Problem 8.56 The stationary blocks A, B, and C each
have a mass of 200 kg. Between all contacting surfaces,
s = 0.6. What force F is necessary to start B moving
downward?
F
B
A
C
80
80
The wedge angle is 10 for each side. The block A
cannot move, hence th
Problem 8.92 The thrust bearing is supported by contact of the collar C with a xed plate. The area of contact
is an annulus with an inside diameter D1 = 40 mm and
an outside diameter D2 = 120 mm. The coefcient
of kinetic friction between the collar and th
Problem 9.38 The extensional strain corresponding to
a point of a material and the direction of a line of length
dL in the reference state is = 0.15. What is the length
dL of the line in the deformed state?
Solution:
The denition of extensional strain can
Problem 9.30 Shears, such as the familiar scissors,
have two blades which subject a material to shear stress.
For the shearing process shown, draw a suitable freebody diagram and determine the average shear stress the
blades exert on the sheet of material
Problem 9.24 In Problem 9.23, the plane P is 3 ft
from end D of the cranes boom and is perpendicular to
the boom. The cross-sectional area of the boom at P
is 15 in2 . Determine the average normal stress and the
magnitude of the average shear stress in th
A
Problem 8.108 Each of the uniform 1-m bars has a
mass of 4 kg. The coefcient of static friction between
the bar and the surface at B is 0.2. If the system is in
equilibrium, what is the magnitude of the friction force
exerted on the bar at B?
45
O
B
30
Problem 8.31 The cylinder has weight W . The coefcient of static friction between the cylinder and the oor
and between the cylinder and the wall is s . What is the
largest couple M that can be applied to the stationary
cylinder without causing it to rotat
Problem 16.62 Determine the deection v as a function of x and conrm the results in Appendix E.
Solution:
The expressions for bending moment in the two sections of the beam
are:
M0a = w0
x2
a2
ax +
2
2
MaL = 0
Considering the interval 0 x a and beginning
Problem 16.65 For the beam in Problem 16.64 determine the deection as a function of x in the region
0 x L/2.
Solution:
Free Body Diagram:
Summing vertical forces on the beam
Fy = 0 = Ay + By F
[1]
Summing moments about point A on the beam
MA = 0 = MA + By
Problem 8.97 The mass of the block A is 18 kg. The
rope is wrapped one and one-fourth turns around the
xed wooden post. The coefcients of friction between
the rope and post are s = 0.15 and k = 0.12. What
force would the person have to exert to raise the
Problem 9.19 For the truss in Problem 9.18, determine Free Body Diagram:
the average normal stress in member BD acting on a
plane perpendicular to the axis of the member.
Solution:
To solve directly for the axial load in member BD of the truss, sum
moment
Problem 9.12 Figure (a) is a diagram of the bones and
biceps muscle of a persons arm supporting a mass. Figure (b) is a biomedical model of the arm in which the
biceps muscle AB is represented by a bar with pin supports. The suspended mass is m = 2 kg and
Problem 8.46 To obtain a preliminary evaluation of
the stability of a turning car, imagine subjecting the stationary car to an increasing lateral force F at the height
of its center of mass, and determine whether the car will
slip (skid) laterally before
Problem 8.76 A turnbuckle, used to adjust the length
or tension of a bar or cable, is threaded at both ends.
Rotating it draws threaded segments of a bar or cable
together or moves them apart. Suppose that the pitch
of the threads is p = 3 mm their mean r
Problem 8.83 The pulley of 50-mm radius is mounted
on a shaft of 10-mm radius. The shaft is supported by
two journal bearings. The mass of the block A is 8 kg.
Neglect the weights of the pulley and shaft. If a force
T = 84 N is necessary to raise the bloc
Problem 8.88 The disk D is rigidly attached to the
vertical shaft. The shaft has at ends supported by thrust
bearings. The disk and the shaft together have a mass
of 220 kg and the diameter of the shaft is 50 mm. The
vertical force exerted on the end of t
Problem 8.70 The vise exerts 80-lb forces on A. The
threaded shafts are subjected only to axial loads by the
jaws of the vise. The pitch of their threads is p = 1/8 in.,
the mean radius of the threads is r = 1 in., and the
coefcient of static friction bet
Problem 8.103 The mass of the block A is 14 kg. The
coefcient of kinetic friction between the rope and the
cylinder is 0.2. If the cylinder is rotated at a constant
rate, rst in the counterclockwise direction and then in
the clockwise direction, the diffe
Problem 9.8 The prismatic bar has a solid circular Free Body Diagram:
cross section with 30-mm radius. It is suspended from
one end and is loaded only by its own weight. The mass
density of the homogeneous material is 2800 kg/m3 . Determine the average no
Problem 9.1 The prismatic bar has a circular cross
section with 50-mm radius and is subjected to 4-kN axial
loads. Determine the average normal stress at the plane
P.
Free Body Diagrams:
Solution:
The cross-sectional area of the bar is:
A = r 2 = (0.05 m)
Problem 16.57 Use the solution of Problem 16.56
to determine the bending moment M in the beam as a
function of x.
Solution:
Superimposing the deections
and
from Appendix E, we get:
v=
F x2
M 0 x2
w 0 x2
6L2 4Lx + x2
(3L x)
24EI
6EI
2EI
Substituting the
Problem 17.21 Suppose that you want to increase the
wall thickness of the cross section of the column in Problem 17.20, while keeping the 0.08-m dimension xed, so
that the columns buckling load is 700 kN. What is the
necessary wall thickness?
Solution:
Th
Problem 9.48 When the truss is subjected to the vertical force F , joint A moves a distance v = 0.3 m vertically and a distance u = 0.1 m horizontally. If the
extensional strain AB in the direction parallel to member AB is uniform throughout the length of
Problem 10.1 A prismatic bar with cross-sectional
area A = 0.1 m2 is loaded at the ends in two ways:
(a) by 100-Pa uniform normal tractions; (b) by 10-N axial
forces acting at the centroid of the bars cross section.
What are the normal and shear stress di
Problem 10.32
Bar AB has cross-sectional area A = 100 mm2 and
modulus of elasticity E = 102 Gpa. The distance H =
400 mm. If a 200-kN downward force is applied to
bar CD at D, through what angle in degrees does bar
CD rotate? (You can neglect the deformat
Problem 10.37 In Problem 10.36, what is the resulting Free Body Diagram:
displacement of point C?
Solution:
Substituting Equation [2] into Equation [1]:
We can use either the left-hand or right-hand portion of the bar to
determine the displacement of poin
Problem 10.20 The truss in Problem 10.19 is constructed of a material that will safely support a normal
stress of 8 ksi and a shear stress of 3 ksi. Based on these
criteria, what is the largest force F that can safely be
applied
Solution:
We have seen fro
Problem 10.26 What tensile force would have to be
exerted on the right end of the bar in Problem 10.25 to
increase its length to 9.02 in.? What is the bars diameter
after this load is applied?
Solution:
The strain in the bar will be:
=
L L
9.02 in 9.00 in
Problem 10.42 The bar in Problem 10.40 consists of Free Body Diagram:
a material that will safely support a normal stress of
40 MPa. If F2 = 20 kN, what is the largest safe value
of F1 ?
Solution:
We see that section B has a cross-sectional area which is
Problem 9.55 In Problem 9.54, the angle between the
lines L1 and L2 at the point where they intersect is 90.2 .
What is the shear strain referred to the directions L1 and
L2 at that point?
Solution:
The change in the angle between L1 and L2 increases by 0