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Fatigue
corresponds to Sk
stress when
NSC 19
= 105 MPa r = . This stress factored as described
= 85.2 MPa r = . This
Technical Digest 2019
Design Example
An example fatigue check on a connection detail for a bracing member taken
from the design example in SCI’s publication P365 Steel building design:
medium rise braced frames is illustrative.
The ultimate design load in the bracing member from ground to first floor is
539 kN. 60.9% of this force is due to wind load and it includes an amplification
factor of 1.17. The serviceability load due to wind alone is therefore:
537.4
1.17
× 0.609 ×
1
1.5
= 187.2 kN
The bracing member chosen is a 168 x 6.3 CHS in S355 material. A Tee or
spade end connection is adopted and the double-sided fillet weld between
the end plate on the tube and the projecting plate is designed in accordance
with clause 7.6 of BS EN 1993-1-8 which determines the effective lengths of
the weld. If the welds are sized according to the design load, as allowed in
clause 7.3.1(6) of BS EN 1993-1-8, 8 mm leg fillet welds are adequate (weld
throat = 5.7 mm). The connection detail is illustrated in Figure 3.
Fatigue Check
Checks on two welds are necessary for the end connection: the tube to end
plate and the end plate to spade end welds. The relevant detail categories are
40 and 36*; the latter category has a modified curve in accordance with clause
7.1(3) Note 3 in Part 1-9. The curves are shown in Figure 4.
Fatigue damage is defined in Annex A para. A.5 of Part 1-9 as:
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
5.7
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
5.7
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
Figure 3: Bracing connection
Figure 4: Fatigue strength curves
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