Analisis Optimasi Profil Rangka Baja Dalam Perencanaan Bangunan Industri

TUGAS AKHIR BENTANG 20 m
20 m
DIMENSIONING
BAB IIIGORDING

cos
sin

20
20

=
=

Gaya angin
z1
z2

=
=


0,940
0,342

=
=

1,5 m
20 m

H =
h =

7m
5,250 m

65 kg/cm2

=
1,5
10,0


a
L

/ cos
/ cos

=
=

=
=
=

6m
240 Mpa
160 Mpa

Mutu Baut
Mutu Las


=
=

1,596 m
10,642 m

Asumsikan jarak gording =

1,400 m
==>

Maka banyak gording untuk bentang z 1 + z2
Asumsikan berat sendiri atap

=

Berat sendiri gording

S b .Y


=

×

q cos

1,596

4,00 =
q=

q total = ( 5,600

+

10,642 ) / 1,400 =

8,7


5,600 kg/m
q kg/m

+ q ) kg/m

9

buah

+

MX1

= q total × cos × L2 / 8
5,600 + q ) × cos
20 ×
= (
23,6803 + 4,2286 q ) kg m
= (


6,0 2 / 8

MY1

= q total × sin × L2 / 8
5,600 + q ) × sin
20 ×
= (
8,6189
= (
+ 1,5391 q ) kg m

6,0 2 / 8

S b .X
q s in

n=(

4,00 kg/m2


Dimensi Gording
A. Dimensi Gording Variasi Tanpa Ada Track Stang
1. Muatan Tetap
Berat sendiri atap
1,4
=

q

Jarak Portal ( )
Mutu Profil
Mutu Profil

Page 1

360 Mpa
360 Mpa

TUGAS AKHIR BENTANG 20 m


2. Muatan Angin
2a.
Angin Datang
qa =
65
kg/cm2
Koefisien =
0.02 × × 0.4
20
= 0,02 ×
qa datang
Koefisien
=
× Jarak Gording
×
0,000
=
× 1,4 × 65
0,000

kg/m
=
q d a ta n g

qa

0,4

= 0,000

MX2a

= qa datang × L2 / 8
= 0,000
× 6,0
kg m
= 0,0000

MY2a


=

S b .X

2 /8

0

S b .Y

2b.

Angin Pergi
qa =
65
kg/cm2
Koefisien =
-0,4
qa datang
Koefisien

=
× Jarak Gording
-0,400
=
× 1,4 × 65
-36,400
kg/m
=
q p e rg i

×

qa

MX2b

= qa datang × L2 / 8
= -36,400
× 6,0 2 / 8
kg m
= -163,8000

MY2b

=

S b .X

0

S b .Y

3. Muatan Tak Terduga
P

P = 100 kg

Sb.Y
Sb.X
P sin
P cos

MX3

= P × cos × / 4
cos
= 100
×
= 140,954 kg m

20

×

6,0

/4

MY3

= P × sin × / 4
sin
= 100
×
= 51,3030 kg m

20

×

6,0

/4

Kombinasi Momen
Akibat Muatan 1 + Muatan 2a (Angin Datang)
MX Total
23,6803
4,2286
=(
+
MY Total
8,6189
1,5391
=(
+
Akibat Muatan 1 + Muatan 2b (Angin Pergi)
MX Total
23,6803
4,2286
=(
+
MY Total
8,6189
1,5391
=(
+

q ) + ( 0,0000 )
q) +( 0 )

=(
=(

+
+

4,2286 q ) kg m
1,5391 q ) kg m

q ) + ( -163,800 )
q) +( 0 )

= ( -140,120 +
= ( 8,6189 +

4,2286 q ) kg m
1,5391 q ) kg m

=(
=(

164,634
59,9219

+
+

4,2286 q ) kg m
1,5391 q ) kg m

=(
=(

164,634
59,9219

+
+

4,2286 q ) kg m
1,5391 q ) kg m

Akibat Muatan 1 + Muatan 3 (Muatan Tak Terduga)
MX Total
23,6803
4,2286 q ) + ( 140,954 )
=(
+
MY Total
8,6189
1,5391 q ) + ( 51,3030 )
=(
+
Maka momen maksimum yang menentukan :
Dicoba profil Channel Lips
Data:
q
=
Wx
=
Wy
=
q total
=(

