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Introduction to Mechanical Engineering Design 17
maximum allowable parameter. Here the parameter can be load, stress, deflection, etc.
Thus, the design factor n d is defined as
loss-of-function parameter
n d = (1–1)
maximum allowable parameter
If the parameter is load, then the maximum allowable load can be found from
loss-of-function load
Maximum allowable load = (1–2)
n d

EXAMPLE 1–1 Consider that the maximum load on a structure is known with an uncertainty of ±20 per-
cent, and the load causing failure is known within ±15 percent. If the load causing fail-
ure is nominally 2000 lbf, determine the design factor and the maximum allowable load
that will offset the absolute uncertainties.

Solution To account for its uncertainty, the loss-of-function load must increase to 1/0.85, whereas
the maximum allowable load must decrease to 1/1.2. Thus to offset the absolute uncer-
tainties the design factor, from Eq. (1–1), should be
1/0.85
Answer n d = = 1.4
1/1.2
From Eq. (1–2), the maximum allowable load is found to be
2000
Answer Maximum allowable load = = 1400 lbf
1.4

Stochastic methods (see Chap. 20) are based on the statistical nature of the design
parameters and focus on the probability of survival of the design’s function (that is, on
reliability). Sections 5–13 and 6–17 demonstrate how this is accomplished.

1–11 Design Factor and Factor of Safety

A general approach to the allowable load versus loss-of-function load problem is the
deterministic design factor method, and sometimes called the classical method of
design. The fundamental equation is Eq. (1–1) where n d is called the design factor. All
loss-of-function modes must be analyzed, and the mode leading to the smallest design
factor governs. After the design is completed, the actual design factor may change as
a result of changes such as rounding up to a standard size for a cross section or using
off-the-shelf components with higher ratings instead of employing what is calculated
by using the design factor. The factor is then referred to as the factor of safety, n. The
factor of safety has the same definition as the design factor, but it generally differs
numerically.
Since stress may not vary linearly with load (see Sec. 3–19), using load as the loss-of-
function parameter may not be acceptable. It is more common then to express the design
factor in terms of a stress and a relevant strength. Thus Eq. (1–1) can be rewritten as
loss-of-function strength S
n d = = (1–3)
allowable stress σ(or τ)