tugas mektek v 2

33
7/23/2019 Tugas Mektek v 2 http://slidepdf.com/reader/full/tugas-mektek-v-2 1/33 Diketahui Struktur Portal dengan : P = 7 ton A = 0,1 cm q = 12 t/m E = 2.10 kg/cm = !00 cm tan "! = 7 co# "! = $%D = 7 $D = 1 7 $D α = "! A B C D 7 m 2 m 10 m P q C' 3 o α D C C' o o 2

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Page 1: Tugas Mektek v 2

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Diketahui Struktur Portal dengan :

P = 7 ton A = 0,1 cm

q = 12 t/m E = 2.10 kg/cm = !00 cm

tan "! = 7 co# "! =

$%D

= 7 $D =

17 $D

α = "!

A

B C

D

7 m

2 m

10 m

P

q

C'

3o

α

D

C

C'

o o

2

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0 0.7"07"07"07 222.2222222222 0 )0.7"07"07"07

$o# 270 Sin 270 0 0 0)Sin 270   $o# 270 0 0 0

0 0 1 0 0

0 0 $o# 270 Sin 270 0

0 0   )Sin 270   $o# 270 0

0 0 0 0 0

0 )1 0 0 01 0 0 0 0

0 0 1 0 0

0 0 0 )1 0

0 0 1 0 0

0 0 0 0 0

0 1 0 0 0

)1 0 0 0 0

0 0 1 0 1

0 0 0 )1 0

0 0 0 0 0

0 0 0 0 0

1 =

- g1 =   - 

1

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3 a 3a

0.001+" 0 0.7" 0 0

0 0.022 0 )0.022 0

0.7" 0 ""2.*+" 0 0

0 )0.022 0 0.022 0

0 0 0 0 0

0.7" 0 221."51 0 0

θ 

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7

$D

7

0.70710+7512* 5**"*"*4++

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""".""""""""""

00

0

0

0

1

00

0

0

0

1

0

0

0

0

0

1

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0.7"

0 3

221."51   θb

0 a

0 3a

"""."""

θa

θa

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Elemen 2

i = 6

  = $6 $

'0,1('200(0 0

  )'0,1('200(0

1000 1000

0

  12'200('!00( +'200('!00(

0

  )12'200('!00(

1000 1000 1000

0  +'200('!00( "'200('!00(

0  )+'200('!00(

1000 1000 1000

)'0,1('200(0 0

  '0,1('200(0

1000 1000

0  )12'200('!00( )+'200('!00(

0  12'200('!00(

1000 1000 1000

0  +'200('!00( 2'200('!00(

0  )+'200('!00(

1000 1000 1000

0.02 0 0 )0.02 0

0 0.0012 0.+ 0 )0.0012

0 0.+ "00 0 )0.+

)0.02 0 0 0.02 0

0 )0.0012 )0.+ 0 0.0012

& → 8α = 0

2=

3 3

3   3

2

2 2

2

2 2

o

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0 0 0 0 0

0.02 0 0 )0.02 0

0 0.0012 0.+ 0 )0.00120 0.+ "00 0 )0.+

)0.02 0 0 0.02 0

0 )0.0012 )0.+ 0 0.0012

0 0.+ 200 0 )0.+

1 0 0 0 0

0 1 0 0 00 0 1 0 0

0 0 0 1 0

0 0 0 0 1

0 0 0 0 0

3 c 3c

0.02 0 0 )0.02 00 0.0012 0.+ 0 )0.0012

0 0.+ "00 0 )0.+

)0.02 0 0 0.02 0

0 )0.0012 )0.+ 0 0.0012

0 0.+ 200 0 )0.+

θ 

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3 c 3c

0.02 0 0 )0.02 0

0 0.0012 0.+ 0 )0.0012

0 0.+ "00 0 )0.+

)0.02 0 0 0.02 0

0 )0.0012 )0.+ 0 0.00120 0.+ 200 0 )0.+

θ 

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01000000000 1000000

+'200('!00(

1000

2'200('!00(

1000

0

)+'200('!00(

1000

"'200('!00(

1000

0

0.+

200

0

)0.+

2

2

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1

0 0.02 0 0

0.+ 0 0.0012 0.+200 0 0.+ "00

0 )0.02 0 0

)0.+ 0 )0.0012 )0.+

"00 0 0.+ 200

0

00

0

0

1

0 0.+ 3

200

0 c

)0.+ 3c

"00

θc

θ 

θc

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0

0.+ 3

200

0 c

)0.+ 3c"00

θc

θ 

θc

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)0.02 0 0

0 )0.0012 0.+0 )0.+ 200

0.02 0 0

0 0.0012 )0.+

0 )0.+ "00

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Elemen 4

 9 9 9 9 9 9 9 

i = $

  = Dα = 315

 9 9 9 9 9 9 9 

'0,1('200( 0 0   )'0,1('200( 0**0 **0

0  12'200('!00( +'200('!00(

0  )12'200('!00(

**0 **0 **0

0  +'200('!00( "'200('!00(

0  )+'200('!00(

**0 **0 **0

)'0,1('200(

0 0

  '0,1('200(

0**0 **0

0  )12'200('!00( )+'200('!00(

0  12'200('!00(

**0 **0 **0

0  +'200('!00( 2'200('!00(

0  )+'200('!00(

**0 **0 **0

0.0202020202 0 0 )0.0202020202 0

0 0 00124+7422 0 +12152"40" 0 )0 00124+7422

- 4=

C

D

x

y

o

4 4

4   4

2

2 2

2

2 2

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0.70710+7512 0.70710+7512 0 0 0

