Page 428 - Mechanical Behavior of Materials

Section 9.3 Sources of Cyclic Loading 429

The safety factor in stress can be calculated from the stress amplitude σ a1 corresponding to
Point (1), which is obtained by substituting N = 2000 cycles into Eq. 9.6:
ˆ
B B −0.0977
σ a1 = AN f = AN ˆ = 1643(2000) = 782 MPa

Hence, the safety factor in stress is
782 MPa
σ a1
X S = = = 1.564 Ans.
ˆ σ a 500 MPa
However, due to the Eq. 9.6 form of the stress–life curve, this latter calculation can be
accomplished more efficiently from X N and Eq. 9.12:

X S = X −B = 97.1 −(−0.0977) = 1.564
N
Discussion Note that the modest value of safety factor in stress of X S = 1.56 corresponds
to the quite large safety factor in life of X N = 97.1, as expected from the rather large value of
−1/B = 10.2 for the stress–life curve.

9.3 SOURCES OF CYCLIC LOADING

Some practical applications involve cyclic loading at a constant amplitude, but irregular load versus
time histories are more commonly encountered. Examples are given in Figs. 9.7 to 9.10. Loads on
components of machines, vehicles, and structures can be divided into four categories, depending
on their source. Static loads do not vary and are continuously present. Working loads change with
time and are incurred as a result of the function performed by the component. Vibratory loads are
relatively high-frequency cyclic loads that arise from the environment or as a secondary effect of
the function of the component. These are often caused by fluid turbulence or by the roughness
of solid surfaces in contact with one another. Accidental loads are rare events that do not occur
under normal circumstances.
For example, consider highway bridges. Static loads are caused by the always-present weight
of the structure and roadway. Cyclic working loads are caused by the weights of vehicles, especially
heavy trucks, moving across the bridge. Vibratory loads are added to the working loads and
are caused by tires interacting with the roughness of the roadway, including the bouncing of
vehicles after hitting potholes. Long-span bridges are also subject to vibratory loading due to wind
turbulence. Accidental loading could be caused by a truck hitting an overpass bridge because the
truck was too high for the clearance available, or by an earthquake.
Working loads and vibratory loads, and often their combined effects, are the cyclic loads that
can cause fatigue failure. However, the damage due to cyclic loads is greater if the static loads
are more severe, so these also need to be considered. Accidental loads may play an additional role,
themselves causing fatigue failure, or damaging a component so that it is more susceptible to fatigue
caused by subsequent, more ordinary loads.