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BAN NO.3 CONTOH SOAL  Kontr uksi Bergoya ng I I 1). Hitung Nilai K EI 15 2 EI 12  EI 10 2). Menentukan Momen Frimer (MF) 12 X 9 X 6  2 15  2 -12  X 9  2 X 6 15  2 24 X 12 8 = -  = 0 3). Tentukan nilai R ( ) 15 10 30 30 30 = 17.28 = -25.92 MF DC = = 3 R R BC R CD = MF CD X = 0 = MF AB = 2 R 3 K BC = x 30 R AB  = x 30 = K CB  = SOLUSI 5 K BD =  K DB  = X = 36 Kip ft Kip ft K AB =  K BA  = X = 2 Kip ft MF BC = - MF CB  = = MF BA SLOFE DEFLECTION 2I  10 M 24 k  A B C D 6 M 6 M 12 k 6 M 9 M

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    BAN NO.3

    CONTOH SOAL Kontr uksi Bergoyang

    I

    I

    1). Hitung Nilai K

    EI

    15

    2 EI

    12

    EI

    10

    2). Menentukan Momen Frimer (MF)

    12 X 9 X 6 2

    15 2

    -12 X 9 2 X 6

    15 2

    24 X 12

    8

    = - = 0

    3). Tentukan nilai R ( )

    15

    10

    30

    30

    30

    = 17.28

    = -25.92

    MFDC

    =

    =

    3 R

    RBC

    RCD

    =

    MFCD

    X =

    0

    =

    MFAB =

    2 R

    3

    KBC =

    x 30

    RAB = x 30

    =

    KCB =

    SOLUSI

    5

    KBD = KDB = X =

    36 Kip ft

    Kip ft

    KAB = KBA = X = 2

    Kip ft

    MFBC = - MFCB = =

    MFBA

    SLOFE DEFLECTION

    2I

    10 M

    24 k

    A

    B C

    D

    6 M 6 M

    12 k

    6 M

    9 M

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    Masukkan kembali nilai yang didapat kedalam rumus Slope Deflection

    = + K ( -2 A - B + 2 R )

    = + 2 { ( -2 x ) - ( + ( 2 x ) }

    = + 2 ( + )

    = + 2 ( )

    = +

    =

    = + K ( -2 B - A + 2 R )

    = + 2 { ( -2 x ) - ( ) + 2 x ) }

    = + 2 ( + )

    = + 2 ( )

    = +

    =

    = + K ( -2 B - C + 0 R )

    = + 5 { ( -2 x ) - ( ) + 0 x ) }

    = + 5 ( + )

    = + 5 ( )

    = +

    =

    = + K ( -2 C - B + 0 R )

    = + 5 { ( -2 x ) - ( ) + 0 x ) }

    = + 5 ( + )

    = + 5 ( )

    = +

    =

    = + K ( -2 C - D + 3 R )

    = + 3 { ( -2 x ) - ( ) + 3 x ) }

    = + 3 ( + )= + 3 ( )

    = +

    =

    = + K ( -2 D - C + 3 R )

    = + 3 { ( -2 x ) - ( ) + 3 x ) }

    = + 3 ( + )

    = + 3 ( )

    = +

    =

    -MFDC

    57.311

    27.28

    19.104

    0.0 0

    0.00

    0.0 -54.55

    0.0 0.00

    57.311

    27.275 2.76

    -2.76

    -1.99

    19.104

    38.207

    19.104

    38.207

    1.99

    73.545

    -36 -5.521

    2.7604

    19.104

    0

    19.104

    0

    19.104

    1.99

    -27.28

    -25.92 -3.976

    -25.92

    -7.51

    -36 2.7604

    -36

    MDC

    17.28 -8.64

    17.28 -17.28

    0.00

    -25.92

    0.0 -5.521

    0.0

    -25.92 23.603

    -2.32

    36

    17.28 22.43

    1.9881

    17.28 -44.86 -1.99

    2.76

    36 -3.976 -2.76

    MCD MFCD

    MBC MFBC

    1.9881 22.43

    -22.43

    MCB -MFCB

    36 -6.74

    36

    24.51

    73.54

    0.0

    MAB MFAB

    2.32

    MBA -MFBA

    -33.68

    11.80

    -36 -37.54

    -73.54

    0.0

    0.0

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    8). Lakukaan pemotongan pada masing-masing titik ( Free body )

