V. CSA S16-14 - 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).
L = 4 m
Tf = 630 kN
The material used is G40.21 300W steel (Fy = 300 MPa, Fu = 450 MPa) (FYLD and FU)
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:
| A = 2,480 mm2 |
| rmin = 13.3 mm |
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:
An2 = 1.00×(76 - 9.5) ×9.5 = 632 mm2
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:
Ane = 632 + 530 = 1,162 mm2
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:
Tr = 0.90×2,480×300 = 670 kN
Checking the rupture limit state:
Tr = 0.75×2,324×450 = 784 kN
Yielding governs, and the critical ratio is: 630/670 = 0.94.
Comparison
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Canada\CSA S16-14 - Axial Tension.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 22-Apr-14
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 2014
FYLD 300000 ALL
FU 450000 ALL
SNUG 0 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD Output
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: 0.941(PASS) LOAD: 1 LOCATION : 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 : 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 (N MM): 300.000 FU (N MM): 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.: 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 - ( S16-14) v1.0 ******************************************** ALL UNITS ARE - KN MET (UNLESS OTHERWISE Noted) COMPRESSION: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION: 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: 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