Page 206 - Mechanical Behavior of Materials

Section 5.3 Elastic Deformation 207

Figure E5.2

ε x = 600 × 10 −6 , ε y = 2550 × 10 −6 , ε z =−1350 × 10 −6

These strains are related to the changes in length L, circumference (πd), diameter d, and
thickness t, as follows:
L (πd) d t
ε x = , ε y = = , ε z =
L πd d t

Substituting the strains and the known dimensions gives
L = 6.00 mm, d = 7.65 mm, t =−6.75 × 10 −3 mm Ans.

Thus, there are small increases in length and diameter, and a tiny decrease in the wall thickness.

Example 5.3
A sample of material subjected to a compressive stress σ z is confined so that it cannot deform
in the y-direction, as shown in Fig. E5.3. Assume that there is no friction against the die, so that
deformation can freely occur in the x-direction. Assume further that the material is isotropic and
exhibits linear-elastic behavior.
σ
z z

material y

rigid die

x

Figure E5.3