    B 2I C

    I

    I

    a). potongan A & B

    Kf

    HB = Kip

    HA = Kip

    1. Reaksi perletakan

    = 0

    - x 15 + P x 9 + = 0

    - 15 HB + 12 x 9 + = 0- 15 HB + + = 0

    - 15 HB + = 0

    = / -15

    = Kip ( )

    = 0

    HA x 15 - P x 6 + = 0

    15 HA - 12 x 6 + = 0

    15 HA - +

    15 HA = 0

    = / 15

    = Kip ( )

    2). Momen dan Lintang

    = x X = x X - P ( X - 9 )

    = X = X - X +

    = X +

    = =

    73.542.32

    4.65

    2.32

    7.35

    69.7

    4.65

    2.32

    0

    HA

    HB

    0

    12

    2.32

    73.54

    -7.35 108

    -7.35

    108 2.32

    110.3

    2.32

    2.32

    72 2.32

    -110.3

    4.65

    -69.7

    HB

    Mx 4.65

    Interval 0 x 9

    Mx

    108

    Interval 9 x 15

    DxDx 4.65

    2.32

    0

    4.65

    7.35

    4.65

    RHA

    RHA

    RHB

    RHB

    D

    A

    24 k

    6 6

    12 k

    6 ft

    9 ft

    B

    C

    10 ft

    12 k

    6 ft

    9 ft

    A

    B

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    Tabel Momen dan Lintang pada potongan A & B

    b. Potongan B & C

    24 K

    B C

    = K = K

    1. Reaksi perletakan

    = 0- x 12 + P x 6 + - = 0

    - 12 RC + 24 x 6 + - = 0

    - 12 RC + + - = 0

    - 12 RC + = 0

    = / -12

    = K ( )

    = 0

    RB x 12 - P x 6 - + =

    12 RB - 24 x 6 - + = 0

    12 RB - - + = 0

    12 RB = 0

    = /

    = K ( )

    2. Momen dan Lintang

    = x X - =

    = X -

    73.54

    73.54

    6

    2.32

    2.32

    2.32

    Nilai Momen

    Kip ft

    41.81

    Kip ft

    23.23

    6.06

    6

    Nilai LintangX Rumus Momen Rumus Lintang

    0 0.00

    9

    Kip

    Kip ft

    Kip

    2 9.29 Kip ft 4.65 Kip

    1

    Kip ft 4.65 Kip

    4.65

    13.94

    Kip ft

    Kip ft 4.65

    37.16 Kip ft 4.65

    7 32.52

    4.65

    4.65

    4 18.58

    Kip

    Kip

    Kip

    4.65

    4.65

    4.65

    Kip

    6 27.87 Kip ft

    13 12.39 Kip ft

    9 41.81 Kip ft

    8

    10

    12

    Kip ft

    Kip ft

    27.10

    4.65

    Kip

    Kip ft

    Kip

    Kip ft Kip

    Kip ft

    Kip

    -7.35

    Kip

    -7.35

    -2.32

    Kip

    Kip ft Kip

    -7.35

    11

    14

    3

    5

    -7.35 Kip

    -7.35

    -7.35

    Kip

    -7.35

    -72.8

    Interval 0 x 6

    RC 73.54

    2.32

    15

    6.06

    Dx2.32

    17.94

    2.32

    72.77 12

    MC

    6.06 2.32

    Mx RBV

    2.32 73.54

    17.94RBV 6.06

    RCV

    RBV

    73.54

    2.32 73.54

    144

    RCV

    73.54

    2I

    34.46

    19.75

    5.04

    MB

    RCV -215.23

    215.23

    144

    RBV

    7,35 X + 108 7,35

    4,65 X 4,65

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    = x X - P ( X - 6 ) -

    = X - X + -

    = X +

    =

    Tabel Momen dan Lintang pada potongan A & B

    C). Potongan C & D

    = K

    = K

    1. Reaksi perletakan

    = 0

    x 10 - = 0

    = / 10

    = kip ( )