7,51 kg/m
44,27 cm3
12,26 cm3
5,600
+

MX Total
MY Total

C 150×65×20×3.2

7,510 ) =

Ix
Iy

=
=
F
=
13,110 kg/m

23,6803
8,6189

332 cm4
53,8 cm4
9,567 cm2

ix
iy
E

=
=
=

5,89 cm
2,37139 cm

2100000 kg/cm2

Page 2

TUGAS AKHIR BENTANG 20 m

Kontrol Tegangan
MX
MY
=
+
Terjadi
WX
WX
( 16463,4
+
=

profil

422,86
44,27

Kontrol Lendutan
5
qTotal × cos × L4
FX
=
384
E × Ix
5
0,131
cos
×
=
384
2100000
= 0,905 cm
FY

=
=
=

F

5
qTotal × cos × L4
384
E × Iy
5
0,131
cos
×
384
2100000
2,032 cm

=

Fizin

FX2 + FY2
=

F <

L
180

600
180

=

Fizin

0,905

=

..

=

×

7,5

)

+

( 5992,19

+

153,91 ×
7,5
)
12,26
1026,659 kg/cm2

1 P × cos × L3
48
E × Ix
20
× 600 4
+
×
332

1
48

100

20 ×
× cos
2100000 × 332

600 3

1 P × cos × L3
48
E × Iy
20
× 600 4
+
×
53,8

1
48

100

20 ×
× cos
2100000 × 53,8

600 3

1600 kg/cm2
1600 kg/cm2

..

+

+

+ 2,032 2

2

=

2,224 cm

3,333 cm

OK

B. Dimensi Gording Variasi Dengan Track Stang
Direncanakan gading-gading kap memiliki 3 medan ekonomis
G a d in g K a p

2,00 m

Ly

S b .Y
S b .X

2,00 m

Lx

T ra c k S ta n g

2,00 m
G a d in g K a p

1. Muatan Tetap
q total
= ( 5,600

+ q ) kg/m

MX1

= q total × cos × LX2 / 8
5,600
+ q) ×
cos
= (
23,6803
4,2286
= (
+

20 ×
q ) kg m

6,0 2

/8

MY1

= q total × sin × LY2 / 8
5,600
+ q) ×
sin
= (
0,9577
0,1710
= (
+

20 × (
q ) kg m

6,0 /

3

2. Muatan Angin
2a.
Angin Datang
=
MX2a
=
MY2a
2b.

Angin Pergi
=
MX2b
=
MY2b

0,0000 kg m
0 kg m
-163,8000 kg m
0 kg m

3. Muatan Tak Terduga
MX3
= P × cos × X / 4
cos
= 100
×
= 140,954 kg m
MY3

)2 / 8

= P × sin × Y / 4
sin
= 100
×
= 17,1010 kg m

20

×

6,0

20

×(

6,0 /

/4

3 )/4

Page 3

OK

TUGAS AKHIR BENTANG 20 m

Kombinasi Momen
Akibat Muatan 1 + Muatan 2a (Angin Datang)
MX Total
23,6803
4,2286
=(
+
MY Total
0,9577
0,1710
=(
+
Akibat Muatan 1 + Muatan 2b (Angin Pergi)
MX Total
23,6803
4,2286
=(
+
MY Total
0,9577
0,1710
=(
+

q ) + ( 0,0000 )
q) +( 0 )

=(
=(

+
+

4,2286 q ) kg m
0,1710 q ) kg m

q ) + ( -163,800 )
q) +( 0 )

