1. - deukisi.deu.edu.tr/emine.cinar/statics/spring18 statics/b18... · 2018-03-08 · 4. the...
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1. The uniform I-beam has a mass of 60 kg per meter of its length.
Determine the tension in the two supporting cables and the reaction
at D.
PROBLEMS
m = 60 kg/m, determine the tension in the two supporting cables and the reaction at D.
PROBLEMS
mGmDmCmBmA )0,0,3(,)0,0,0(,)3,2,5(,)3,2,5(,)0,0,5(
ABT
ACT
W
DN
x
y
z
G
kj
ACAC
kj
ABAB
kjTT
kjTT
83.055.0
83.055.0
606.3
32
606.3
32
)(8.470881.98602
Nkks
mm
m
kgW
kNN DD
NN
jNjkNiki
NrWrM
D
DD
DADAGA
52.1883
056.941758.47082
00 //
m = 60 kg/m, determine the tension in the two supporting cables and the reaction at D.
PROBLEMS
mGmDmCmBmA )0,0,3(,)0,0,0(,)3,2,5(,)3,2,5(,)0,0,5(
ABT
ACT
W
DN
x
y
z
G
NTT
TF
TTF
kjTT
kjTT
ACAB
ABz
ACABy
ACAC
ABAB
98.1701
052.18838.4708)83.0(20
0
83.055.0
83.055.0
PROBLEMS
2. A 36 kg sheet of plywood rests on two small wooden blocks as
shown. It is allowed to lean 20° from the vertical under the action
of a force P which is perpendicular to the sheet. Friction at all
surfaces of
blocks A and B is
sufficient to
prevent slipping.
Determine the
magnitude P and
the vertical
reaction forces
at A and B.
PROBLEMS m = 36 kg. Friction at all surfaces of blocks A and B is sufficient to
prevent slipping. Determine the magnitude P and the vertical
reaction forces at A and B.
PROBLEMS
3. The uniform 7 m steel shaft
has a mass of 200 kg and end
A is supported by the ball-and-
socket connection in the
horizontal x-y plane. The ball
end B rests against the smooth
vertical walls. One of the
vertical walls supporting end B
of the shaft is turned through a 30° angle as shown. Calculate the
magnitudes of the forces and exerted on the ball end B of the
shaft by the vertical walls C and D, respectively.
P
R
PROBLEMS m = 200 kg, ball-and-socket connection at A, end B rests against the smooth vertical walls.. Calculate magnitudes of forces and exerted on B by the vertical walls C and D. P
R
P
xA
yA
zA
W
G
RTop view
x
y
30
P
RyR
xR
30
jRiRjRiRRN
jPPN
NkkW
kAjAiAA
yxD
C
zyx
30sin30cos
)(1962)81.9(200
PROBLEMS m = 200 kg, ball-and-socket connection at A, end B rests against the
smooth vertical walls.. Calculate magnitudes of forces and exerted
on B by the vertical walls C and D. P
R
P
xA
yA
zA
W
G
R
mGmBmA )5.1,3,1(,)3,0,0(,)0,6,2(
058861962
30sin330cos330cos630sin232
019625.1330sin30cos362
0
0
//
ij
iRjRkRkRiPkP
kkjijRiRjPkji
WrRPr
M
AGAB
A
G
m5.3
m5.3
m325.626 22
m3
m5.1
m3m1jRiRR
jPPNkW
30sin30cos
,)(1962
PROBLEMS m = 200 kg, ball-and-socket connection at A, end B rests against the
smooth vertical walls.. Calculate magnitudes of forces and exerted
on B by the vertical walls C and D. P
R
P
xA
yA
zA
W
G
R
030cos630sin22
196230cos3
588630sin33
0
kRRP
jR
iRP
M A
jRiRRjPPNkWkAjAiAA zyx
30sin30cos,,)(1962,
j
NR
R
17.755
196230cos3
i
NP
RP
42.1584
588630sin3317.755
4. The uniform panel door has a
mass of 30 kg and is prevented
from opening by the strut C,
which is a light two-force member
whose upper end is secured under
the door knob and whose lower
end is attached to a rubber cup
which does not slip on the floor.
Of the door hinges A and B, only
B can support force in the
vertical z-direction. Calculate the
compression C in the strut and
the horizontal components of the
forces supported by hinges A and
B when a horizontal force P = 200
N is applied normal to the plane
of the door as shown.
