PROBLEM 11.1
KNOWN:
A steel rod (circular cross-section) having:
6
2
m
10 in
0.25 in
30
10
lb/in
40 lb
m
L
D
E
m
=
=
=
×
=
FIND:
The change in length of the rod,
L
δ
,
ASSUMPTIONS:
Rod is elastically deformed, such that
m
E
σ
ε
=
⋅
SOLUTION:
The force resulting from 40 lb
m
in standard gravity is
(
)
(
)
2
m
m
2
40 lb
32.174 ft/sec
40 lb
ft lb
32.174
lb sec
N
c
ma
F
g
=
=
=
⎛
⎞
⎜
⎟
⎝
⎠
The resulting uniaxial stress is
N
a
c
F
A
σ
=
where
(
)
2
2
2
2
0.25
0.049 in
4
40 lb
814.9 lb/in
0.049 in
c
a
A
π
σ
=
=
=
=
and
2
5
6
2
814.9 lb/in
2.716
10
30
10
lb/in
a
a
m
E
σ
ε
−
=
=
=
×
×
The change in length is then
(
)
(
)
5
2.716
10
10 in
0.00027 in
a
L
L
δ
ε
−
=
⋅
=
×
=
10 in
D=0.25 in
F
N
Cross
Section, A
c

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PROBLEM 11.2
KNOWN:
A steel rod (circular cross-section) having:
10
0.3 m
5 mm
20
10
Pa
50 kg
m
L
D
E
m
=
=
=
×
=
FIND:
The change in length of the rod,
L
δ
.
ASSUMPTIONS:
Rod is elastically deformed, such that
m
E
σ
ε
=
⋅
SOLUTION:
The force resulting from 50 kg in standard gravity is
(
)
(
)
2
2
50 kg
9.8 m/s
kg m
1.0
s
N
N
c
ma
F
g
=
=
⎛
⎞
⎜
⎟
⎝
⎠
490 N
N
F
=
The resulting uniaxial stress is
N
a
c
F
A
σ
=
where
(
)
2
3
5
2
6
-5
2
5
10
1.96
10
m
4
490 N
25
10
Pa
1.96
10
m
c
a
A
π
σ
−
−
=
×
=
×
=
=
×
×
and
6
6
10
25
10
Pa
125
10
20
10
Pa
a
a
m
E
σ
ε
−
×
=
=
=
×
×
The change in length is then
(
)
(
)
6
6
0.3
125
10
37.5
10
m
a
L
L
δ
ε
−
−
=
⋅
=
×
=
×
0.3 m
D=5 mm
F
N
Cross
Section, A
c

PROBLEM 11.3
KNOWN:
An electrical coil with
20,000
0.051 in
2.0 in
N
D
r
=
=
=
FIND:
The resistance,
R
.
SOLUTION:
We know
e
c
L
R
A
ρ
=
where
6
1.673 10
cm
e
ρ
−
=
×
Ω
for copper, and
(
)
2
2
5
2
0.051
1.42
10
ft
4
4
12
c
A
D
π
π</