Civil Engineering Reference
In-Depth Information
U n i a x i a l t e n s i o n
1.0
Pu r e s h e a r
Un i a x i a l
co m p r e s s i o n
-
1.0
1.0
0
P r i n c i p a l s t r es s
rati o
1
/
f
y
2
M a x i m u m d i s t o r t i o n - e n e r g y
cr i t e r i o n
2
-
1
2
+
1
2
=
f
y
2
-
1.0
Figure 1.7
Yielding under biaxial stresses.
failure may occur. High-cycle fatigue is only a design consideration when a large
number of loading cycles involving tensile stresses is likely to occur during the
design life of the structure (compressive stresses do not cause fatigue). This is
often the case for bridges, cranes, and structures which support machinery; wind
and wave loading may also lead to fatigue problems.
Factors which significantly influence the resistance to fatigue failure include
the number of load cycles
N
, the range of stress
σ
=
σ
max
−
σ
min
(1.3)
during a load cycle, and the magnitudes of local stress concentrations. An indi-
cation of the effect of the number of load cycles is given in Figure 1.8, which
shows that the maximum tensile stress decreases from its ultimate static value
f
u
in an approximately linear fashion as the logarithm of the number of cycles,
N
,
increases.Asthenumberofcyclesincreasesfurtherthecurvemayflattenoutand
the maximum tensile stress may approach the endurance limit
σ
L
.
Theeffectsofthestressmagnitudeandstressratioonthefatiguelifearedemon-
stratedinFigure1.9.Itcanbeseenthatthefatiguelife
N
decreaseswithincreasing
stress magnitude
σ
max
and with decreasing stress ratio
R
=
σ
min
/σ
max
.
Theeffectofstressconcentrationistoincreasethestresslocally,leadingtolocal
damage and crack initiation. Stress concentrations arise from sudden changes in
the general geometry and loading of a member, and from local changes due to
bolt and rivet holes and welds. Stress concentrations also occur at defects in the
member,oritsconnectorsandwelds.Thesemaybeduetotheoriginalrollingofthe
steel, or due to subsequent fabrication processes, including punching, shearing,
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