PROBLEMS
NjPNkkW
kBjBiBBjAiAA
kjFnFF
kjkj
n
zyxyx
CDHCC
DH
200,3.294)81.9(30
,
8.06.0
8.06.025.1
75.0
O (0, 0, 0) A (-1.2, 0, 1.8) B (-1.2, 0, 0.2) G (-0.6, 0, 1)
E (0, 0, 2) D (-0.2, 0, 1) H (-0.2, 0.75, 0) m
Of the door hinges A and B, only B can support force in the vertical z-direction, calculate the compression C in the strut and the horizontal components of the forces supported by hinges A and B E
G
W
Ax Ay
Bx
By
Bz FC
D
H
O
P PROBLEMS
kFjAFiAFM
jAiAkjki
kjFkikkiM
M
CxCyCB
yx
CB
B
2406.058.1766.18.03606.148.0
6.12008.12.1
8.06.08.03.2948.06.0
0
NA
NAFAj
NAAFi
NFFk
xy
xCx
yyC
CC
06.138
64.89,58.1768.06.1
105,6.136048.0
400,2406.0
NB
NBFBAF
NABBAF
xy
yCyyy
xxxxx
47.170
14506.02000
64.8900
Of the door hinges A and B, only B can support force in the vertical z-direction, calculate the compression C in the strut and the horizontal components of the forces supported by hinges A and B
E
G
W
Ax Ay
Bx
By
Bz FC
D
H
O
P
PROBLEMS
PROBLEMS
5. The shaft, lever and
handle are welded together
and constitute a single rigid
body. Their combined mass is
28 kg with mass center at G.
The assembly is mounted on
bearings A and B, and rotation
is prevented by link CD.
Determine the forces
exerted on the shaft by the
bearings A and B while the 30
N·m couple is applied to the
handle as shown. Would these
forces change if the couple were applied to the shaft AB rather than to the
handle?
PROBLEMS Determine the forces exerted on the shaft by the bearings A and B while the 30 N·m couple is applied to the handle as shown. Would these forces change if the couple were applied to the shaft AB rather than to the handle?
Ax
Ay
Bx
By
W
F
C
PROBLEMS 6. Under the action of the 40 N·m
torque applied to the vertical shaft,
the restraining cable AC limits the
rotation of the arm OA and
attached shaft to an angle of 60°
measured from the y axis. The
collar D fastened to the shaft
prevents downward motion of the
shaft in its bearing. Calculate the
bending moment M, the compression
P and the shear force V in the
shaft at section B. (Bending
moment, expressed as a vector, is
normal to the shaft axis and shear
force is also normal to the shaft
axis.)
PROBLEMS collar D prevents downward motion of the shaft in its bearing, calculate the bending moment M, the compression P and the shear force V in the shaft at section B.
(Bending moment, expressed as a vector, is normal to the shaft axis and shear force is also normal to the shaft axis.)
xB
T
yB
zB
xM
yM
kjiTkji
TT
76.038.053.0263.0
2.01.01386.0
mCmB
mA
)2.0,18.0,0(,)11.0,0,0(
)0,08.0,1386.0()0,60cos16.0,60sin16.0(
040
76.038.053.018.009.0
0400 /
jMiMk
kjiTjk
jMiMkTrM
yx
yxBCB
040095.0047.0
106.0
kTjMT
iMTM
y
xB
PROBLEMS collar D prevents downward motion of the shaft in its bearing, calculate the bending moment M, the compression P and the shear force V in the shaft at section B.
(Bending moment, expressed as a vector, is normal to the shaft axis and shear force is also normal to the shaft axis.)
xB
T
yB
zB
xM
yM
kjiTT
76.038.053.0
mNMi
mNMj
NTk
x
y
63.44
79.19
05.421
mNMMM yx 82.4822
NPBTBF
NBV
NBTBF
NBTBF
zzz
xy
yyy
xxx
19.320,076.00
62.273
19.160,038.00
89.221,053.00
7. The electric sander has a mass of 3
kg with mass center at G and is held in a
slightly tilted position (z-axis vertical)
so that the sanding disk makes contact
at its top with the surface being
sanded. The sander is gripped by its
handles at B and C. If the normal force
R against the disk is maintained at 20 N
and is due entirely to the force
component Bx (i.e., Cx = 0), and if the
friction force F acting on the disk is 60
percent of R, determine the
components of the couple M which must
be applied to the handle at C to hold
the sander in position. Assume that half
of the weight is supported at C.
