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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

    = "!

    A

    B C

    D

    7 m

    2 m

    10 m

    P

    q

    C'

    3o

    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

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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 b

    0 a

    0 3a

    """."""

    a

    a

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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

    & 8= 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.+

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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.+

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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

    c

    c

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    0

    0.+ 3

    200

    0 c

    )0.+ 3c"00

    c

    c

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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 = $

    = D = 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

    c

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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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    d

    )0."425 c

    )0."425 3c

    202.0202

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

    "0".0"0"

    c

    d

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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

    c

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    d

    0 a

    0 3a

    0

    0

    0 3

    0 b)0."425 c

    )0."425 3c

    202.0202

    )0."425 d

    )0."425 3d

    "0".0"0"

    a

    c

    d

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    KONDISI BATAS

    [! = [K! ["!

    ;a =

    a = >A

    ; = 0

    = 1/2.q.l

    ;c = 0c = 1/2.q.l

    ;d = D?

    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

    c

    2

    2

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    d 3d d

    0 0 0

    0 0 0 30 0