V. CSA S16-09 - Axial Tension
Design of a double-angle member subject to tension load.
Reference
Kulak, G.L. and G.Y. Grondin. 2010. Limit States Design in Structural Steel. 9th Edition. Markham, ON:CISC. Example 3.1
Problem
Design a tension diagonal in an all-welded truss (SNU
0
for welded). Attached to WT 265x61.5 chords (tw = 13.1
mm).
The material used is G40.21 300W steel (Fy = 300
MPa,
Fu = 450
MPa) (FYLD
and
FU
)
Calculations
Gross area is used for welded connections.
Tr ≥ Tf , so solve for A:
Select a pair of angles with at least this gross area: try a 2- 76x64x9.5, with long legs back-to-back:
Calculate the effective net area due to shear lag. The average weld length is taken as (120 mm + 250 mm)/2 = 185 mm.
The long leg does not have a reduction in area shear lag, thus:
The outstanding (short) leg has an eccentricity of half the leg length, or 64/2 = 32 mm.
The total net area for the pair of angles for the rupture limit state is:
For the pair of angles,
Ane = 2×1,1162 =
2,324 mm2
; the ratio of net section area to gross area =
2,324 / 2,480 = 0.937 (NSF
).
Checking the yielding limit state:
Checking the rupture limit state:
Yielding governs, and the critical ratio is: 630/670 = 0.94.
Comparison
Criteria | Reference | STAAD.Pro | Difference |
---|---|---|---|
Tf (kN) | 670 | 669.6 | negligible |
Critical Ratio | 0.94 | 0.941 | negligible |
SELECT
facility is used in place of a code
CHECK
,
STAAD.Pro will actually select a 2-L 102x89x6.4
member, which has a critical ratio of 0.997 (per Cl. 13.2) and an area of 2,340
mm2, thus more economical (the
NSF
used for this size is 0.923).
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 - Axial Tension.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 22-Mar-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 4 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 LD L76X64X9.5
*1 TABLE T W530x123
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MY MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
JOINT LOAD
2 FX 630
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PRINT SUPPORT REACTION ALL
PARAMETER 1
CODE CANADIAN 2009
FYLD 300000 ALL
FU 450000 ALL
SNUG 0 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: 0.941(PASS) LOAD: 1
LOCATION (MET): 0.00 CONDITION: Cl. 13.9.1
SECTION: LD L76X64X9.5 (CANADIAN SECTIONS)
UNIT: KN MET
STRENGTH CHECKS:
CRITICAL RATIO: 0.941(PASS) LOAD CASE: 1 LOCATION (MET): 0.00 CONDITION: Cl. 13.9.1
DESIGN FORCES: Fx: 630.00(T) Fy: 0.00 Fz: 0.00
Mx: 0.00E+00 My: 0.00E+00 Mz: 0.00E+00
UNIT: CM
SECTION PROPERTIES: AZZ: 11.195 AYY: 13.616 CW: 0.000
SZZ: 26.578 SYY: 26.229
IZZ: 137.969 IYY: 166.556
UNIT: NEW MM
MATERIAL PROPERTIES: FYLD: 300.000 FU: 450.000
ACTUAL MEMBER LENGTH(MET): 4.000