= ( -140,120 +
= ( 0,9577 +

4,2286 q ) kg m
0,1710 q ) kg m

=(
=(

164,634
18,0587

+
+

4,2286 q ) kg m
0,1710 q ) kg m

=(
=(

164,634
18,0587

+
+

4,2286 q ) kg m
0,1710 q ) kg m

Akibat Muatan 1 + Muatan 3 (Muatan Tak Terduga)
MX Total
23,6803
4,2286 q ) + ( 140,954 )
=(
+
MY Total
0,9577
0,1710 q ) + ( 17,1010 )
=(
+
Maka momen maksimum yang menentukan :

MX Total
MY Total

Dicoba profil Channel Lips
C 125×50×20×2.3
Data:
q
4,51 kg/m
Ix
=
=
Wx
21,92 cm3
Iy
=
=
Wy
6,22 cm3
F
=
=
q total
5,600
4,510 ) =
10,110 kg/m
=(
+

Kontrol Tegangan
MX
MY
=
+
Terjadi
WX
WX
( 16463,4
+
=

=
=
=

F

422,86
21,92

FX2 + FY2
=

F <

×

4,5

1
48
20
×
×
137

)

( 1805,87

+

P × cos × LX3
E × Ix
600 4
1
+
48

+

5
1
qTotal × cos × LY4
P × cos × LY3
+
384
E × Iy
48
E × Iy
5
0,101
cos
20 × ( 600 / 3 )4
×
384
2100000
×
20,6
0,148 cm

=

Fizin

137 cm4
20,6 cm4
5,747 cm2

L
180

Fizin

2,027

=
600
180

=
..

ix
iy
E

4,88 cm
1,89 cm
2100000 kg/cm2

=

=
=

profil

Kontrol Lendutan
5
qTotal × cos × LX4
FX
=
384
E × Ix
5
0,101
cos
×
=
384
2100000
= 2,027 cm
FY

23,6803
0,9577

=

2

+ 0,148 2

=

+

+

17,10
4,5
×
)
6,22
1140,803 kg/cm2

100

20 ×
× cos
2100000 × 137

1
48

100

1600 kg/cm2
1600 kg/cm2

..

OK

600 3

20 × ( 600 /
× cos
2100000 × 20,6

3 )3

2,032 cm

3,333 cm

OK

Kesimpulan : Profil gording yang di pakai adalah Channel Lips
Y
t

X

h
Cx
d

Cy
b

Jumlah profil Channel Lips C yang diperlukan :

h
b
d
t
F
q
Wx
Wy
Ix
Iy

C 125×50×20×2.3
=
=
=
=
=
=
=
=
=
=

125
50
20
2,3
5,747
4,51
21,92
6,22
137
20,6
n =

mm
mm
mm
mm

cm2
kg/m
cm3
cm3
cm4
cm4

( Jumlah Lapangan Gording ) + 1

=

9

+ 1 =

10

buah

Page 4

8,74

TUGAS AKHIR BENTANG 20 m
BAB II
DIMENSI BATANG TARIK (TRACK STANG)

2

m

2

m

2

m
b

a

a = 1,400
m
b = 1,038
m
Berat sendiri atap
Jarak batang tarik
Berat sendiri gording (q)
Beban tak terduga

a

=
=
=
=

4,00
2
4,51
100

Beban yang bekerja
Atap
A. Tipe 1 =
Gording
Beban Tak Terduga
A. Tipe 2 =

Atap
Gording
Beban Tak Terduga

Beban yang dipikul oleh track stang :
NTotal
8
= N1
+
Dibutuhkan

:

Terjadi

d
d
6

a

a

kg/m2
m
kg/m
kg
= 2,00
= 2,00
= 100

×
×
×

1,04
4,51
sin

×
×

= 2,00
= 2,00
= 100

×
×
×

1,4
4,51
sin

×
×

=

1600

kg/cm2

1600

kg/cm2

NTotal
1600 /4
369,069
1600
×
0,542
cm

d

d =

a

20

20

4,00
sin

× sin
20

20
N1

4,00
sin

× sin
20

20
N2

=
=
=
=

2,840
3,085
34,202
40,127

kg
kg
kg
kg

=
=
=
=

3,831
3,085
34,202
41,118

kg
kg
kg
kg

+

+

369,069 kg

profil

NTotal
A
NTotal

d2/4

Ambil :

