Real Life Example
in
Mechanics of Material's
By Sina Abedini n

ELEMENTARY STRESS SYSTEMS
1.Stress and strain in uni -axial solid hollow bars
Explain:
Work through the example below:
An iPod ; with a mass 30 grams in dangled its earplug cable.
a)Assuming that copper wire of diameter 0.40mm
inside the cable carries the entire load ; evaluate the
stress in the wire due to the weight of the iPod
b)If the wire in (a) is1.50m long ; by how much will it
stretch?
c)Assuming that the plastic insulation ; which fits snugly
over the wire and has an external diameter of 1mm ;
carries the entire load ; evaluate the stress in insulation
due to the weight of iPod
d)If the insulation is made from uPVC calculate the
extension of the insulation in circumstances described
in (c)

𝑎)𝜎 =
𝐹
𝐴
=
𝑚𝑔
𝜋
4
𝑑2
=
30 × 10−3
× 9.81
𝜋
4
× (0.4 × 10−3)2
0.4mm
𝐹
=
𝑚𝑔
=
30
×
10
−3
×
9.81
2.3 × 106
𝑁
𝑚2
1.5m
𝑏)δ =
𝑃𝑙
𝐴𝐸
=
𝑚𝑔 × 𝑙
𝜋
4
𝑑2 × 𝐸
=
30 × 10−3
× 9.81 × 1.5
𝜋
4
× (0.4 × 10−3)2× 110 × 109
31.9 × 10−6
𝑚

0.4mm
1mm
1.5m
𝐹
=
𝑚𝑔
=
30
×
10
−3
×
9.81
0.2mm
c)𝜎 =
𝐹
𝐴
=
𝑚𝑔
𝜋
4
𝑑0
2
−𝑑1
2
𝐸
=
30×10−3×9.81
𝜋
4
(0.0012−0.0042)
0.29
𝑁
𝑚2
𝑑)𝛿 =
𝑃𝑙
𝐴𝐸
=
𝑚𝑔𝑙
𝜋
4
𝑑0
2
− 𝑑1
2
𝐸
=
30 × 10−3 × 9.81 × 1.5
𝜋
4
(0.0012 − 0.0042) × (2 × 109)
3.35 × 10−4𝑚