Technical
Index log10Ngint ni nEi=ni+1-ni γMfγFfΔS Δσi NRi nEi /NRi cum nEi /NRi
0 0 1 1 116 116 83000 0.0 0.0
1 0.68 4 3 104 110 97200 0.0 0.0
2 1.36 22 18 90.0 96.8 141000 0.0 0.0
3 2.04 109 87 77.9 83.9 216000 0.0 0.0
4 2.72 526 417 66.8 72.4 338000 0.001 0.002
5 3.40 2520 1997 56.5 61.6 546000 0.004 0.005
6 4.08 12100 9567 46.9 51.7 926000 0.010 0.016
7 4.76 57900 45831 38.1 42.5 1660000 0.028 0.043
8 5.44 277000 219568 30.1 34.1 3230000 0.068 0.111
9 6.12 1330000 1051898 22.8 26.4 8660000 0.121 0.233
10 6.80 6370000 5039407 16.2 19.5 39700000 0.127 0.356
Table 1: Calculation steps for 10 intervals
NSC 27
June 19
nEi
NRi
D= n
d i
where nEi is the number of cycles associated with the stress
range γFfΔσi for band i in the factored spectrum and NRi is the
endurance in cycles from the fatigue strength curve for a stress
range of γMfγFfΔσi . According to the UK National Annex, γMf = 1.1
and γFf = 1.0.
The factored stress range spectrum is found from Figure 2.
Stress ranges Δσi corresponding to equal intervals of log10Ng
along the horizontal axis are considered in calculating the
fatigue damage. The values of Ng range between 1.0 at 100%
of Sk multiplied by the partial factors and the value of Ng at the
factored cut-off limit ΔσL. 100 intervals are chosen to achieve
good convergence. The number of cycles nEi of the occurrence
each stress range is calculated from the spectrum and the
number of cycles to failure NRi for the stress range is calculated
from the fatigue strength curve (Figure 3). The ratio of nEi /NRi is
summed to calculate the fatigue damage.
Taking the details in turn, the effective length of the 8 mm
fillet weld between the tube and end plate is 334 mm. The
force /mm is:
187
334
= 0.56 kN/mm
The throat thickness is 5.7 mm. The fatigue direct stress is:
0.56 × 103
= 105 MPa r = . This stress factored as described
5.7
corresponds to Sk in the curve in Figure 2. The weld detail class is
40, described as “circular structural hollow section fillet welded
end to end with an intermediate plate” in Table 8.6 of Part 1-9.
An example of the steps in the summation are given in the
Table 1 for 10 intervals.
Using 100 intervals gives cumulative damage of 0.320.
For the tube to end plate weld, the damage summation
equals 0.32 < 1.0 so the detail is satisfactory.
The second detail is the double-sided fillet weld between the
end plate and the spade-end. The effective length of the weld
between the tube and end plate is 388 mm. The force /mm is:
187
388
= 0.48 kN/mm
The fatigue direct stress is:
0.48 × 103
= 85.2 MPa r = . This
5.7
stress when factored corresponds to Sk in the curve in Figure 2.
The weld detail class is 36*, described as “root failure in partial
penetration Tee-butt joints or fillet welded joint …” in, Table 8.5
of Part 1-9.
For the spade end to end plate weld, the damage summation
equals 0.296 < 1.0 so the detail is satisfactory.
Conclusion
The foregoing examples indicate that for a bracing end
connection, the predicted fatigue damage according to EC3
Part 1-9 indicates a fatigue life in excess of the normal 50 year
design life of a building. This supports the inclusion of clause
2.4.3 in BS 5950:2000 and suggests that following the historical
practice in the UK of not carrying out fatigue checks on bracing
in conventional buildings is justified when designing to
BS EN 1993-1-1 and Part 1-9.
References
1 Introduction to fatigue design to BS EN 1993-1-1, New Steel
Construction, September 2018
/Design_codes_and_standards#National_Annexes
/Steel_construction_products#Structural_hollow_sections
/Braced_frames#Vertical_bracing