N2

a

/

4

mm

Page 5

TUGAS AKHIR BENTANG 25 m
BAB III
DIMENSIONING
GORDING
Dimensioning Gording

cos
sin

20
20

=
=

Gaya angin
z1
z2

=
=

0,940
0,342

=
=

1,5 m
25 m

H =
h =

7m
5,250 m

65 kg/cm2

=
1,5
12,5

a
L

/ cos
/ cos

=
=

=
=
=

6m
240 Mpa
160 Mpa

Mutu Baut
Mutu Las

=
=

1,596 m
13,302 m

Asumsikan jarak gording =

1,400 m
==>

Maka banyak gording untuk bentang z 1 + z2
Asumsikan berat sendiri atap

=

Berat sendiri gording

S b .Y

=

×

q cos

1,596

4,00 =
q=

q total = ( 5,600

+

13,302 ) / 1,400 = 10,6

5,600 kg/m
q kg/m

+ q ) kg/m

11

buah

+

MX1

= q total × cos × L2 / 8
5,600 + q ) × cos
20 ×
= (
23,6803 + 4,2286 q ) kg m
= (

6,0 2 / 8

MY1

= q total × sin × L2 / 8
5,600 + q ) × sin
20 ×
= (
8,6189
= (
+ 1,5391 q ) kg m

6,0 2 / 8

S b .X
q s in

n=(

4,00 kg/m2

Dimensi Gording
A. Dimensi Gording Variasi Tanpa Ada Track Stang
1. Muatan Tetap
Berat sendiri atap
1,4
=

q

Jarak Portal ( )
Mutu Profil
Mutu Profil

Page 1

360 Mpa
360 Mpa

TUGAS AKHIR BENTANG 25 m

2. Muatan Angin
2a.
Angin Datang
qa =
65
kg/cm2
Koefisien =
0.02 × × 0.4
20
= 0,02 ×
qa datang
Koefisien
=
× Jarak Gording
×
0,000
=
× 1,4 × 65
0,000
kg/m
=
q d a ta n g

qa

0,4

= 0,000

MX2a

= qa datang × L2 / 8
= 0,000
× 6,0
kg m
= 0,0000

MY2a

=

S b .X

2 /8

0

S b .Y

2b.

Angin Pergi
qa =
65
kg/cm2
Koefisien =
-0,4
qa datang
Koefisien
=
× Jarak Gording
-0,400
=
× 1,4 × 65
-36,400
kg/m
=
q p e rg i

×

qa

MX2b

= qa datang × L2 / 8
= -36,400
× 6,0 2 / 8
kg m
= -163,8000

MY2b

=

S b .X

0

S b .Y

3. Muatan Tak Terduga
P

P = 100 kg

Sb.Y
Sb.X
P sin
P cos

MX3

= P × cos × / 4
cos
= 100
×
= 140,954 kg m

20

×

6,0

/4

MY3

= P × sin × / 4
sin
= 100
×
= 51,3030 kg m

20

×

6,0

/4

Kombinasi Momen
Akibat Muatan 1 + Muatan 2a (Angin Datang)
MX Total
23,6803
4,2286
=(
+
MY Total
8,6189
1,5391
=(
+
Akibat Muatan 1 + Muatan 2b (Angin Pergi)
MX Total
23,6803
4,2286
=(
+
MY Total
8,6189
1,5391
=(
+

q ) + ( 0,0000 )
q) +( 0 )

=(
=(

+
+

4,2286 q ) kg m
1,5391 q ) kg m

q ) + ( -163,800 )
q) +( 0 )

