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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

    -