V.CSA S16-09 - 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:
M1 = -540 kN·m
M2 = -185 kN·m
And the maximum moment in the span is:
M3 = 256 kN·m
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)
Assume a Class 2 section:
Mr = ϕMp = ϕZxFy
Thus,
Try a W460x82:
Zx = 1,830×(10)3 mm3, tf = 16.0 mm, bf = 191.0 mm, tw = 9.9 mm, D = 460.0 mm
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.
Mr = 0.9×1,830×(10)3×350 [(10)-6] = 576.5 kN·m
Ratio = 540 / 576.5 = 0.937
Comparison
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Canada\S16 2009\CSA S16-09 - 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:
Solving this yields wf = 40.033 kN/mSTAAD 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 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 2009
LAT 1 ALL
FYLD 350000 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
SELECT ALL
PERFORM ANALYSIS
FINISH
STAAD.Pro Output
STAAD SPACE -- PAGE NO. 5 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: 0.832(PASS) LOAD: 1 LOCATION (MET): 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 (MET): 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: 48.896 CW: 1340255.500 SZZ: 1806.818 SYY: 194.258 IZZ: 47700.008 IYY: 2030.000 UNIT: NEW MM MATERIAL PROPERTIES: FYLD: 350.000 FU: 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.(MET): 0.000 ALLOWABLE SLENDERNESS RATIO: 300.000 SECTION CLASS: COMPRESSION: Class 4 FLEXURE: Class 2 FLANGE: 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 - ( S16-09) v1.1 ******************************************** ALL UNITS ARE - KN MET (UNLESS OTHERWISE Noted) COMPRESSION: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET): 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: 48.896 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(MET): 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 - ( S16-09) 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 -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 2.53E+02 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 - S16-09 (v1.1) ********************************************** 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 (MET): 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 (MET): 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: 43.956 CW: 1340255.500 SZZ: 1608.696 SYY: 194.764 IZZ: 37000.004 IYY: 1860.000 UNIT: NEW MM MATERIAL PROPERTIES: FYLD: 350.000 FU: 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.(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 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 - ( S16-09) v1.1 *********************************************** ALL UNITS ARE - KN MET (UNLESS OTHERWISE Noted) COMPRESSION: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET): 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 1279.603 0.000 Cl. 13.3.5(a) 1 0.000 INTERMEDIATE: Fe:(N MM) λ n: 194.448 1.342 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: 43.956 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(MET): 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 - ( S16-09) 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 -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 2.53E+02 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 --------------------