V. CSA S16-14 - Select a Beam
Select a wide-flange shape for the given beam span.
Reference
Kulak, G.L. and G.Y. Grondin. 2010. Limit States Design in Structural Steel. 9th Edition. Markham, ON:CISC. Example 5.2
Problem
A beam must be selected to span 11.0 m. The end moment of the span are:
And the maximum moment in the span is:
The beam is braced at 2.5 m from the center of each supporting
column (thus
Lb = 6.0 m)
(LT 6.0
).
The material used is G40.21 350W steel (Fy = 350
MPa) (FYLD
)
Calculations
Assume a Class 2 section:
Thus,
Try a W460x82:
Evaluate the slenderness effects of the beam flanges:
Evaluate the slenderness effects of the beam web:
The assumptions are valid and this beam is sufficient to support the given moments.
Ratio = 540 / 576.5 = 0.937
Comparison
Criteria | Reference | STAAD.Pro | Difference |
---|---|---|---|
Section | W460x82 * | W460x82 | none |
Mr (kN·m) | 576.5 ** | 576 | negligible |
Critical Ratio | 0.937 ** | 0.937 | none |
- *The reference also tries a W530x82, which is stiffer for the same weight. STAAD.Pro selects the shallower beam.
- ** The reference does not calculate the resisting moment capacity nor the critical ratio for either section size, but they are evaluated here for completeness.
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\Canada\CSA S16-14 - Select a Beam.STD is typically installed with the program.
In order to model this beam in STAAD.Pro, we need to determine the distributed load which would result in the same mid-span moment on a beam with the given end moments. From the AISC Streel Construction Manual, p 3-222:
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 FIXED BUT FX MY MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GY -40.033
JOINT LOAD
1 MZ 540
2 MZ -185
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
SELECT ALL
PERFORM ANALYSIS
FINISH
STAAD Output
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: 0.832(PASS) LOAD: 1
LOCATION : 0.00 CONDITION: Cl. 13.8
SECTION: ST W530X82 (CANADIAN SECTIONS)
UNIT: KN MET
STRENGTH CHECKS:
CRITICAL RATIO: 0.832(PASS) LOAD CASE: 1 LOCATION : 0.00 CONDITION: Cl. 13.8
DESIGN FORCES: Fx: 0.00(T) Fy: 252.45 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: 252.454 1042.826 0.242 Cl. 13.4.1.1 1 0.000
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
INTERACTION: RATIO: CRITERIA: LOAD CASE: LOCATION:
FLEXURE AND AXIAL TENSION:
C/S STRENGTH: 0.832 Cl. 13.9.1 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
FLEX AND SHEAR: 0.715 Cl. 14.6(a) 1 0.000
BIAXIAL FLEX: 0.832 Cl. 13.8 1 0.000
INTERMEDIATE:
FLEXURE AND AXIAL TENSION:
C/S STRENGTH: Tf: -0.00E+00 Tr: 3.31E+03 Mfz: -5.40E+02 Mrz: 6.49E+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 -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
FLEX SHEAR: Mfz: -5.40E+02 Mrz: 6.49E+02 Vfy: 2.52E+02 Vry: 1.04E+03
BIAX FLEX: Mfz: -5.40E+02 Mrz: 6.49E+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
45. SELECT ALL