    = 0

    - HD x 10 - = 0

    HD = / -10

    HD = kip ( )

    2). Momen dan Lintang

    = x X

    = X

    =

    -7.35

    Dx 7.35

    7.35

    Interval 0 x 10

    Mx 7.35

    73.5

    Hc

    Hc 7.35

    73.5

    HD

    HC

    Hc

    73.5

    73.5

    0

    73.5

    Interval 6 x 12

    Mx RBV

    6.06 24 144

    0

    1

    Dx -17.9

    X Rumus Momen

    Kip ft 6.06

    3.75 Kip ft 6.06

    -17.9 141.68

    2 9.81 Kip ft 6.06

    Kip

    Nilai Momen Nilai Lintang

    Kip-2.32

    4 21.94 Kip ft 6.06

    Kip

    3 15.88 Kip ft 6.06 Kip

    6 34.07 Kip ft 6.06

    Kip

    5 28.00 Kip ft 6.06 Kip

    7 16.13

    8 -1.80

    -17.94 Kip

    Kip

    Kip

    Kip ft -17.94

    11 -55.61 Kip ft

    Kip

    12 -73.54

    10

    Kip ft -17.94

    6

    Kip ft -17.94

    9 -19.74

    Kip ft -17.94

    -37.67

    Kip ft

    Kip

    Kip ft -17.94 Kip

    Kip-17.94

    34.07

    Kip

    2.32

    2.32

    Rumus Lintang

    7.35

    Hc 7.35

    Hc

    6,06 X - 2,32 6,06

    -17,9X + 141,68 -17,9

    C

    D

    I 10 ft

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    Tabel Momen dan Lintang pada potongan A & B

    GAMBAR MOMEN, LINTANG DAN NORMAL

    Kip ft

    Kip ft

    Kip ft

    Kip ft

    0

    0

    Gambar Momen

    -2.32

    10

    9

    1

    X

    Kip ft 7.35

    Nilai Momen Nilai Lintang

    Kip

    Kip73.54

    Kip

    66.19 Kip ft 7.35 Kip

    8 58.84 Kip ft 7.35

    Kip

    Kip7 51.48 Kip ft 7.35

    6 44.13 Kip ft 7.35

    5 36.77 Kip ft

    3 22.06 Kip ft

    14.71 Kip ft 7.35

    7.35

    2

    Rumus Momen Rumus Lintang

    0

    7.35 Kip

    4

    Kip ft 7.35 Kip

    Kip ft 7.35

    Kip

    Kip

    Kip

    0.00

    73.54

    34.07

    73.54

    7.35

    29.42 Kip ft 7.35

    41.81

    -7,35 X -7,35

    A

    B

    C

    D

    - 2,32 Kip ft

    (+

    (+

    (-)

    (-)

    (+

    (-)

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    kip

    7.35 kip

    4.65 kip -7.35Kip

    0 7.35 kip

    kip

    0

    Gambar Lintang

    Kip

    kip

    Gambar Normal

    6.06

    17.94

    6.06

    -17.94

    A

    B

    C

    D

    (+

    (+

    (-)(-) (-)

    A

    B C

    D

    (-)

    -

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    Detail Asumsi Pembebanan

    ASUMSI PEMBEBANAN

    q1 - Beban Mati

    Balok Ukuran 30 x 30 cm = x x =

    q1 = x = 0.353 T/1.2 0.294

    SLOPE DEFLECTION

    SO US

    0.35 0.35 2.4

    4 M

    q1

    A B

    C

    D

    E

    4.5 M 4.5 M

    EI EI

    0.01 M Keramik

    0.02 M Spesi K

    0.12 M Plat Lan

    0.35 x 0.35 M B

    2.25 M

    2.25 M

    EI EI

    q2

    2.25 M

    4.5 M

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    q2 - Beban Hidup + Beban Mati

    - Beban Hidup

    Untuk Ruang Pertemuan =

    Wu1 = x =

    - Beban Mati

    ~ Plat Lantai = x = T/m2

    ~ Spesi Keramik = x = T/m2

    ~ Keramik = x = /m +T/m

    Wu2 = x =

    Wu = Wu1 + Wu2 =

    PENYELESAIAN

    Dari penyelesaian diatas dapat saya gambarkan sebagai berikut :

    q2 = T/m' q2 = Wu x

    =

    =

    q1 = T/m'

