safe life method and the damage tolerant method. The safe life
method of assessment is considered in what follows. For some
circumstances, a simple method of fatigue assessment can be
used which does not refer to a load spectrum. The method is set
out in EC3-1-9 and involves verification in the stress domain; it is
Sections 5 and 6 of the standard provide details of how to
calculate the stresses for assessing the fatigue performance of
a detail. Nominal values of stresses should be calculated at the
serviceability limit state according to elastic theory, excluding
stress concentration effects. The nominal direct and shear
stresses should be calculated at the site of potential initiation
of a fatigue crack. The nominal stresses are modified by a stress
concentration factor if the relevant nominal stress is affected by a
local geometric feature, such as an opening with radiused corners.
Stress concentration factors are provided in Figure 4 of PD6695-1-
9:2008. Stresses in welds are calculated using a different formula
from that given in BS EN 1993-1-8 for weld design, as indicated
in Section 5(6). For certain details shown in Table B.1 of EC3-1-9,
fatigue resistance can be determined using the geometrical (hot
spot) stress method. Stress ranges for fatigue design are based on
nominal stresses, modified nominal stresses or geometrical (hot
spot) stress ranges.
For the structure and loading under consideration, the relevant
part of EN 1993 may provide parameters for calculating the design
value of the nominal stress ranges for fatigue verification. Using
this approach, the design value of the nominal, modified nominal
or geometrical stress range factored for fatigue must be less than
the reference fatigue strength at 2 million cycles for each detail
identified in tables 8.1 to 8.10.
The design value of nominal stress ranges is given in Section 6.2
of EC3-1-9 as
γFf ΔσE,2 = λ1 × λ2 × λ3 × λ4 … × λn × Δσ(γFf Qk)
for direct stresses where Δσ(γFf Qk) is the stress range caused by
the fatigue loads specified in EN 1991 and the λi are damage
equivalent factors depending on the spectra in the relevant parts
of EN 1993. The product of the damage equivalent factors λi
adjusts the stress ranges caused by the fatigue loads into stress
ranges corresponding to 2 × 106 cycles.
The fatigue verification involves checking that the nominal,
modified nominal or geometrical stress ranges due to frequent
loads Ψ1Qk do not exceed the following limits:
Δσ ≤ 1.5fy for direct stress ranges
Δτ ≤ (1.5fy) ⁄ √3 for shear stress ranges
Under fatigue loading, the following two inequalities should
The design value of the nominal stress ranges should therefore
be less than the reference fatigue strength at 2 million cycles for
that particular detail.
In addition, for stress ranges of combined shear and direct
stress a further inequality should be satisfied:
( ) 3 Ff E,2
( Ff E,2
C Mf 1.0
Lambda values which allow this approach are given in BS EN
1991-3 for cranes and in BS EN 1993-2 for bridges.
UK National Annex
The UK National Annex to EC3-1-9 states that where no λi values
are given the relevant parts of EC3, the verification should be
based on the damage accumulation equation which is essentially
the equation for Miner’s rule:
The most comprehensive load model available should be used
to establish a spectrum of stress ranges. The spectrum consists of
a series of bands of stress Δσi which should be multiplied by the
load factor γFf. The reference fatigue strength values ΔσC divided
by γMf are used to obtain the endurance value NRi for each band.
In the equation for damage, nEi is the number of cycles
associated with the stress range γFf Δσi for band i in the factored
spectrum and NRi is the endurance in cycles obtained from the
factored – NR
curve for a stress range of γFf Δσi.
It is intended to give a more detailed discussion of a fatigue
check in an example in a subsequent article.