PARAMETERS: KZ: 1.000 KY: 1.000 NSF: 1.000 SLF: 1.000
SLENDERNESS: ACTUAL SLENDERNESS RATIO: 169.588 LOAD: 1 LOC.(MET): 0.000
ALLOWABLE SLENDERNESS RATIO: 300.000
SECTION CLASS:
COMPRESSION: Class 1
FLEXURE: Class 3
FLANGE: Class 3
UNIT: KN MET
TENSION: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET):
YIELDING: 630.000 669.600 0.941 Cl. 13.2 1 0.000
RUPTURE: 630.000 837.000 0.753 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: 0.000 141.791 0.000 Cl. 13.3 1 0.000
MINOR: 0.000 166.729 0.000 Cl. 13.3 1 0.000
INTERMEDIATE: Ag:(CM) KL/r: Fe:(N MM) λ n:
MAJOR: 24.800 169.796 70.178 2.068 1.340
MINOR: 24.800 154.539 84.719 1.882 1.340
FLEX TOR BUCK: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET):
0.000 164.708 0.000 Cl. 13.3 1 0.000
INTERMEDIATE: Fe:(N MM) λ n:
83.506 1.895 1.340
SHEAR: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET):
MAJOR: 0.000 226.444 0.000 Cl. 13.4.3 1 0.000
MINOR: 0.000 196.070 0.000 AISC G2-1 1 0.000
INTERMEDIATE: Aw:(CM) Kv: Ka: Fcri:(N MM) Fcre:(N MM) Fs:(N MM)
MAJOR: 13.616 1.200 0.000 0.000 0.000 0.000
MINOR: 11.195
UNIT: KN MET
YIELDING: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET):
MAJOR: 0.00E+00 7.18E+00 0.000 Cl. 13.5(b) 1 0.000
MINOR: 0.00E+00 7.08E+00 0.000 Cl. 13.5(b) 1 0.000
INTERMEDIATE: Mp: Se: My:
MAJOR: 1.44E+01 0.00E+00 0.80E+01
MINOR: 0.00E+00 0.00E+00 0.79E+01
UNIT: KN MET
LAT TOR BUCK: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(MET):
MAJOR: 0.00E+00 1.17E+01 0.000 Cl. 13.6(e)(i) 1 0.000
INTERMEDIATE: Iyc(CM): w 2: w 3: b x: Mu: rt: Myr: Lu: Lyr:
MAJOR: 4.07E+01 2.50 1.00 0.59 3.65E+01 0.02 5.58E+00 0.52 25.18
UNIT: KN MET
INTERACTION: RATIO: CRITERIA: LOAD CASE: LOCATION(MET):
FLEXURE AND AXIAL TENSION:
C/S STRENGTH: 0.941 Cl. 13.9.1 1 0.000
FLEXURE AND AXIAL COMPRESSION:
C/S STRENGTH: 0.000 Cl. 13.8.3 1 0.000
MEMBER STRENGTH: 0.000 Cl. 13.8.3 1 0.000
LTB STRENGTH: 0.000 Cl. 13.8.3 1 0.000
FLEX AND SHEAR: 0.000 Cl. 14.6(a) 1 0.000
BIAXIAL FLEX: 0.000 Cl. 13.8 1 0.000
STAAD SPACE -- PAGE NO. 7
INTERMEDIATE:
FLEXURE AND AXIAL TENSION:
C/S STRENGTH: Tf: 6.30E+02 Tr: 6.70E+02 Mfz: 0.00E+00 Mrz: 7.18E+00
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 0.00E+00 0.00E+00 6.70E+02 7.18E+00 7.08E+00 N/A 1.74E+02 2.11E+02 0.60 0.60 1.00 1.00
MEM STR: 0.00E+00 0.00E+00 0.00E+00 1.42E+02 7.18E+00 7.08E+00 N/A 1.74E+02 2.11E+02 0.60 0.60 1.00 1.00
LTB STR: 0.00E+00 0.00E+00 0.00E+00 1.65E+02 7.18E+00 7.08E+00 N/A 1.74E+02 2.11E+02 0.60 0.60 1.00 1.00
FLEX SHEAR: Mfz: 0.00E+00 Mrz: 7.18E+00 Vfy: 0.00E+00 Vry: 2.26E+02
BIAX FLEX: Mfz: 0.00E+00 Mrz: 7.18E+00 Mfy: 0.00E+00 Mry: 7.08E+00
-------------------- END OF DESIGN OUTPUT OF MEMBER 1 --------------------
***NOTE:OMEGA1 AND OMEGA2 ARE CALCULATED USING C/S MOMENT OF ANALYTICAL MEMBERS