= ( -140,120 +
= ( 8,6189 +

4,2286 q ) kg m
1,5391 q ) kg m

=(
=(

164,634
59,9219

+
+

4,2286 q ) kg m
1,5391 q ) kg m

=(
=(

164,634
59,9219

+
+

4,2286 q ) kg m
1,5391 q ) kg m

Akibat Muatan 1 + Muatan 3 (Muatan Tak Terduga)
MX Total
23,6803
4,2286 q ) + ( 140,954 )
=(
+
MY Total
8,6189
1,5391 q ) + ( 51,3030 )
=(
+
Maka momen maksimum yang menentukan :
Dicoba profil Channel Lips
Data:
q
=
Wx
=
Wy
=
q total
=(

7,51 kg/m
44,27 cm3
12,26 cm3
5,600
+

MX Total
MY Total

C 150×65×20×3.2

7,510 ) =

Ix
Iy

=
=
F
=
13,110 kg/m

23,6803
8,6189

332 cm4
53,8 cm4
9,567 cm2

ix
iy
E

=
=
=

5,89 cm
2,37139 cm

2100000 kg/cm2

Page 2

TUGAS AKHIR BENTANG 25 m

Kontrol Tegangan
MX
MY
=
+
Terjadi
WX
WX
( 16463,4
+
=

profil

422,86
44,27

Kontrol Lendutan
5
qTotal × cos × L4
FX
=
384
E × Ix
5
0,131
cos
×
=
384
2100000
= 0,905 cm
FY

=
=
=

F

5
qTotal × cos × L4
384
E × Iy
5
0,131
cos
×
384
2100000
2,032 cm

=

Fizin

FX2 + FY2
=

F <

L
180

600
180

=

Fizin

0,905

=

..

=

×

7,5

)

+

( 5992,19

+

153,91 ×
7,5
)
12,26
1026,659 kg/cm2

1 P × cos × L3
48
E × Ix
20
× 600 4
+
×
332

1
48

100

20 ×
× cos
2100000 × 332

600 3

1 P × cos × L3
48
E × Iy
20
× 600 4
+
×
53,8

1
48

100

20 ×
× cos
2100000 × 53,8

600 3

1600 kg/cm2
1600 kg/cm2

..

+

+

+ 2,032 2

2

=

2,224 cm

3,333 cm

OK

B. Dimensi Gording Variasi Dengan Track Stang
Direncanakan gading-gading kap memiliki 3 medan ekonomis
G a d in g K a p

2,00 m

Ly

S b .Y
S b .X

2,00 m

Lx

T ra c k S ta n g

2,00 m
G a d in g K a p

1. Muatan Tetap
q total
= ( 5,600

+ q ) kg/m

MX1

= q total × cos × LX2 / 8
5,600
+ q) ×
cos
= (
23,6803
4,2286
= (
+

20 ×
q ) kg m

6,0 2

/8

MY1

= q total × sin × LY2 / 8
5,600
+ q) ×
sin
= (
0,9577
0,1710
= (
+

20 × (
q ) kg m

6,0 /

3

2. Muatan Angin
2a.
Angin Datang
=
MX2a
=
MY2a
2b.

Angin Pergi
=
MX2b
=
MY2b

0,0000 kg m
0 kg m
-163,8000 kg m
0 kg m

3. Muatan Tak Terduga
MX3
= P × cos × X / 4
cos
= 100
×
= 140,954 kg m
MY3

)2 / 8

= P × sin × Y / 4
sin
= 100
×
= 17,1010 kg m

20

×

6,0

20

×(

6,0 /

/4

3 )/4

Page 3

OK

TUGAS AKHIR BENTANG 25 m

Kombinasi Momen
Akibat Muatan 1 + Muatan 2a (Angin Datang)
MX Total
23,6803
4,2286
=(
+
MY Total
0,9577
0,1710
=(
+
Akibat Muatan 1 + Muatan 2b (Angin Pergi)
MX Total
23,6803
4,2286
=(
+
MY Total
0,9577
0,1710
=(
+

q ) + ( 0,0000 )
q) +( 0 )

=(
=(

+
+

4,2286 q ) kg m
0,1710 q ) kg m

q ) + ( -163,800 )
q) +( 0 )

