124
4 Stress–Strain Relations
ε x = 0.01, ε y = −0.03, ε z = 0.02,
γ xy = 0.01, γ yz = −0.05, γ xz = −0.02.
Determine the components of strain tensor at this point if E = 200 × 10
6 kPa
and G = 80 × 10
6 kPa.
11. The stress components at a point are given as:
σ x = 250 kPa; τ xy = 210 kPa
σ y = −290 kPa; τ yz = 150 kPa
σ z = 210 kPa; τ xz = −170 kPa
Determine the strain components at this point if E = 210 × 10
6 kPa and ν =
0.3.
12. If a material has a Poisson’s ratio of ν = 0.5, show that
G =
1
3
E
K = ∞
Volumetric strain (ε v ) = 0.
13. A square plate 10 mm thick is subjected to a tensile stress σ x = 140 MPa in one
direction and compressive stress σ y = −140 MPa in another direction. Find
the change in volume of the plate if E = 82.6 GPa and ν = 0.29.
14. A hard rubber block completely confined in the x-direction but free to expand in
both the y and z directions is subjected to compressive stress σ y = −2 MPa in
y-direction as shown in figure below. Calculate the stress σ x in the x-direction.
What is the change in volume of the block if E = 2 MPa and ν = 0.5 (Fig. 4.7).
Fig. 4.7 Rubber block
subjected to compressive
stress