Page 33 - Mechanical Behavior of Materials

32 Chapter 1 Introduction

of the American Institute of Steel Construction, used for buildings and similar applications, safety
factors for design against yielding under static loading are generally in the range 1.5 to 2.0, with
1.5 applying for bending stress in the most favorable situations. Elsewhere, safety factors even as
low as 1.2 are sometimes used, but this should be contemplated only for situations where there
is quite thorough engineering analysis and few uncertainties, and also where failure has economic
consequences only.
For the basic requirement of avoiding excessive deformation due to yielding, the failure stress
is the yield strength of the material, σ o , and the service stress is the largest stress in the component,
calculated for the conditions expected in actual service. For ductile materials, the service stress
employed is simply the net section nominal stress, S, as defined for typical cases in Appendix A,
Figs. A.11 and A.12. However, the localized effects of stress raisers do need to be included in the
service stress for brittle materials, and also for fatigue of even ductile materials. Where several
causes of failure are possible, it is necessary to calculate a safety factor for each cause, and the
lowest of these is the final safety factor. For example, safety factors might be calculated not only for
yielding, but also for fatigue or creep. If cracks or sharp flaws are possible, a safety factor for brittle
fracture is needed as well.
Safety factors in stress are sometimes supplemented or replaced by safety factors in life. This
safety factor is the ratio of the expected life to failure to the desired service life. Life is measured by
time or by events such as the number of flights of an aircraft:
failure life
X 2 = (1.2)
desired service life
For example, if a helicopter part is expected to fail after 10 years of service, and if it is to be replaced
after 2 years, there is a safety factor of 5 on life. Safety factors in life are used where deformation
or cracking progresses gradually with time, as for creep or fatigue. As the life is generally quite
sensitive to small changes in stress, values of this factor must be relatively large, typically in the
range X 2 = 5to20.
The use of safety factors as in Eq. 1.1 is termed allowable stress design. An alternative is
load factor design. In this case, the loads (forces, moments, torques, etc.) expected in service are
multiplied by a load factor, Y. The analysis done with these multiplied loads corresponds to the
failure condition, not to the service condition.

(load in service) × Y = load causing failure (1.3)

The two approaches give generally similar results, depending on the details of how they are applied.
In some cases, they are equivalent, so that X 1 = Y. The load factor approach has the advantage
that it can be easily expanded to allow different load factors to be employed for different sources of
loading, reflecting different uncertainties in how well each is known.

1.3.3 Prototype and Component Testing
Even though mechanical behavior of materials considerations may be involved in the design process
from its early stages, testing is still often necessary to verify safety and durability. This arises
because of the assumptions and imperfect knowledge reflected in many engineering estimates of
strength or life.