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 (t_w = 13.1 mm).

L = 4 m

T_f = 630 kN

The material used is G40.21 300W steel (F_y = 300 MPa, F_u = 450 MPa) (FYLD and FU)

Calculations

Gross area is used for welded connections.

T_{r} = {}_{\max}{\begin{matrix} ϕ A F_{y} = 0.9 \times 300 \times A = 270 A \\ ϕ_{u} A F_{u} = 0.75 \times 450 \times A = 338 A \end{matrix}

T_r ≥ T_f , so solve for A:

A = \frac{630 \times {(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

r_min = 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:

A_n2 = 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 - \frac{32}{250}) \times 64 \times 9.5 = 530 {mm}^{2}

The total net area for the pair of angles for the rupture limit state is:

A_ne = 632 + 530 = 1,162 mm²

For the pair of angles, A_ne = 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:

T_r = 0.90×2,480×300 = 670 kN

Checking the rupture limit state:

T_r = 0.75×2,324×450 = 784 kN

Yielding governs, and the critical ratio is: 630/670 = 0.94.

Comparison

Table 1. Comparison of results
Criteria	Reference	STAAD.Pro	Difference
T_f (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).

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 ***********