This preview shows pages 1–3. Sign up to view the full content.
STATICS AND MECHANICS OF MATERIALS, 2
nd
Edition
RILEY, STURGES AND MORRIS
83
457
Determine the movement of the pointer of Fig. P457 with respect to the scale zero when the temperature
increases 80
q
F.
The coefficients of thermal expansion are 6.6(10
±
6
)/
q
F for the steel and 12.5(10
±
6
)/
q
F for the
aluminum.
SOLUTION
The steel post and the steel scale each stretch the same amount
² ³² ³² ³
6
6.6 10
80 20
0.01056 in.
so
GG
±
u
The aluminum post stretches
6
12.5 10
80 20
0.02000 in.
a
G
±
u
Therefore, the motion of the pointer relative to the zero
on the steel scale is
51
p
as
±
0.0472 in.
p
n
.....................................................................................................................
Ans.
458
A bronze [
D
B
= 16.9(10
±
6
)/
q
C] sleeve with an inside diameter of 99.8 mm is to be placed over a solid steel [
D
S
= 11.9(10
±
6
)/
q
C] cylinder, which has an outside diameter of 100 mm.
If the temperatures of the cylinder and
sleeve remain equal, how much must the temperature be increased in order for the bronze sleeve to slip over
the steel cylinder?
SOLUTION
6
6
100
11.9 10
100
99.8
16.9 10
99.8
dT
T
±
±
´
u
'
´
u
'
403 C
T
'
q
................................................................................................................................
Ans.
459
A steel [
E
= 30,000 ksi and
D
= 6.5(10
±
6
)/
q
F] surveyor’s tape ½in. wide
u
1/32in. thick is exactly 100 ft
long at 72
q
F and under a pull of 10 lb.
What correction should be introduced if the tape is used to make a
100ft measurement at a temperature of 100
q
F and under a pull of 25 lb.
SOLUTION
1
LLL
T
EL
L
L
VG
HD
cc
±
´
'
±
where
L
is the length at 72
q
F and zero force.
When
10 lb
P
,
² ³
² ³
10
640 psi
12 132
V
,
100 ft
L
c
, and
6
100
640
10
30 10
L
±
´
u
99.99787 ft
L
Then, when
25 lb
P
,
² ³
² ³
25
1600 psi
, and
28 F
T
' q
² ³² ³
6
6
1600
1
6.5 10
28
30 10
L
L
±
c
´
u
u
100.02140 ft
L
0.02140 ft
0.257 in.
L
correction
0.257 in.
±
............................................................................................................
Ans.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document STATICS AND MECHANICS OF MATERIALS, 2
nd
Edition
RILEY, STURGES AND MORRIS
84
460
A 25mm diameter aluminum [
D
= 22.5(10
±
6
)/
q
C,
E
= 73 GPa, and
Q
= 0.33] rod hangs vertically while
suspended from one end.
A 2500kg mass is attached at the other end.
After the load is applied, the
temperature decreases 50
q
C.
Determine
(a)
The axial stress in the rod.
(b)
The axial strain in the rod.
(c)
The change in diameter of the rod.
SOLUTION
(a)
² ³² ³
² ³
62
2
2500 9.81
49.962 10 N/m
50.0 MPa
0.025
4
V
S
u
#
......................................................
Ans.
(b)
² ³² ³
6
66
9
49.962 10
22.5 10
50
441 10 m/m
73 10
a
T
E
HD
±±
u
´
'
´
u
±
±
u
u
......................
Ans.
(c)
² ³
² ³² ³
6
9
49.962 10
0.33
22.5 10
50
1350.86 10 m/m
73 10
t
T
E
HQD
§·
u
±
´ ' ±
´
u
±
±
u
¨¸
u
©¹
² ³² ³
6
1350.86 10
25
0.0338 mm
dt
d
GH
±
±
u
±
...........................................................
Ans.
461
The rigid yokes
B
and
C
of Fig. P461 are securely fastened to the 2in. square steel (
E
30,000 ksi) bar
AD
.
Determine
(a)
The maximum normal stress in the bar.
(b)
The change in length of segment
AB
.
(c)
The change in length of segment
BC
.
(d)
The change in length of the complete bar.
SOLUTION
(a)
3
max
max
82 10
20,500 psi
20.5 ksi
22
P
A
u
u
.................................................................
Ans.
(b)
² ³² ³
² ³² ³
3
6
82 10
8 12
0.0656 in.
30 10
2 2
AB
PL
EA
G
uu
...........
Ans.
(c)
² ³² ³
² ³² ³
3
6
12 10
5 12
0.00600 in.
30 10
2 2
BC
±u
u
±
..............
Ans.
² ³² ³
² ³² ³
3
6
45 10
4 12
0.01800 in.
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 02/11/2009 for the course CIVIL ENGI 560 taught by Professor Brody during the Fall '08 term at University of Maryland Baltimore.
 Fall '08
 Brody

Click to edit the document details