Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-07 GTBL042-Callister-v2 August 6, 2007 12:43

198 • Chapter 7 / Mechanical Properties

EXAMPLE PROBLEM 7.2

Computation of Load to Produce Specified Diameter Change

A tensile stress is to be applied along the long axis of a cylindrical brass rod that

has a diameter of 10 mm (0.4 in.). Determine the magnitude of the load required

to produce a 2.5× 10 −^3 mm (10−^4 in.) change in diameter if the deformation is

entirely elastic.

Solution

This deformation situation is represented in the accompanying drawing.

z

F

F

x

d 0

di

li l 0

z ll

0

li – l 0

= l 0

x dd

0

di – d 0

= d 0

=

=

When the forceFis applied, the specimen will elongate in thezdirection and

at the same time experience a reduction in diameter,d,of2.5× 10 −^3 mm in

thexdirection. For the strain in thexdirection,

x=

d

d 0

=

− 2. 5 × 10 −^3 mm

10 mm

=− 2. 5 × 10 −^4

which is negative, since the diameter is reduced.

It next becomes necessary to calculate the strain in thezdirection using

Equation 7.8. The value for Poisson’s ratio for brass is 0.34 (Table 7.1), and

thus

z=−

x

ν

=−

(− 2. 5 × 10 −^4 )

0. 34

= 7. 35 × 10 −^4

The applied stress may now be computed using Equation 7.5 and the modulus

of elasticity, given in Table 7.1 as 97 GPa (14× 106 psi), as

σ=zE=(7. 35 × 10 −^4 )(97× 103 MPa)= 71 .3 MPa