= ( -140,120 +
= ( 0,9577 +

4,2286 q ) kg m
0,1710 q ) kg m

=(
=(

164,634
18,0587

+
+

4,2286 q ) kg m
0,1710 q ) kg m

=(
=(

164,634
18,0587

+
+

4,2286 q ) kg m
0,1710 q ) kg m

Akibat Muatan 1 + Muatan 3 (Muatan Tak Terduga)
MX Total
23,6803
4,2286 q ) + ( 140,954 )
=(
+
MY Total
0,9577
0,1710 q ) + ( 17,1010 )
=(
+
Maka momen maksimum yang menentukan :

MX Total
MY Total

Dicoba profil Channel Lips
C 125×50×20×2.3
Data:
q
4,51 kg/m
Ix
=
=
Wx
21,92 cm3
Iy
=
=
Wy
6,22 cm3
F
=
=
q total
5,600
4,510 ) =
10,110 kg/m
=(
+

Kontrol Tegangan
MX
MY
=
+
Terjadi
WX
WX
( 16463,4
+
=

=
=
=

F

422,86
21,92

FX2 + FY2
=

F <

×

4,5

1
48
20
×
×
137

)

( 1805,87

+

P × cos × LX3
E × Ix
600 4
1
+
48

+

5
1
qTotal × cos × LY4
P × cos × LY3
+
384
E × Iy
48
E × Iy
5
0,101
cos
20 × ( 600 / 3 )4
×
384
2100000
×
20,6
0,148 cm

=

Fizin

137 cm4
20,6 cm4
5,747 cm2

L
180

Fizin

2,027

=
600
180

=
..

ix
iy
E

4,88 cm
1,89 cm
2100000 kg/cm2

=

=
=

profil

Kontrol Lendutan
5
qTotal × cos × LX4
FX
=
384
E × Ix
5
0,101
cos
×
=
384
2100000
= 2,027 cm
FY

23,6803
0,9577

=

2

+ 0,148 2

=

+

+

17,10
4,5
×
)
6,22
1140,803 kg/cm2

100

20 ×
× cos
2100000 × 137

1
48

100

1600 kg/cm2
1600 kg/cm2

..

OK

600 3

20 × ( 600 /
× cos
2100000 × 20,6

3 )3

2,032 cm

3,333 cm

OK

Kesimpulan : Profil gording yang di pakai adalah Channel Lips
Y
t

X

h
Cx
d

Cy
b

Jumlah profil Channel Lips C yang diperlukan :

h
b
d
t
F
q
Wx
Wy
Ix
Iy

C 125×50×20×2.3
=
=
=
=
=
=
=
=
=
=

125
50
20
2,3
5,747
4,51
21,92
6,22
137
20,6
n =

mm
mm
mm
mm

cm2
kg/m
cm3
cm3
cm4
cm4

( Jumlah Lapangan Gording ) + 1

=

11

+ 1 =

12

buah

Page 4

10,6

TUGAS AKHIR BENTANG 25 m
BAB II
DIMENSI BATANG TARIK (TRACK STANG)

2

m

2

m

2

m
b

a

a = 1,400
m
b = 0,898
m
Berat sendiri atap
Jarak batang tarik
Berat sendiri gording (q)
Beban tak terduga

a

=
=
=
=

4,00
2
4,51
100

Beban yang bekerja
Atap
A. Tipe 1 =
Gording
Beban Tak Terduga
A. Tipe 2 =

Atap
Gording
Beban Tak Terduga

Beban yang dipikul oleh track stang :
NTotal
10
= N1
+
Dibutuhkan

:

Terjadi

d
d
6

a

a

kg/m2
m
kg/m
kg
= 2,00
= 2,00
= 100

×
×
×

0,9
4,51
sin

×
×

= 2,00
= 2,00
= 100

×
×
×

1,4
4,51
sin

×
×

=

1600

kg/cm2

1600

kg/cm2

NTotal
1600 /4
450,922
1600
×
0,599
cm

d

d =

a

20

20

4,00
sin

× sin
20

20
N1

4,00
sin

× sin
20

20
N2

=
=
=
=

2,458
3,085
34,202
39,745

kg
kg
kg
kg

=
=
=
=

3,831
3,085
34,202
41,118

kg
kg
kg
kg

+

+

450,922 kg

profil

NTotal
A
NTotal

d2/4

Ambil :