    1). Menentukan Momen Frimer (MF)

    0.353

    2.756

    1.225

    1.2 0.354 0.425

    2.756

    2 0.021 0.042

    1 0.024 0.024

    0.5 0.8 T/

    T/

    1.225 T/m

    0.354

    500 Kg/m

    0.12 2.4 0.288

    1.6

    4 M

    A B

    C

    D

    E

    4.5 M 4.5 M

    EI EI

    EI EI

    2.25 M

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    1 5

    12 96

    x 2 x

    = +

    = TM

    1 5

    12 96

    x 2 x

    = +

    = TM

    2). Rumus Slope Deflection

    MAB = 1 EI x B - MBD = x (

    = EI B - = EI B

    MBA = 1 EI x 2 B + MDB = x (

    4.5

    = EI B + = EI D

    MBC = 1 EI x 2 B MDE = 1 EI x 2 D

    4 4

    = EI B = EI D

    MCB = 1 EI x B MED = 1 EI x D

    = EI B = EI D

    3). Joint Condition

    MBA + MBC + MBD = 0

    0.5 0.5

    4 4

    0.25 0.25

    3.502 1 EI

    4.5

    0.44 3.502 0.44

    3.502 1 EI

    0.22 3.502 0.44

    2.

    9

    0.5954 2.91

    4.5 4.5

    +

    5

    3.502

    + qL2

    =

    0.353 4.5

    12

    3.502

    - MFDB = MFBD = qL2

    qL2

    +

    5 2.

    9=

    0.353 4.5

    12

    0.5954 2.91

    = qL2- MFAB = MFBA +

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    = TM

    MBD = x + x -

    = - -

    = TM

    MDB = x + x +

    = + +

    = TM

    MDE = x

    = TM

    MED = x

    = TM

    6). Free Body

    = T/m1

    TM TM TM

    = /m1

    M

    TM

    4.5 4.

    0.308

    -3.85

    -0.963

    3.365 3.776 4.084

    0.3528

    2.756

    -1.712 0.14 3.50

    5.351

    0.5 -3.85

    -1.926

    0.25

    0.62 3.502

    0.22 -3.85 3.502

    -4.084

    0.44 -3.85 0.22

    0.274 0.86 3.50

    0.154

    0.44 0.62

    q1

    q2

    A B q1

    B

    B

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    RAV = - = T

    -

    V = 0RAV + RBV = R1 + R2

    + = +=

    b). Momen dan Lintang

    2. Titik potongan A dan B

    = T/m

    TM TM

    = T/m1

    T T

    M M

    M

    ~ Menghitung momen dari titik A ke titik BR1 =

    TM = T/m =

    =

    = T/m

    RAV = T R2 =

    M

    = X =

    ==

    ~ Bidang MomenMx = x X - - R 1 x - R2 (

    Interval 0 X 2,25

    RAV 3.365 X

    2

    0.3528

    X

    2.25q2' 2.76

    2.25

    3.365 2.756

    x3.803 q2'

    =2.25 2.76

    3.803 RBV= 3.985

    4.5

    3.365 3.776

    0.3528

    17.112

    2.25 2.25

    7.788 7.788

    2.756

    RAV=

    3.803

    4.5

    3.803 3.985 1.59 6.201

    q1

    q2

    A

    q1

    q2

    A B

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    = X - - X2

    - X2

    (

    = X - X2

    - X3

    -

    ~ Bidang Lintang

    Dx = - X - X2

    ~ Menghitung momen dari titik B ke titik A

    TM

    RBV = T

    M

    ~ Bidang Momen

    Mx = - x -X - + R 1 x + R2

    = X - - X + X (

    = X - X - X -

    ~ Bidang Lintang Dx = - f' (Mx) / Dx

    Dx = + X + X2

    3. Titik potongan B dan C

    2.25

    X Rumus Momen Rumus Lintang

    0

    -X

    3.776

    -3.985 0.3528 0.612

    2

    3.985 0.1764 0.204

    x 3.985

    2

    3.985 3.776 0.353 0.612

    Interval 0 X 2,25

    RBV 3.776

    2.25

    2.25

    3.776

    0

    3.803 0.3528 0.612

    X Rumus Momen Rumus Lintang

    0.1764 0.204

    3.803 3.365 0.353 0.612

    3.365

    2

    3.803

    3.803 X - 0.1764 X2 - 0.204 X3- 3.365 3.803 - 0.3528 X- 0.612 X2

    q1

    q2

    A

    3.985 X - 0.1764 X2 - 0.204 X3- 3.776 - 3.985 + 0.3528 X+ 0.612 X2

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    T

    TM

    4 M

    TM

    T

    a). Reaksi Perletakan

    = 0- x 4 + + = 0

    - 4 + = 0

    - =

    -

    = 0

    - x 4 + + = 0

    - 4 + = 0

    = T

    b). Momen dan Lintang

    T

    TM

    T

    4 M

    T

    TM

    T

    7.598

    0.308

    0.116

    0.116

    0.154

    7.598

    0.116

    -4

    0.462 0.116

    4

    0.462

    = -0.462

    MC

    0.308 0.154

    MB0.154 0.308

    0.462

    =

    7.598

    0.308

    0.154

    7.598

    B

    C

    RCH

    RCH

    RCH

    B

    C

    RCH

    RBH

    RBH

    RBH

    RCH

    RBH

    RBH

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    - RDV = -

    RDV = - = T

    -

    MD = 0

    RBV x - R1 x - R2 x -RBV - x - x -

    RBV - - - + = 0

    RBV - = 0

    - RBV = -

    RBV = - = T

    -

    V = 0R

    BV

    + RDV

    = R1

    + R2

    + = +

    =

    b). Momen dan Lintang

    = T/m

    TM TM

    = T/m

    T T

    M M

    M

    R1TM = T/m

    1

    = T/m1

    RBV = T R23.612 q2'

    4.084 2.756

    X

    0.3528

    x

    3.612 RDV= 4.176

    4.5

    16.256 3.612

    4.5

    2.25 2.25

    7.788 7.788

    2.756

    4.084

    RBV =

    3.612 4.176 1.59 6.201

    5.351

    0.3528

    5.351

    4.5 16.256

    4.5 16.256

    4.5 3.572 13.95 4.084

    4.0844.5 1.59 2.25 6.201 2.25 4.

    18.791 4.176

    4.5

    4.5 2.25 2.25

    4.5 18.791

    q1

    q2

    B

    q1

    q2

    B D

    q2'

