246
CHAPTER 3
Torsion
Problem 3.10-3 A thin-walled aluminum tube of rectangular
cross section (see figure) has a centerline dimensions b 6.0 in.
and h 4.0 in. The wall thickness t is constant and equal to
0.25 in.
t
h
(a) Determine the shear stress in the
SECTION 3.3
Solution 3.3-2
185
Circular Bars and Tubes
Torsion of a drill bit
d
T
T
(b) RATE OF TWIST
From Eq. (3-14):
d
4.0 mm
T
0.3 N m
G
75 GPa
(a) MAXIMUM SHEAR STRESS
u
u
From Eq. (3-12):
tmax
16T
d3
tmax
0.3 N m
(75 GPa)
32
(4.0
mm) 4
16(0.3 N m )
3
Torsion
Torsional Deformations
d
Problem 3.2-1 A copper rod of length L 18.0 in. is to be twisted
by torques T (see figure) until the angle of rotation between the ends
of the rod is 3.0.
If the allowable shear strain in the copper is 0.0006 rad, what i
SECTION 2.12
Solution 2.12-9
177
Elastoplastic Analysis
Rigid bar supported by two wires
STRESSES
L
A
B
C
FB
A
sB
3L
4
FC
A
sC
sC
2sB
(7)
Wire C has the larger stress. Therefore, it will yield first.
D
(a) YIELD LOAD
P
b
A
yield stress
E
b
cross-sectiona
SECTION 2.12
171
Elastoplastic Analysis
Elastoplastic Analysis
The problems for Section 2.12 are to be solved assuming that the
material is elastoplastic with yield stress Y , yield strain Y , and
modulus of elasticity E in the linearly elastic region (se
160
CHAPTER 2
Axially Loaded Members
Stress Concentrations
The problems for Section 2.10 are to be solved by considering the
stress-concentration factors and assuming linearly elastic behavior.
P
P
d
b
Problem 2.10-1 The flat bars shown in parts (a) and (
SECTION 2.5
Misfits and Prestrains
Steel wires
Problem 2.5-20 Prestressed concrete beams are sometimes
manufactured in the following manner. High-strength steel wires are
stretched by a jacking mechanism that applies a force Q, as represented
schematicall
SECTION 2.5
Solution 2.5-9
111
Thermal Effects
Rectangular bars held by pins
C
0.5 in. 2.0 in.
1.0 in. 2.0 in.
0.5 in. 2.0 in.
A
C
Pin
Diameter of pin: dP
Area of pin: AP
4
Copper
7
in.
16
d2
P
SUBSTITUTE NUMERICAL VALUES:
( 3.5 10 6 F )(100 F )(18,000 ks
102
CHAPTER 2
Axially Loaded Members
Problem 2.4-15 A rigid bar AB of length L 66 in. is hinged to a support
at A and supported by two vertical wires attached at points C and D (see
figure). Both wires have the same cross-sectional area (A 0.0272 in.2) an
SECTION 2.4
Statically Indeterminate Structures
Problem 2.4-4 A bar ACB having two different cross-sectional areas A1
and A2 is held between rigid supports at A and B (see figure). A load P
acts at point C, which is distance b1 from end A and distance b2
30
CHAPTER 1
Tension, Compression, and Shear
Problem 1.6-7 A special-purpose bolt of shank diameter d 0.50 in.
passes through a hole in a steel plate (see figure). The hexagonal head
of the bolt bears directly against the steel plate. The radius of the ci
26
CHAPTER 1
Tension, Compression, and Shear
Problem 1.6-2 Three steel plates, each 16 mm thick, are joined
by two 20-mm diameter rivets as shown in the figure.
P/2
P/2
P
(a) If the load P 50 kN, what is the largest bearing stress
acting on the rivets?
(b
SECTION 1.5
Solution 1.5-6
Linear Elasticity, Hookes Law, and Poissons Ratio
Brass specimen in tension
d
10 mm
Gage length L
P
20 kN
50 mm
0.122 mm
d
(a) MODULUS OF ELASTICITY
0.00830 mm
s
e
E
AXIAL STRESS
P
20 kN
254.6 MPa
A 4 (10 mm) 2
Assume is below t
18
CHAPTER 1
Tension, Compression, and Shear
Problem 1.4-4 A circular bar of magnesium alloy is 800 mm long.
The stress-strain diagram for the material is shown in the figure. The
bar is loaded in tension to an elongation of 5.6 mm, and then the load
is r
6
CHAPTER 1
Tension, Compression, and Shear
Problem 1.2-8 A long retaining wall is braced by wood
shores set at an angle of 30 and supported by concrete
thrust blocks, as shown in the first part of the figure. The
shores are evenly spaced, 3 m apart.
For
1
Tension, Compression,
and Shear
P1
Normal Stress and Strain
A
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
SECTION 4.5
Problem 4.5-20 The beam ABCD shown in the figure has
overhangs that extend in both directions for a distance of 4.2 m
from the supports at B and C, which are 1.2 m apart.
Draw the shear-force and bending-moment diagrams for this
overhanging be
266
CHAPTER 4
Solution 4.3-12
Shear Forces and Bending Moments
Beam with trapezoidal load
Free-body diagram of section CB
50 kN/m
30 kN/m
A
Point C is at the midpoint of the beam.
40 kN/m
B
30 kN/m
V
M
3m
RA
MB
FVERT
0
RA (3 m )
( 30 kN m )(3 m )(1.5 m )
SECTION 3.10
Problem 3.10-11 A tubular aluminum bar (G 4 106 psi) of square
cross section (see figure) with outer dimensions 2 in. 2 in. must resist a
torque T 3000 lb-in.
Calculate the minimum required wall thickness tmin if the allowable
shear stress is
SECTION 3.8
Problem 3.8-10 A solid steel bar of diameter d1 25.0 mm is
enclosed by a steel tube of outer diameter d3 37.5 mm and inner
diameter d2 30.0 mm (see figure). Both bar and tube are held
rigidly by a support at end A and joined securely to a rigi
SECTION 3.7
Solution 3.7-9
Motor-driven shaft
A
B
L1
C
L2
6 ft
L2
150 hp
125 hp
275 hp
L1
DIAMETER BASED UPON ALLOWABLE SHEAR STRESS
The larger torque occurs in segment AB
16TAB
d3
4 ft
tmax
d
1000 rpm
allow
G
d
1.5
11.5
106 psi
2 nT
33,000
H
hp
n
rpm
d4
SECTION 3.5
Solution 3.5-3
Pure Shear
211
Tubular bar
T
T
d1 d2
L
d2
4.0 in.
max
T
70.0 k-in.
6400 psi
max
70,000 lb-in.
max
L
f
6400 psi
48 in.
Torsion formula: tmax
Td2
2tmax
IP
Tr
IP
32
4
d1 )
32
[ (4.0 in.) 4
32
4
d1 ]
Solve for d1: d1
2Ltmax
Gd2
2 (4
204
CHAPTER 3
Torsion
Problem 3.4-9 A tapered bar AB of solid circular cross section is twisted
by torques T 36,000 lb-in. (see figure). The diameter of the bar varies
linearly from dA at the left-hand end to dB at the right-hand end. The bar
has length L
SECTION 3.3
191
Circular Bars and Tubes
Problem 3.3-11 A hollow steel shaft used in a construction auger
has outer diameter d2 6.0 in. and inner diameter d1 4.5 in. (see
figure). The steel has shear modulus of elasticity G 11.0 106 psi.
For an applied tor