)0.70710+7512 0.70710+7512 0 0 0

0 0 1 0 0

0 0 0 0.70710+7512 0.70710+7512

0 0 0 )0.70710+7512 0.70710+7512

0 0 0 0 0

0.0202020202 0 0 )0.0202020202 0

0 0.00124+7422 0.+12152"40" 0 )0.00124+7422

0 0.+12152"40" "0".0"0"0"0"0" 0 )0.+12152"40"

)0.0202020202 0 0 0.0202020202 0

0 )0.00124+7422 )0.+12152"40" 0 0.00124+7422

0 0.+12152"40" 202.0202020202 0 )0.+12152"40"

0.70710+7512 )0.70710+7512 0 0 0

0.70710+7512 0.70710+7512 0 0 0

0 0 1 0 0

0 0 0 0.70710+7512 )0.70710+7512

0 0 0 0.70710+7512 0.70710+7512

0 0 0 0 0

- g4 =   - 4

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c 3c d 3d

0.01072 )0.00*! 0."425 )0.01072 0.00*!

)0.00*! 0.01072 0."425 0.00*! )0.01072

0."425 0."425 "0".0"0" )0."425 )0."425

)0.01072 0.00*! )0."425 0.01072 )0.00*!0.00*! )0.01072 )0."425 )0.00*! 0.01072

0."425 0."425 202.0202 )0."425 )0."425

θc

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0

)+'200('!00(

**0

2'200('!00(

**0

0

)+'200('!00(

**0

"'200('!00(

**0

0 *702**000 *50100

)0 +12152"40"

2

2

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0

0

0

0

0

1

0 *702**000 *50100

)0.+12152"40"

202.0202020202

0

)0.+12152"40"

"0".0"0"0"0"0"

0 0.01"25"*5! 0.00057"!017 0."425754"5 )0.01"25"*5!

0 )0.01"25"*5! 0.00057"!017 0."425754"5 0.01"25"*5!

0 0 0.+12152"40" "0".0"0"0" 0

0 )0.01"25"*5! )0.00057"!017 )0."425754"5 0.01"25"*5!

0 0.01"25"*5! )0.00057"!017 )0."425754"5 )0.01"25"*5!

1 0 0 +12152"40" 202 020202 0

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θd

)0."425 c

)0."425 3c

202.0202

)0."425 d)0."425 3d

"0".0"0"

θc

θd

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)0.00057"!02 )0."425754"5

)0.00057"!02 )0."425754"5

)0.+12152"4 202.020202

0.00057"!02 )0."425754"5

0.00057"!02 )0."425754"5

0 +12152"4 "0" 0"0"0"

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a 3a a 3 c 3c d 3d

0.022 0 0 0 )0.022 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0 0 """.""" 0.7" 0 221."51 0 0 0 0 0

0 0 0.7" 0.021+" 0 0.7" )0.02 0 0 0 0

)0.022 0 0 0 0.0242 0.+ 0 )0.0012 0.+ 0 0

0 0 221."51 0.7" 0.+ 5"2.*+" 0 )0.+ 200 0 00 0 0 )0.02 0 0 0.04072 )0.00*! 0."425 )0.01072 0.00*!

0 0 0 0 )0.0012 )0.+ )0.00*! 0.011*2 )0.1+72 0.00*! )0.01072

0 0 0 0 0.+ 200 0."425 )0.1+72 50".0"0" )0."425 )0."425

0 0 0 0 0 0 )0.01072 0.00*! )0."425 0.01072 )0.00*!

0 0 0 0 0 0 0.00*! )0.01072 )0."425 )0.00*! 0.01072

0 0 0 0 0 0 0."425 0."425 202.0202 )0."425 )0."425

θ    θc

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θd

0 a

0 3a

0

0

0 3

0   θb)0."425 c

)0."425 3c

202.0202

)0."425 d

)0."425 3d

"0".0"0"

θa

θc

θd

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KONDISI BATAS

[! = [K! ["!

;a =

<a = A3

>a = >A

; = 0

< = )1/2 q.l

> = 1/2.q.l

;c = 0<c =   )1/2 q.l

>c = 1/2.q.l

;d = D?

<d = D3

>d = >D

a = 03a = 0

a = 0

= Ada

3 = Ada

= Ada

c = Ada

3c Ada

A

B C

P

#A$

#D

#A%

&A

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D

q

#D%

&D

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3 c 3c a 3a a

0 0.021+" 0 0.7" )0.02 0 0 0 0 0.7"

)1/2 q.l   0 0.0242 0.+ 0 )0.0012 0.+ )0.022 0 01/2 q.l 0.7" 0.+ 5"2.*+" 0 )0.+ 200 0 0 221."51

0 )0.02 0 0 0.04072 )0.00*! 0."425 0 0 0

1/2 q.l 0 )0.0012 )0.+ )0.00*! 0.011*2 )0.1+72 0 0 0

)1/2 q.l   = 0 )0.+ 200 0."425 )0.1+72 50".0"0" 0 0 0

A? 0 0 0 0 0 0.022 0 0

A3 0 0 0 0 0 0 0 0 0

>A 0.7" 0 221."51 0 0 0 0 0 """."""

D? 0 0 0 )0.01072 0.00*! )0."425 0 0 0

D3 0 0 0 0.00*! )0.01072 )0."425 0 0 0

>D 0 0 0 0."425 0."425 202.0202 0 0 0

θ    θc

2

2

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d 3d   θd

0 0 0

0 0 0 30 0 0   θb

)0.01072 0.00*! )0."425 c

0.00*! )0.01072 )0."425 3c

)0."425 )0."425 202.0202

0 0 0 a

0 0 0 3a

0 0 0

)0.00*! 0.01072 )0."425 d

)0.00*! 0.01072 )0."425 3d

)0."425 )0."425 "0".0"0"

θc

θa

θd