STEEL DESIGN
STAAD SPACE -- PAGE NO. 8
STAAD.PRO MEMBER SELECTION - S16-14 (v1.0)
**********************************************
ALL UNITS ARE - KN MET (UNLESS OTHERWISE Noted)
-------------------- START OF DESIGN OUTPUT OF MEMBER 1 --------------------
MEMBER NO: 1 CRITICAL RATIO: 0.937(PASS) LOAD: 1
LOCATION : 0.00 CONDITION: Cl. 13.8
SECTION: ST W460x82 (CANADIAN SECTIONS)
UNIT: KN MET
STRENGTH CHECKS:
CRITICAL RATIO: 0.937(PASS) LOAD CASE: 1 LOCATION : 0.00 CONDITION: Cl. 13.8
DESIGN FORCES: Fx: 0.00(T) Fy: 252.45 Fz: 0.00
Mx: 0.00E+00 My: 0.00E+00 Mz: 5.40E+02
UNIT: CM
SECTION PROPERTIES: AZZ: 61.120 AYY: 45.540 CW: 915745.312
SZZ: 1608.696 SYY: 194.764
IZZ: 37000.004 IYY: 1860.000
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: 260.108 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 3276.000 0.000 Cl. 13.2 1 0.000
RUPTURE: -0.000 3510.000 0.000 Cl. 13.2 1 0.000
STAAD SPACE -- PAGE NO. 9
STAAD.PRO MEMBER SELECTION - ( S16-14) v1.0
***********************************************
ALL UNITS ARE - KN MET (UNLESS OTHERWISE Noted)
COMPRESSION: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION:
MAJOR: 0.000 2261.248 0.000 Cl. 13.3.5(a) 1 0.000
MINOR: 0.000 253.374 0.000 Cl. 13.3.5(a) 1 0.000
INTERMEDIATE: Ag(CM): KL/r: Fe(N MM): λ n:
MAJOR: 96.728 58.319 594.890 0.767 1.340
MINOR: 96.728 260.107 29.905 3.421 1.340
FLEX TOR BUCK: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET ):
0.000 1194.071 0.000 Cl. 13.3.5(a) 1 0.000
INTERMEDIATE: Fe(N MM): λ n:
176.181 1.409 1.340
SHEAR: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET ):
MAJOR: 252.454 946.776 0.267 Cl. 13.4.1.1 1 0.000
MINOR: -0.000 1155.168 0.000 AISC G2-1 1 0.000
INTERMEDIATE: Aw(CM): Kv: Ka: Fcri(N MM): Fcre(N MM): Fs(N MM):
MAJOR: 45.540 5.347 0.042 290.187 514.950 231.000
MINOR: 61.120
UNIT: KN MET
YIELDING: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET ):
MAJOR: -5.40E+02 5.76E+02 0.937 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: 6.41E+02 0.00E+00 0.00E+00
MINOR: 1.06E+02 0.00E+00 0.00E+00
UNIT: KN MET
INTERACTION: RATIO: CRITERIA: LOAD CASE: LOCATION:
FLEXURE AND AXIAL TENSION:
C/S STRENGTH: 0.937 Cl. 13.9.1 1 0.000
FLEXURE AND AXIAL COMPRESSION:
C/S STRENGTH: 0.796 Cl. 13.8.2 1 0.000
MEMBER STRENGTH: 0.796 Cl. 13.8.2 1 0.000
FLEX AND SHEAR: 0.802 Cl. 14.6(a) 1 0.000
BIAXIAL FLEX: 0.937 Cl. 13.8 1 0.000
INTERMEDIATE:
FLEXURE AND AXIAL TENSION:
C/S STRENGTH: Tf: -0.00E+00 Tr: 3.28E+03 Mfz: -5.40E+02 Mrz: 5.76E+02
STAAD SPACE -- PAGE NO. 10
STAAD.PRO MEMBER SELECTION - ( 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 -5.40E+02 0.00E+00 3.05E+03 5.76E+02 9.54E+01 0.85 6.19E+03 3.11E+02 0.74 0.60 1.00 1.00
MEM STR: 0.00E+00 -5.40E+02 0.00E+00 2.26E+03 5.76E+02 9.54E+01 0.85 6.19E+03 3.11E+02 0.60 0.74 1.00 1.00
FLEX SHEAR: Mfz: -5.40E+02 Mrz: 5.76E+02 Vfy: 2.52E+02 Vry: 9.47E+02
BIAX FLEX: Mfz: -5.40E+02 Mrz: 5.76E+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