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본문내용
Tension, Compression,
and Shear
Normal Stress and Strain
Problem 1.2-1 A solid circular post ABC (see figure) supports
a load P1 2500 lb acting at the top. A second load P2 is
uniformly distributed around the shelf at B. The diameters of
the upper and lower parts of the post are dAB 1.25 in. and
dBC 2.25 in., respectively.
(a) Calculate the normal stress AB in the upper part of the post.
(b) If it is desired that the lower part of the post have the
same compressive stress as the upper part, what should be
the magnitude of the load P2?
Solution 1.2-1 Circular post in compression
1
Tension, Compression,
and Shear
1
A
B
C
P1
dAB
dBC
P2
P1 2500 lb
dAB 1.25 in.
dBC 2.25 in.
(a) NORMAL STRESS IN PART AB
(b) LOAD P2 FOR EQUAL STRESSES
AB 2040 psi
Solve for P2: P2 5600 lb —
sBC
P1P2
ABC
2500 lbP2
4
(2.25 in.)2
sAB
P1
AAB
2500 lb
4
(1.25 in.)2 2040 psi—
ALTERNATE SOLUTION
∴ P22.24 P15600 lb—
dBC
dAB
1.8
P1P2
dBC
2
P1
dAB
2 or P2P1 B ¢
dBC
dAB
≤
2
1 R
sAB
P1
AAB
P1
4 dAB
2 sBCsAB
sBC
P1P2
ABC
P1P2
4 dBC
2
A
B
C
P1
P2
Piston rod
5 mm
50 mm
225 mm
P = 40 N
Problem 1.2-2 Calculate the compressive stress c in the circular
piston rod (see figure) when a force P 40 N is applied to the
brake pedal.
Assume that the line of action of the force P is parallel to the
piston rod, which has diameter 5 mm. Also, the other dimensions
shown in the figure (50 mm and 225 mm) are measured perpendicular
to the line of action of the force P.
Solution 1.2-2 Free-body diagram of brake pedal
Problem 1.2-3 A steel rod 110 ft long hangs inside a
tall tower and holds a 200-pound weight at its lower end
(see figure).
If the diameter of the circular rod is 1⁄4 inch, calculate
the maximum normal stress max in the rod, taking
into account the weight of the rod itself. (Obtain the
weight density of steel from Table H-1, Appendix H.)
2 CHAPTER 1 Tension, Compression, and Shear
F compressive force in piston rod
d diameter of piston rod
5 mm
EQUILIBRIUM OF BRAKE PEDAL
F(50 mm) P(275 mm) 0
COMPRESSIVE STRESS IN PISTON ROD (d 5 mm)
sc
F
A
220 N
4
(5 mm)2 11.2 MPa—
FP¢
275 mm
50 mm
≤ (40 N) ¢
275
50
≤220 N
©MA0
50 mm
225 mm
P = 40 N
F
A
in.
200 lb
110 ft
1
4
and Shear
Normal Stress and Strain
Problem 1.2-1 A solid circular post ABC (see figure) supports
a load P1 2500 lb acting at the top. A second load P2 is
uniformly distributed around the shelf at B. The diameters of
the upper and lower parts of the post are dAB 1.25 in. and
dBC 2.25 in., respectively.
(a) Calculate the normal stress AB in the upper part of the post.
(b) If it is desired that the lower part of the post have the
same compressive stress as the upper part, what should be
the magnitude of the load P2?
Solution 1.2-1 Circular post in compression
1
Tension, Compression,
and Shear
1
A
B
C
P1
dAB
dBC
P2
P1 2500 lb
dAB 1.25 in.
dBC 2.25 in.
(a) NORMAL STRESS IN PART AB
(b) LOAD P2 FOR EQUAL STRESSES
AB 2040 psi
Solve for P2: P2 5600 lb —
sBC
P1P2
ABC
2500 lbP2
4
(2.25 in.)2
sAB
P1
AAB
2500 lb
4
(1.25 in.)2 2040 psi—
ALTERNATE SOLUTION
∴ P22.24 P15600 lb—
dBC
dAB
1.8
P1P2
dBC
2
P1
dAB
2 or P2P1 B ¢
dBC
dAB
≤
2
1 R
sAB
P1
AAB
P1
4 dAB
2 sBCsAB
sBC
P1P2
ABC
P1P2
4 dBC
2
A
B
C
P1
P2
Piston rod
5 mm
50 mm
225 mm
P = 40 N
Problem 1.2-2 Calculate the compressive stress c in the circular
piston rod (see figure) when a force P 40 N is applied to the
brake pedal.
Assume that the line of action of the force P is parallel to the
piston rod, which has diameter 5 mm. Also, the other dimensions
shown in the figure (50 mm and 225 mm) are measured perpendicular
to the line of action of the force P.
Solution 1.2-2 Free-body diagram of brake pedal
Problem 1.2-3 A steel rod 110 ft long hangs inside a
tall tower and holds a 200-pound weight at its lower end
(see figure).
If the diameter of the circular rod is 1⁄4 inch, calculate
the maximum normal stress max in the rod, taking
into account the weight of the rod itself. (Obtain the
weight density of steel from Table H-1, Appendix H.)
2 CHAPTER 1 Tension, Compression, and Shear
F compressive force in piston rod
d diameter of piston rod
5 mm
EQUILIBRIUM OF BRAKE PEDAL
F(50 mm) P(275 mm) 0
COMPRESSIVE STRESS IN PISTON ROD (d 5 mm)
sc
F
A
220 N
4
(5 mm)2 11.2 MPa—
FP¢
275 mm
50 mm
≤ (40 N) ¢
275
50
≤220 N
©MA0
50 mm
225 mm
P = 40 N
F
A
in.
200 lb
110 ft
1
4
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