N2

a

/

4

mm

Page 5

TUGAS AKHIR BENTANG 30 m
BAB III
DIMENSIONING
30  GORDING

20
20
20

 




G 
1
2

=
=
=

1,5
15,0

L

=
=

1,5 
30 

7
5,250 

H =
 =

J  P   ()
M P 

65 
2

=



=
=

0,364
0,940
0,342

/
 =%
/
 =%

1,596 
15,963 

A

  &    %



6
240 M
160

M B 
M L

=
=

5,459554

=

1,400 
==>

M $     $   1 + 2
A

  $ 
  

=

B 
  

=

S b .Y



q cos

4,00 =
=

    = (

1,596

+

15,963 ) / 1,400 = 12,5 "

5,600 

5,600

 


+  ) 


13

$ 

+

M

=     
  2 / 8
5,600
+  ) 
20 
= (
23,6803
= (
+ 4,2286  )  

6,0 2 / 8

M

=     
   2 / 8
5,600
+  ) 

20 
= (
8,6189
= (
+ 1,5391  )  

6,0 2 / 8

S b .X
q s in

%(

4,00 
2

D
  
A. D
    
   !  # 
1. M    
B 
  
1,4
=

q

=
=

1
P'() *

360 M
360 M

TUGAS AKHIR BENTANG 30 m

2. M12324 Q4:E4
22L
A4:E4 R2324:
2
65
+, =
6:,?,@A
KC7DEFE74
J2826 GC89E4:
=
0,000
1,4 - 65
=
0,000
6:,?,@A - B2 / 8
= 0,000
- 6,0
6: ;
= 0,0000

M./J

=

S b .X

2 /8

0

S b .Y

2KL

A4:E4 M78:E
2
+, =
65
6:,?,@A
=
-0,400
1,4
=
-36,400
6:,?,@A - B2 / 8
= -36,400
= -163,8000
=

-

6,0 2 / 8
6: ;

0

S b .Y

3. M12324 526 57891:2
P

P = 100 kg

Sb.Y
Sb.X
P sin
P cos

M=l

= P - HCF N - m < P
HCF
= 100
140,954 6: ;
=

20

-

6,0

/4

M.l

= P - FE4 N - m < P
FE4
= 100
51,3030 6: ;
=

20

-

6,0

/4

KC;KE42FE iC;74
W A6EK23 i12324 j k i12324 g2 (A4:E4 R2324:)
Ma ^_?,`
23,6803
4,2286
=(
+
M] ^_?,`
8,6189
1,5391
=(
+
W A6EK23 i12324 j k i12324 gK (A4:E4 M78:E)
Ma ^_?,`
23,6803
4,2286
=(
+
M] ^_?,`
8,6189
1,5391
=(
+

0,0000
+) +(
+) +( 0 )

)

=(
=(

+
+

4,2286 + ) 6: ;
1,5391 + ) 6: ;

-163,800
+) +(
+) +( 0 )

)

= ( -140,120 +
= ( 8,6189 +

4,2286 + ) 6: ;
1,5391 + ) 6: ;

)
)

=(
=(

164,634
59,9219

+
+

4,2286 + ) 6: ;
1,5391 + ) 6: ;

=(
=(

164,634
59,9219

+
+

4,2286 + ) 6: ;
1,5391 + ) 6: ;

W A6EK23 i12324 j k i12324 h (M12324 526 57891:2)
Ma ^_?,`
23,6803
4,2286 + ) + (
=(
+
M] ^_?,`
8,6189
1,5391 + ) + (
=(
+

140,954
51,3030

M262 ;C;74 ;26FE;1; Z24: ;747431624 \
DEHCK2 b8CDEX cd2447X BEbF
+
D232\
=
Y[
YZ
+ 3C32X

=
=

=(

7,51 6: