Page 228 - Materials Science and Engineering An Introduction

200 • Chapter 6 / Mechanical Properties of Metals

where N¿ is greater than unity. Thus, the material to be used for the particular applica-
tion is chosen so as to have a yield strength at least as high as this value of s d .
safe stress Alternatively, a safe stress or working stress, s w , is used instead of design stress.
This safe stress is based on the yield strength of the material and is defined as the yield
strength divided by a factor of safety, N, or

Computation of safe s y
(or working) stress s w = (6.24)
N
Utilization of design stress (Equation 6.23) is usually preferred because it is based
on the anticipated maximum applied stress instead of the yield strength of the material;
normally, there is a greater uncertainty in estimating this stress level than in the speci-
fication of the yield strength. However, in the discussion of this text, we are concerned
with factors that influence the yield strengths of metal alloys and not in the determina-
tion of applied stresses; therefore, the succeeding discussion deals with working stresses
and factors of safety.
The choice of an appropriate value of N is necessary. If N is too large, then com-
ponent overdesign will result; that is, either too much material or an alloy having a
higher-than-necessary strength will be used. Values normally range between 1.2 and
4.0. Selection of N will depend on a number of factors, including economics, previous
experience, the accuracy with which mechanical forces and material properties may be
determined, and, most important, the consequences of failure in terms of loss of life and/
or property damage. Because large N values lead to increased material cost and weight,
structural designers are moving toward using tougher materials with redundant (and
inspectable) designs, where economically feasible.

DESIGN EXAMPLE 6.1

Specification of Support-Post Diameter
A tensile-testing apparatus is to be constructed that must withstand a maximum load of 220,000 N
(50,000 lb f ). The design calls for two cylindrical support posts, each of which is to support half of
the maximum load. Furthermore, plain-carbon (1045) steel ground and polished shafting rounds
are to be used; the minimum yield and tensile strengths of this alloy are 310 MPa (45,000 psi) and
565 MPa (82,000 psi), respectively. Specify a suitable diameter for these support posts.
Solution
The first step in this design process is to decide on a factor of safety, N, which then allows
determination of a working stress according to Equation 6.24. In addition, to ensure that the
apparatus will be safe to operate, we also want to minimize any elastic deflection of the rods
during testing; therefore, a relatively conservative factor of safety is to be used, say N = 5. Thus,
the working stress s w is just

s y
s w =
N
310 MPa
= = 62 MPa (9000 psi)
5
From the definition of stress, Equation 6.1,
d 2 F
A 0 = a b p =
2 s w