# 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)

## Calculations

Gross area is used for welded connections.

$T r = { ϕ A F y = 0.9 × 300 × A = 270 A ϕ u A F u = 0.75 × 450 × A = 338 A max ⁡$

Tr ≥ Tf , so solve for A:

$A = 630 × ( 10 ) 3 270 = 2 , 333 mm 2$

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.

$A n 3 = ( 1 − 32 250 ) × 64 × 9.5 = 530 mm 2$

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

Table 1. Comparison of results
Tf (kN) 670 669.6 negligible
Critical Ratio 0.94 0.941 negligible
Note: If the member 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).

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
1 TABLE LD L76X64X9.5
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MY MZ
2 FX 630
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PRINT SUPPORT REACTION ALL
PARAMETER 1
FYLD 300000 ALL
FU 450000 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH


                       STAAD.PRO CODE CHECKING - (CAN/CSA-S16-01  ) V2.1
********************************************
ALL UNITS ARE - KNS  MET  (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
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)
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
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