# 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)

## 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\S16 2014\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
1 TABLE LD L76X64X9.5
*1 TABLE T W530x123
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
SNUG 0 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH


                       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 (MET): 0.00  CONDITION: Cl. 13.9.1
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:     169.796  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 - (          S16-14)   v1.0
********************************************
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