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    M= X

    ~ Bidang Momen

    Mx = x X - - R 1 x - R2

    = X - - X2

    - X2

    = X - X2 - X3 -

    ~ Bidang Lintang

    Dx = - X - X2

    ~ Menghitung momen dari titik B ke titik D

    TM

    RDV = T

    M

    ~ Bidang MomenMx = - x -X - + R 1 x + R2

    = X - - X2

    + X2

    (

    2

    4.176 5.351 0.353 0.612

    Interval 0 X 2,25

    RDV 5.351 -X

    2.25

    2.25

    5.351

    x 4.176

    0

    X Rumus Momen Rumus Lintang

    0.353 0.612

    2

    3.612 0.1764 0.204 4.084

    Interval 0 X 2,25

    3.612 0.3528 0.612

    2

    3.612 4.084

    RBV 4.084 X

    2.25q2' 2.8

    2.25

    2.8 2.25

    3.612 X - 0.1764 X2 - 0.204 X3- 4.084 3.612 - 0.3528 X- 0.612 X2

    q1

    q2

    D

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    = X - X - X -

    ~ Bidang Lintang Dx = - f' (Mx) / Dx

    Dx = + X + X2

    5. Titik potongan B dan C

    T

    TM

    4 M

    TM

    T

    a). Reaksi Perletakan

    = 0

    x 4 - - = 04 Rc - = 0

    = T

    = 0

    x 4 - - = 0

    4 - = 0

    2.890 0.722

    4

    2.890

    ME

    1.926 0.963

    MD

    0.963 1.9262.890

    =

    4.176

    1.926

    0.963

    4.176

    2.25

    X Rumus Momen Rumus Lintang

    0

    5.351

    -4.176 0.3528 0.612

    2

    4.176 0.1764 0.204

    4.176 X - 0.3528 X2 - 0.612 X3- 5.351 - 4.176 - 0.3528 X- 0.612 X2

    D

    E

    REH

    RDH

    REH

    RDH

    REH

    RDH

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    = T

    b). Momen dan Lintang

    TM

    TMT

    4 M

    T

    TMTM

    ~ Bidang Momen

    Mx = x X -

    = X -

    ~ Bidang Lintang

    Dx =

    Rumus Lintang

    TM

    TM

    TM

    9) Gambar

    4 0.963 0.722

    2.25 -0.301 0.722

    1.926

    0.722 1.926

    Nilai Momen Nilai Lintan

    0 -1.926 0.722

    0.722

    X Rumus Momen

    4.176

    1.9260.722

    0.722

    0.9634.176

    Interval 0 X 4

    0.722

    4=

    2.890

    0.722 X - 1.926

    D

    E

    0.722

    RDH

    RDH

    REH

    RDH

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    TM TM

    TM

    TM

    TM

    TM

    TM

    Gambar Momen

    T

    T

    T T

    T

    T

    T

    Gambar Lintang

    -0.282

    -0.116

    -3.985

    0.826

    1.973

    -0.154 0.

    3.612

    -0.091 -0.116

    3.803

    -3.365 -4.084

    -3.776

    0.308(+) (+)

    (-) (-)(-)

    (-)

    (+)

    (-)

    (-)

    (+)

    A

    B

    C

    A B

    C

    (+)

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    T

    Gambar Normal

    7.598

    (-)

    A B

    C

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    /m1

    0.294

    Garis leleh

    rmik

    tai

    alok

    q1

    q2

    4.5 M

    4.5 M

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    t

    x

    T/m'

    2.25

    0

    2

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    x 2

    x 2

    D

    2 B + D ) -

    + EI D -

    2 D + B ) +

    + EI B +

    3.502

    3.502

    0.22 3.502

    0.22 3.502

    56 4.5

    6

    56 4.5

    6

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    EI D - ) = 0

    .. Pers ( 1 )

    .. Pers ( 2 )

    3.502

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    4 M

    TM

    L

    x = T

    - = 0

    - = 0

    + = 0

    + = 03.77665

    3.776

    76

    4.5 6.201

    3.365

    3.365

    5

    0.963

    C

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    x

    x

    X

    1 x al x t

    20.5 x X x X

    X x XX

    X - 2 X )

    3

    2.25

    0.6120.5 1.225

    0.3528

    2.76

    0.3528 X

    q1 X

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    1 X )

    3

    ( -X + 2 X )3

    -1 X )

    3

    1.973 TM -0.091

    -3.985 TTM

    T

    Nilai Momen Nilai Lintang

    -3.776

    1.973 TM -0.091 T

    Nilai Momen Nilai Lintang

    -3.365 TM 3.803 T

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    x L

    x = T

    - = 0

    - = 04.08451

    4.5

    4.084

    4.5

    6 6.201

    L

    g

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    + = 0+ = 0

    = x

    = x

    = X

    = 1 x al x t

    0.3528

    0.3528 X

    q1 X

    5.35184 5.351

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    2

    = 0.5 x X x X

    = X x X

    = X

    ( X + 2 X )

    3

    ( 1 X )

    3

    ( -X + 2 X )

    3

    -1 X )

    T

    T0.826 TM -0.282

    3.612

    Nilai Lintang

    -4.084 TM

    Nilai Momen

    0.5 1.225

    0.612

    2.8

    2.25

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    3

    ( )

    0.826 TM -0.282

    -4.176 TTM

    T

    Nilai Momen Nilai Lintang

    -5.351

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    ( )

    TM-5.351

    g

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    TM

    TM

    T

    T

    TM

    0.722

    0.722

    -4.176

    63

    -1.926

    (+)

    (-)

    (-)

    (+)

    (-)

    D

    E

    D

    E

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    T

    11.774

    3.803

    15.576

    7.788

    7.788

    15.576

    4.176

    (-)

    D

    E