slayt 1 - deu.edu.trkisi.deu.edu.tr/emine.cinar/b15 statics_frames and machines... · the toggle...
TRANSCRIPT
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1. The toggle pliers are used for a variety of clamping
purposes. For the handle position given by a = 10° and for a
handle grip P = 150 N, calculate the clamping force FC
produced.
Note that pins
A and D are
symmetric
about the
horizontal
centerline of
the tool.
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2. The elements of a rear suspension for a front-wheel-drive car are shown in the figure. Determine the magnitude of the force at each joint if the normal force F exerted on the tire has a magnitude of 3600 N.
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magnitudes of forces at each joint
FCD
Bx
By
a
x
y
09.12280
60tan 1
a
NBFBF
NBFBF
NF
FF
M
yCDyy
xCDxx
CD
CDCD
B
400003600sin0
18560cos0
1898
0)70(sin)305(cos)165(3600
0
a
a
aa
NB 441040001856 22
CD
FCD
FCD
Wheel + BC
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NA
NAFAF
NAFAF
NF
F
M
yEFyy
xEFxx
EF
EF
A
455013844330
138404000sin0
433001856cos0
5920
0)350(4000)260(sin
0
22
magnitudes of forces at each joint
Bx
By
x
y
30.65200
435tan 1
FEF
EF
FEF
FEF
Ax
Ay
AEB
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3. The elements of a floor jack are shown in the figure. CDFE
forms a parallelogram. Calculate the force in the hydraulic
cylinder AB corresponding to the 10 kN load. What is the force
in link EF?
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4. Determine the cutting force F applied by the blade DE to the
bar at G in terms of the force P applied to the handle of the
heavy-duty cutter.
Assume that
the cutting
force F is
perpendicular
to the lower
edge of the
blade DE.
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cutting force F applied by the blade DE to the bar at G in terms of the force P applied to the handle, force F is perpendicular to the lower edge of the blade DE.
FBE
a
x
y
ABC
Ax
Ay
4
17
CPF
FFPM
BE
BEBEA
7.23
0)4(sin)17(cos)413(0
12.1028
5tan 1
aa
a
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cutting force F applied by the blade DE to the bar at G in terms of the force P applied to the handle, force F is perpendicular to the lower edge of the blade DE.
FBE=23.7P
a
x
y
Blade DE
Dx
Dy
86
14°
PF
FFPPM D
4.45
0)5(14sin)48(14cos)13(sin7.23)86(cos7.230
60.886
13tan 1
aa
F
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5. The design of a hoisting mechanism for the dump truck is shown in the enlarged view. Determine the compression P in the hydraulic cylinder BE and the magnitude of the force supported by the pin at A for the particular position shown, where BA is perpendicular to OAE and link DC is perpendicular to AC. The dump and its load together have a mass of 9 Mg with center of mass at G.
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6. A basketball hoop whose rim height is adjustable is shown. The supporting post ABCD weighs 400 N with the center of gravity at point C, and backboard-hoop assembly weighs 220 N with the center of gravity at point G. The height of the rim is adjustable by means of the screw and hand crank IJ, where the screw is vertical. If a person with 800 N weight hangs on the rim, determine the support reactions at D and the forces supported by all members. Hint: Member IJ is a two-force member.
800 N
24
7
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mABCD= 400 N (at C), mhoop= 220 N (at G) IJ= two-force member, if a person with 800 N weight hangs on the rim, determine the support reactions at D and the forces supported by all members.
Dx
mNM
M
M
ND
D
F
ND
DF
D
D
D
y
y
y
x
xx
2.1867
0)35.1(768
)3(224)72.0(220
0
1388
0768220400
0
224
02240
220 N
400 N
Dy
MD
800 N
24
7
224 N
768 N
Entire frame
x
y
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mABCD= 400 N (at C), mhoop= 220 N (at G) IJ= two-force member, if a person with 800 N weight hangs on the rim, determine the support reactions at D and the forces supported by all members.
FAE
NF
NF
FFF
NF
FFF
NF
NFF
F
NF
F
M
y
yAEyy
x
xAExx
AE
AEy
AEx
AEy
AEx
AEx
F
2243)1992()1031(
1992
07682200
1031
02240
1584)1004()1225(
1004,5
4
60.0
48.0
1255
0)75.0(768)12.0(22048.0
0
22
22
FAEx
220 N
FAEy
800 N
24
7
224 N
768 N
Fx
Fy
EFGH
x
y
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mABCD= 400 N (at C), mhoop= 220 N (at G) IJ= two-force member, if a person with 800 N weight hangs on the rim, determine the support reactions at D and the forces supported by all members.
FIJ
NB
NBFBFF
NFBFBF
NF
FFF
M
yyyIJy
xxxxx
IJ
yxIJ
B
6740)6661()1031(
666100
103100
4669
0)60.0()48.0(15.0
0
22
Fx
Fy
IBF
Bx
By
IJ two force member
FIJ
FIJ
x
y
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7. The figure shows a wheel puller which is designed to remove a V-belt pulley P from its tight-fitting shaft S by tightening of the central screw. If the pulley starts to slide off the shaft when the compression in the screw has reached 1.2 kN, calculate the magnitude of the force supported by the each jaw at A. The adjusting screws D support horizontal force and keep the side arms parallel with the central screw.