PROBLEMS
R = 20 N
W = 29.43 N
Cz Cy My
Mx
F = 0.6R=12 N
Mz
Bx
Bz
m =3 kg, normal force R =20 N due entirely to force component Bx (i.e., Cx = 0), the friction force F acting on the disk 60 percent of R, determine the components of the couple M which must be applied to the handle at C to hold the sander in position. Assume that half of the weight is supported at C.
PROBLEMS
mmG
mmC
mmB
mmA
)0,0,40(
)300,0,0(
)0,200,40(
)100,0,120(
01220120400
43.294030072.142020040300
0
0 ///
kMjMiMjiik
kikkijik
kMjMiM
jFiRrWrkBiBrM
zyx
zyx
CACGzxCBC
NW
CBCB
F
CNB
zzzz
z
xx
715.142
,43.29
0
0,20
R = 20 N
W = 29.43 N
Cz Cy My
Mx
F = 0.6R=12 N
Mz
Bx
Bz
m =3 kg, normal force R =20 N due entirely to force component Bx (i.e., Cx = 0), the friction force F acting on the disk 60 percent of R, determine the components of the couple M which must be applied to the handle at C to hold the sander in position. Assume that half of the weight is supported at C.
PROBLEMS
mmNM
mmNM
mmNM
z
y
x
2560
6.1411
1856
014404000
8002.11778.5886000
48002944
kM
jM
iMM
z
y
xC
jCy
12
8. Because of friction a very large force T is required to raise the 10 kg body
when the cable is wound around a fixed rough cylinder as shown. For the static
equilibrium values shown, determine all of the reactions at point O. The 0.3 m
dimension refers to the point A where the cable loses contact with the
cylinder. Neglect the weight of the fixed cylinder.
PROBLEMS
Tz
Ty
Tyz
y
z
20
°
x
W=10(9.81)=98.1 N = 0.0981 kN
W
Ox
Oy Oz
MOy
MOx
MOz
kNTTT
kNTTT
kNTT
kNTT
yzz
yzy
yz
x
89.820sin30cos20sin
41.2420cos30cos20cos
98.2530cos
1530sin
A
PROBLEMS Determine all of the reactions at point O, neglect the weight of the fixed cylinder
O (0, 0, 0)
A (30sin60, 30cos60, 800) = (26, 15, 800)
B (0, 30, 1100) mm
B
A
Tx
y
x T
30°
60° 60° 30 mm
z B
Top view
Front view
Determine all of the reactions at point O, neglect the weight of the fixed cylinder
0
89.841.24158001526
0981.0110030
00
?
?
//
kMjMiM
kjikjj
ikjM
MTrWrM
kMjMiMM
kOjOiOO
OzOyOx
O
OOAOBO
OzOyOxO
zyx
mkNMmkNkjiM
mkNmmkNM
mkNmmkNM
mkNmmkNM
kM
jMiMM
OO
Oz
Oy
Ox
Oz
OyOxO
88.22,86.01.124.19
86.072.856
1.1234.12123
4.1965.19394
072.856
34.1212365.19394
kNOTOF
kNOTOF
kNOTOF
zzzz
yyyy
xxxx
89.8,00
41.24,00
902.14,0098.00
kNO
kNkjiO
95.29
89.841.249.14
W
Ox
Oy Oz
MOy
MOx
MOz
PROBLEMS
B
O (0, 0, 0)
A (26, 15, 800)
B (0, 30, 1100) mm
PROBLEMS
9. The two bars AC and CD are homogeneous and each weigh 200 N/m.
Joints A, C and D are ball-and-socket joints and a cable is connected
between B and E. Determine all reactions that act on bar AC.
PROBLEMS AC and CD are homogeneous and each weigh 200 N/m. Joints A, C and D are ball-and-socket joints and a cable is connected between B and E. Determine all reactions that act on bar AC.
10. The structure is subjected to the loadings shown. Member AB is
supported by a ball and socket joint at A and a smooth collar at B. Member
CD is supported by a pin at C which acts like a thrust bearing. Determine the
reactions at A and C.
PROBLEMS
Ball and socket joint at A, smooth collar at B, thrust bearing at C. Determine reactions at A and C.
PROBLEMS
G
G
D
11. A circular plate with a weight of 900 N acting at its center point G is
supported by cord DE and a thrust bearing at B. Shaft AC is fixed and
frictionless. Determine the cable tension and the reactions acting on the
circular plate from the bearing at B.
PROBLEMS
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