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Problem 5.16
In the structures shown, all members have the same
2m
length. Determine all
support reactions.
Problem 5.17
In the structures shown, all members have the same
2m
length. Determine all
support reactions.
Problem 5.18
The top chord of the truss is subjected to a uniform distributed load that
gives rise to the forces
Q
shown. If
QD1kip
, determine all support
reactions.
Problem 5.19
Determine the support reactions for the short flight of stairs due to the forces
shown on the two steps.
Problem 5.20
The forklift has a vehicle weight of
WVD15;000 lb
, fuel weight of
WFD
300 lb
, and operator weight of
WOD160 lb
. If
PD2000 lb
, determine the
reactions on each pair of wheels.
Problem 5.21
A fixture for positioning
40 cm
by
50 cm
size cardboard boxes with weight
WD150 N
in a packaging company is shown. If the weight of the box and its
contents acts through the center of the box, determine the largest value of
if the
magnitude of the reactions at points
A
and
B
may not exceed
800 N
, at which
point the box begins to crush. The notch at point
A
prevents horizontal and
vertical translation of the box and assume the contact at point Bis frictionless.
Solution
Problem 5.22
Bar
ABC
is supported by a roller at
B
and a frictionless collar at
A
that slides on a
fixed bar
DE
. Determine the support reactions at points
A
and
B
. Express your
answers in terms of parameters such as P,a, etc.
Solution
Problem 5.23
A steel I beam is supported by a pin at point
A
and a rocker at
B
, and a cable
applies a
2000 lb
force. The beam is uniform and weighs
26 lb=ft
. Determine
the support reactions.
Problem 5.24
A steel I beam is supported by a pin at point
A
, a vertical link
CD
, and a cable
applies a
2000 lb
force. The beam is uniform and weighs
26 lb=ft
. Determine
the support reactions.
Solution
Problem 5.25
Structure
ABCDE
is supported by a roller at
D
and a frictionless collar at
A
that slides on a fixed bar
F G
. Determine the support reactions at points
A
and
D. Express your answers in terms of parameters such as P,Q,a,b,c, etc.
Problem 5.26
A hand-operated winch for winding and unwinding rope on a spool is shown.
The mean radius of the spool is
8in:
, and the mean radius of the sprocket is
5in
.
The spool, sprocket, and handle
AB
are one piece and rotate on a frictionless
bearing at
B
. The pawl
CD
engages the sprocket at point
D
and prevents the
drum from rotating when PD0. The weights of all members are negligible.
(a)
To wind rope onto the spool, if the operator can apply a maximum
force
PD50 lb
, and if this force is perpendicular to the handle
AB
of
the winch, determine the largest value of
T
the rope may have. Also
determine the reactions at B.
(b)
If
PD0
and
TD75 lb
, determine the reactions at
B
and the force
supported by the pawl CD.
Solution
Problem 5.27
The front view of one of the wings of a Cessna 172 airplane is shown. The
wing is supported by a pin-connected strut
BE
and by a connection at
A
that
may be idealized as a pin. The plane’s mass, including fuel, passengers, and
cargo, is
1000 kg
, and it flies so that it is in static equilibrium. The strut
BE
has
negligible mass, and the wing
ABCD
has
200 kg
mass with center of gravity
at point
B
. Model the wing as a two-dimensional structure where all forces lie
in the same plane.
(a)
Determine the resultant lift force
P
that this wing supports, assuming
this force is vertical and that only the wings provide lift for the plane.
(b) Determine the forces supported by the strut BE and the pin at A.
Solution
W
PP
y
x
Part (a)
The FBD for the airplane is shown, where the weight is
WD1000 kg 9:81 m
s2D9810 N:(1)
The equilibrium equation is
XFyD0W2P WD0)PD4905 N. (2)
Part (b)
The FBD for the wing is shown at the right, where the
weight of the wing is
WwD200 kg 9:81 m
s2D1962 N. (3)
XMAD0WP .2:6 m/Ww.2 m/TBE
1:4
p5:96.2 m/D0)TBE D7698 N, (4)
XFxD0WAxTBE
2
p5:96 D0)AxD6306 N;(5)
XFyD0WAyTBE
1:4
p5:96 WwCPD0)AyD1472 N:(6)
May 11, 2012
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Problem 5.28
The automobile shown has
1200 kg
mass with center of gravity at point
G
, and
all wheels have the same
0:34
m radius. If the automobile has rear wheel drive,
determine the reactions at each pair of wheels when the automobile just begins
to slowly drive over the curb in front of it at point C.
Problem 5.29
Repeat Prob. 5.28 if the automobile has front wheel drive.
Solution
In the FBD for the automobile, note that when the vehicle begins to drive over the curb that
AyD0
. Point
D
is a convenient location to sum moments because the line of action of force
Cn
passes through this point,
hence it produces no moment about point
D
. Also, the moment arm for force
Ct
is easy to obtain (it is 0.34
Problem 5.30
A sliding screen door for a house or apartment is shown. The door has rollers
at points
A
,
B
,
C
, and
D
; the rollers
A
and
B
are a loose fit, and the rollers
C
and
D
are a loose fit. The door weighs
90
N with center of gravity at point
G
. The rollers are frictionless, but when the door slides to the right, horizontal
forces
FtD10
N and
FbD40
N arise due to friction from the weather sealing
along the top and bottom of the door. To slide the door to the right, a person
applies the horizontal force Pat point E.
(a)
Determine the value of
P
so that the door slides to the right with constant
speed.
(b)
For the value of
P
obtained in Part (a), determine which rollers make
contact and the reactions at these rollers.
Problem 5.31
A bucket used in a mining operation for moving ore has frictionless rollers at
points
A
,
B
,
C
, and
D
. The bucket moves up and down a fixed rail
HI
. The
rollers at
A
and
B
are a loose fit on the rail, and the rollers at
C
and
D
are a
loose fit. The mass of the bucket and its contents is 1600 kg.
(a)
Determine the cable force
T
needed to move the bucket up or down the
rail at constant speed.
(b)
For the value of
T
obtained in Part (a), determine which rollers make
contact and the reactions at these rollers.