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compression in the screw =1.2 kN, calculate the magnitude of the force supported by the each jaw at A, adjusting screws D support horizontal force
FCB
x
y
kNFF
kNFFFF
F
F
FFF
FF
FFF
EHCB
EHxCBxEHyCBy
CBx
CBy
EHxCBxx
EHyCBy
EHyCByy
85.0
6.0
145tan
0
2.1
02.10
1.2 kN
FEH
E
H
FEHx
FEHy
FCBx
FCBy
45°
45°
FCBy
FCBy
FCBx
FCBx
FCB
FCB
CB
EC
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compression in the screw =1.2 kN, calculate the magnitude of the force supported by the each jaw at A, adjusting screws D support horizontal force
x
y
kNDF
kNAAA
kNA
A
AAFM
kNFF
kNFAF
xx
yx
x
x
xyCBxD
CBxCBy
CByyy
42.00
626.0
18.0
,)6.0(15)6.0(60150
0)150()15()60(0
6.0
6.00
22
FCBy
FCBy
FCBx
FCBx
FCB
FCB
Ax
Ay
FCBy
FCBx
FCB
45°
CB
Dx
ABD
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F
8. The pruning mechanism of a pole saw is shown as it cuts a branch S. For
the particular position drawn, the actuating cord is parallel to the pole and
carries a tension of 120 N. Determine the shearing force P applied to the
branch by the cutter and the total force supported by the pin at E. The
force exerted by the light return spring at C is small and may be neglected.
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9. A bag of potatoes is
sitting on the chair. The
force exerted by the
potatoes on the frame at
one side of the chair is
equivalent to horizontal and
vertical forces of 24 N and
84 N, respectively, at E and
a force of 28 N
perpendicular to member BH
at G. Find the forces acting
on member BH.
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Dimensions are in centimeters
10. The elevation mechanism of a dumper-truck is comprised of two
identical systems of which one is shown in the figure and each
supports half of the load for the position depicted. Determine the
reactions in bars CD and HI and hydraulic cylinder BC. State
whether they work in
tension or compression.
Three members are
connected at pin B
(members EBD, ABH and
BC). Note that pins A and
D may not necessarily lie
along the same horizontal
line.
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11. The linkage shown is used on a garbage truck to lift a 9000 N dumpster.
Points A to G are pins, and member ABC is horizontal. For the position shown,
when the dumpster just fully lifts off the ground, determine the force in
hydraulic cylinder CF. Roller at G is in contact with the dumpster.
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Ax
Ay
FG
FBD of dumpster
NAFAF
NAFAF
NFFM
yGyy
xGxx
GGA
6910045sin90000
15910045cos0
225000)600()1500(90000
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Ex
Ey
FCD
FG
FBD of member EDG
NEEF
NEEF
NFFM
yyy
xxx
GCDE
5.79549045sin2250045cos1125000
63640045cos11250045cos225000
1125000)300()1500(225000
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Bx
By
FCF
Ex
Ey
From equilibrium of whole system;
NF
FEE
M
CF
CFyx
B
68.118724
0)450(45cos)45cos900900(450)45cos900()1950(9000
0
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12. A hydraulic lift-table is used to raise a 1000 kg crate. It consists of a platform and two identical linkages on which hydraulic cylinders exert equal forces. In the figure only one linkage and one cylinder are shown. Members EDB and CG are each of length 2a and member AD is pinned to the midpoint of EDB. If the crate is placed on the table, so that half of its weight is supported by the system shown, determine the force exerted by each cylinder in raising the crate for =60°, a=0.70 m and L=3.20 m. Show that the result obtained is independent of the distance d.
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FBD of Platform
Two-Force Members: AD, BC, CG, DH.
30o
=60o
FAD
W/2
FC FB
A B C
BCCBCBy
ADADx
FW
FW
FFW
FFF
FFFx
220
20
000
Pulley C FC
C
FCG
30o
FBC
300300
0300
cosFFFcosFF
FsinFF
CGCCCGy
BCCGx
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30o
=60o
FBD of CG
C
G
FCG
=60o 30
30
cos
FF
sin
FF
CCG
BCCG
FBD of BC
FCG
FBC FBC
30tanF
F
C
BC
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30o
=60o
N.F
FF.F.
.tanF.FF.
.F.F..sinF..cosFM
DH
/W
CBDH
F
CBDH
BCBDHDHE
BC
635124
070670
02113070670
021170350021261002120
2
FBD of EDB
B
E
FB
=60o
Ex
o.sin
.
sin
.
m.DHcosEHDEEHDEDH
021260
91270
912602222
aa
D
H
a
Ey
FBC
FDH
0.7 m
0.61 m
1.4 m
Cosine theorem:
Sine theorem:
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13. The mechanism is designed to keep its load level while raising it. A pin
on the rim of the 80 cm diameter pulley fits in a slot on arm ABC. Arm ABC
and DE are each 80 cm long and the package being lifted weighs 80 kN.
The mechanism is
raised by pulling on
the rope that is
wrapped around the
pulley. Determine
the force P applied
to the rope and all
the forces acting on
arm ABC when the
package has been
lifted 80 cm as
shown.
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SOLUTION
FBD of Platform Two force member: ED
69.28 mm
FBD of DE
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FBD of ABC
FBD of the pulley
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14. A simple folding chair comprised of two identical frames, one on each side, is shown in the figure. The half frame shown carries half the weight of a 70 kg person. Determine all the forces acting on member BF. Neglect the weights of the connecting elements (not shown) and the seat, and also the friction at points A, B and F.
Detail of contact at F
Dimensions in “mm”
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Geometry of the Chair
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SOLUTION
Two force member: EG
Equilibrium of the whole system:
FBD of DC
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GE two force member
FBD of BF