
| FLEXURE MAJOR MINOR |
| SECTION : Class 1 Class 1 |
| FLANGE : Class 1 Class 1 |
| WEB (CRITICAL) : Class 1 |
|==========================================================================|
| SLENDERNESS |
| ACTUAL SLENDERNESS RATIO : 190.856 LC : 1 |
| ALLOWABLE SLENDERNESS RATIO: 300.000 LOC : 0.00 |
|--------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 6
STAAD.PRO CODE CHECKING - CSA S16-19 (v1.0)
***********************************************
ALL UNITS ARE IN KN MET UNLESS OTHERWISE Noted
Member : 1 Contd.
|--------------------------------------------------------------------------|
| CHECKS FOR AXIAL TENSION |
|--------------------------------------------------------------------------|
| YIELDING |
| FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: |
| -0.00E+00 2.10E+03 0.000 Cl. 13.2 1 0.000 |
| RUPTURE |
| FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: |
| -0.00E+00 2.25E+03 0.000 Cl. 13.2 1 0.000 |
|--------------------------------------------------------------------------|
| CHECKS FOR AXIAL COMPRESSION |
|--------------------------------------------------------------------------|
| FLEX BUCKLING |
| FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: |
| MAJOR: 0.00E+00 1.56E+03 0.000 Cl. 13.3.4(a) 1 0.000 |
| MINOR: 0.00E+00 3.07E+02 0.000 Cl. 13.3.4(a) 1 0.000 |
| INTERMEDIATE RESULTS: |
| Ag:(CM) Fe:(N MM) λ: n: KL/r: |
| MAJOR: 65.224 641.730 0.739 1.34 56.150 |
| MINOR: 65.224 55.545 2.510 1.34 190.856 |
|--------------------------------------------------------------------------|
| FLEXURAL TORSIONAL BUCKLING |
| FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: |
| 0.00E+00 3.07E+02 0.000 Cl. 13.3.4 1 0.000 |
| INTERMEDIATE RESULTS: |
| Ag:(CM) 65.224 Fe:(N MM) 55.545 λ: 2.510 n: 1.34 |
|--------------------------------------------------------------------------|
| CHECKS FOR SHEAR |
|--------------------------------------------------------------------------|
| SHEAR ALONG Y AXIS |
| FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: |
| 4.50E+01 5.02E+02 0.090 Cl. 13.4.1.1 1 0.000 |
| INTERMEDIATE RESULTS: |
| Aw:(CM) Kv: Ka: Fcri:(N MM) Fcre:(N MM) Fs:(N MM) |
| 24.168 5.347 0.042 326.980 653.808 231.000 |
|--------------------------------------------------------------------------|
| SHEAR ALONG Z AXIS |
| FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: |
| -0.00E+00 8.33E+02 0.000 AISC G2-1 1 0.000 |
| INTERMEDIATE RESULTS: |
| Aw:(CM) |
| 44.088 |
|--------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 7
STAAD.PRO CODE CHECKING - CSA S16-19 (v1.0)
***********************************************
ALL UNITS ARE IN KN MET UNLESS OTHERWISE Noted
Member : 1 Contd.
|--------------------------------------------------------------------------|
| CHECKS FOR BENDING |
|--------------------------------------------------------------------------|
| YIELDING ALONG MAJOR AXIS |
| FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: |
| 8.44E+01 2.649E+02 0.318 Cl. 13.5(a) 1 3.750 |
| INTERMEDIATE RESULTS: Mp: 2.94E+02 Se(CM): 0.00E+00 My: 0.00E+00|
|--------------------------------------------------------------------------|
| YIELDING ALONG MINOR AXIS |
| FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: |
| 0.00E+00 5.954E+01 0.000 Cl. 13.5(a) 1 0.000 |
| INTERMEDIATE RESULTS: Mp: 6.62E+01 Se(CM): 0.00E+00 My: 0.00E+00|
|--------------------------------------------------------------------------|
| LATERAL TORSIONAL BUCKLING (MAJOR AXIS) |
| FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: |
| 8.44E+01 9.838E+01 0.858 Cl. 13.6(a)(ii) 1 3.750 |
| INTERMEDIATE RESULTS: |
| Iyc(CM): w 2: w 3: b x(CM): Mu: rt: Myr: Lu: Lyr: |
| 0.00E+00 1.00 0.00 0.00 1.093E+02 0.00 0.00E+00 0.00 0.00|
|--------------------------------------------------------------------------|
| CHECKS FOR INTERACTION |
|--------------------------------------------------------------------------|
| FLEXURE AND AXIAL TENSION |
| RATIO: CRITERIA: LC: LOC: Tf: Tr: |
| C/S STRENGTH : 0.271 Cl. 13.9.2 1 3.75 -0.00E+00 2.10E+03 |
| MEMBER STRENGTH: 0.858 Cl. 13.9.3 1 0.00 |
| Mfz: Mfy: Mrz: Mry: |
| C/S STRENGTH : 8.44E+01 0.00E+00 2.65E+02 5.95E+01 |
|--------------------------------------------------------------------------|
| FLEXURE AND AXIAL COMPRESSION |
| RATIO: CRITERIA: LC: LOC: Cf: Cr: |
| C/S STRENGTH : 0.271 Cl. 13.8.2 1 3.750 0.00E+00 2.05E+03 |
| MEMBER STRENGTH: 0.271 Cl. 13.8.2 1 3.750 0.00E+00 1.56E+03 |
| LTB STRENGTH : 0.729 Cl. 13.8.2 1 3.750 0.00E+00 3.07E+02 |
| Mfz: Mfy: Mrz: Mry: w 1z: w 1y: |
| C/S STRENGTH : 8.44E+01 0.00E+00 2.65E+02 5.95E+01 0.60 0.60 |
| MEMBER STRENGTH: 8.44E+01 0.00E+00 2.65E+02 5.95E+01 0.60 0.60 |
| LTB STRENGTH : 8.44E+01 0.00E+00 9.84E+01 5.95E+01 0.60 0.60 |
| b : Cez: Cey: U1z: U1y: |
| C/S STRENGTH : 0.85 4.28E+03 3.70E+02 1.00 1.00 |
| MEMBER STRENGTH: 0.85 4.28E+03 3.70E+02 1.00 1.00 |
| LTB STRENGTH : 0.85 4.28E+03 3.70E+02 1.00 1.00 |
|--------------------------------------------------------------------------|
| SHEAR CAPACITY MODIFICATION ( SHEAR AND FLEX ) |
| FORCE: CAPACITY: RATIO: CRITERIA: LC: LOC: |
| 4.50E+01 5.025E+02 0.090 Cl. 14.6 1 0.000 |
|--------------------------------------------------------------------------|
| BIAXIAL FLEXURE |
| RATIO: CRITERIA: LC: LOC: Mfz: Mrz: Mfy: Mry: |
| 0.858 Cl. 13.8 1 3.75 8.44E+01 9.84E+01 0.00E+00 5.95E+01 |