SECTION 1.7
Solution 1.7-14
P
Allowable Stresses and Allowable Loads
Piston and connecting rod
A
M
C
R
L
B
The maximum allowable force P occurs when cos
has its smallest value, which means that has its
largest value.
LARGEST VALUE OF
d diameter of rod A
SECTION 2.8
Problem 2.8-4 A block weighing W 5.0 N drops inside a cylinder
from a height h 200 mm onto a spring having stiffness k 90 N/m
(see figure).
(a) Determine the maximum shortening of the spring due to the
impact, and (b) determine the impact fact
SECTION 2.6
Problem 2.6-17 The normal stress on plane pq of a prismatic bar in
tension (see figure) is found to be 7500 psi. On plane rs, which makes
an angle 30 with plane pq, the stress is found to be 2500 psi.
Determine the maximum normal stress max an
74
CHAPTER 2 Axially Loaded Members
DETERMINE THE ANGLE
From Eq. (2): cos cos u
S elongation of spring
Therefore,
2b cos u cos u
S2 S1 b(cos cos )
For the spring: F k(S)
F bk(cos cos )
Substitute F into Eq. (1):
P cos bk(cos cos )(sin )
or
P
cot u co
56
CHAPTER 1
Tension, Compression, and Shear
Solution 1.8-11
Cage hoisted by a crane
W
From geometry:
L2
b 2
c 2
h2
2
2
(13 ft)2 (3 ft)2 (4 ft)2 h2
Solving, h 12 ft
B
FORCE IN A CABLE
T
TV
A
A
T force in one cable (cable AB)
TV vertical component of T
b
8
CHAPTER 1
Tension, Compression, and Shear
Problem 1.2-10 Solve the preceding problem if the load P 32 kN; the
cable has effective cross-sectional area A 481 mm2; the dimensions of
the crane are H 1.6 m, L1 3.0 m, and L2 1.5 m; and the cable
stretches by
SECTION 3.9
Solution 3.9-8
Strain Energy in Torsion
Cantilever bar with distributed torque
t0
t(x) = t0
dx
x
L
x
x distance from right-hand end of the bar
d
L
STRAIN ENERGY OF ELEMENT dx
ELEMENT d
Consider a differential element d at distance from
the rig
236
CHAPTER 3
Torsion
Strain Energy in Torsion
Problem 3.9-1 A solid circular bar of steel (G 11.4 106 psi)
with length L 30 in. and diameter d 1.75 in. is subjected to
pure torsion by torques T acting at the ends (see figure).
d
T
T
(a) Calculate the amo