V. CSA S16-01 - 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. 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.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Canada\CSA S16-01 - Axial Tension.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 25-June-20
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
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 2001
FYLD 300000 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
STAAD.PRO CODE CHECKING - (CAN/CSA-S16-01 ) V2.1 ******************************************** ALL UNITS ARE - KNS MET (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= 1 LD L76X64X9.5 (CANADIAN SECTIONS) PASS CSA-13.9.A 0.941 1 630.00 T 0.00 0.00 4.00 STAAD SPACE -- PAGE NO. 6 ALL UNITS ARE - KNS MET (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= MEMBER PROPERTIES (UNIT = CM) ----------------------------- CROSS SECTION AREA = 2.48E+01 MEMBER LENGTH = 4.00E+02 IZ = 1.38E+02 SZ = 2.66E+01 PZ = 4.78E+01 IY = 1.67E+02 SY = 2.62E+01 PY = 4.72E+01 IX = 7.51E+00 CW = 0.00E+00 MATERIAL PROPERTIES (UNIT = MPA) -------------------------------- FYLD = 300.0 FU = 450.0 E = 2.05E+05 G = 7.88E+04 SECTION CAPACITIES (UNIT - KN,M) --------------------------------- CR1 = 6.696E+02 CR2 = 1.421E+02 SECTION CLASS 3 CRZ = 1.421E+02 CTORFLX = 1.421E+02 TENSILE CAPACITY = 6.696E+02 COMPRESSIVE CAPACITY = 1.421E+02 FACTORED MOMENT RESISTANCE : MRY = 7.082E+00 MRZ = 7.176E+00 MU = 3.531E+01 FACTORED SHEAR RESISTANCE : VRY = 2.588E+02 VRZ = 2.038E+02 MISCELLANEOUS INFORMATION -------------------------- NET SECTION FACTOR FOR TENSION = 1.000 KL/RY = 154.350 KL/RZ = 169.588 ALLOWABLE KL/R = 300.000 UNSUPPORTED LENGTH OF THE COMPRESSION FLANGE (M) = 4.000 OMEGA-1 (Y-AXIS) = 0.00 OMEGA-1 (Z-AXIS) = 0.00 OMEGA-2 = 1.00 SHEAR FORCE (KNS) : Y AXIS = 0.000E+00 Z AXIS = 0.000E+00 SLENDERNESS RATIO OF WEB (H/W) = 7.00E+00 41. FINISH STAAD SPACE -- PAGE NO. 7 *********** END OF THE STAAD.Pro RUN ***********