Download pdf - Statis Momen

Transcript
  • 8/17/2019 Statis Momen

    1/160

    step 1

    step 2 MOMEN INERSIA. I Rumus Umum :

    = 12274.3

    step 3 MOMEN LAWAN, W Rumus Umum :

    = 1523.71 cm³

    = 724.385 cm³

    step 4 TEGANGAN :

    cm4

    y1

    y2

    5

    25

    5

    20

    z1

    z2

    yb = 16,94

    ya = 8,06

    )Ukuran daamcm!

    "#

    ∫ =   dA I    .2

     ρ 

    2

    2

    3

    22

    2

    1

    3

    11  ...12

    1...

    12

    1 z  AII hb z  AI hb Ix

    tot   +++=

     y

     I W    =

    a ATAS   y

     Ix

    W   =

    b

     BAWAH  y

     IxW    =

  • 8/17/2019 Statis Momen

    2/160

    y1

    z$3

    y2

    ya = 8,06

    yb = 16,94

    z$2

    z$1

    20

    5

    25

    5

    "#

    )Ukuran daamcm!

  • 8/17/2019 Statis Momen

    3/160

    1) TEGANGAN GESER, t  Rumus Umum :

    a!. %aya$ )&'ns!

    1200 ) 25 ( 5 ( 5.56 ! = 2.7157 k*cm+

    25 ( 12274.3056

    b!. ,adan )-'b!

    1200 ) 5 ( 20 ( 6.94 ! = 13.5785 k*cm+

    5 ( 12274.3056

    1200 ) 5 ( ( 8.47 ! = 14.0349 k*cm+

    5 ( 12274.3056

    2) TEGANGAN NORMAL, Rumus Umum :

    = / = = 8.89k*cm+

    225

    3) TEGANGAN LENTUR, Rumus Umum :

    a! . %'ra as == m'n n'a b'rar s'ra aas 'rark )!

    = 720000 = 472.532 k*cm+ )!

    1523.7

    b! . %'ra ,aa == m'n n'a b'rar s'ra aas 'r'kan )!

    = 720000 = 993.946 k*cm+ )!

    724.39

    Ä ;ada ,aas nara %aya$ < ,adan

    τa =

    τb =

    Ä ;ada ars /'ra kba ,aan ,adan %'n yb

    τc =

    5

     I b

    S  D

    .

    .

    =τ  

     N σ  

     A

     P =σ   

     N σ 

     M  σ   W  

     M =σ   

     ATAS 

     I  I  M 

    W  M 

    =σ  

     BAWAH 

     I  I 

     M W 

     M −

    =σ  

  • 8/17/2019 Statis Momen

    4/160

    ambar >aram

     ?kk @rdna >aram

    >aram ?'. 's'r sca'

    2.7157 100 0.02715700113.5785 100 0.135785007

    14.0349 100 0.140348892

    >aram ?'. /rma sca'

    8.88889 100 0.088888889

    8.88889 100 0.088888889

    >aram ?'. #'nur sca'

    472.532 10000 0.047253182

    993.946 10000 0.099394625

    ya =8,06

    yb = 16,94

    z$2

    z$1

    20

    5

    25

    5

    y1

    z$3

    y2

  • 8/17/2019 Statis Momen

    5/160

    Parameter 

    b1 = 25 cm

    h1 = 5 cm

    b2 = 5 cm

    h2 = 20 cm

    STATIS MOMEN KE TEPI ATAS, (ya)

    C = 25 ( 5 = 125 cm+

    CC = 5 ( 20 = 100 cm+

    y1 = 5 * 2 = 2.5 cm

    y2 = 20 5 = 15 cm

    2

    ya = C.y1 CC.y = 8.05556 cmC CC

    yb = )205! ya = 16.9444 cm

    z1 = ya y1 = 5.55556 cm

    z2 = y2 ya = 6.94444 cm

  • 8/17/2019 Statis Momen

    6/160

    z$1 = ya y1 = 5.55556 cm

    z$2 = y2 ya = 6.94444 cm

    z$3 = yb*2 = 8.47222 cm

    b3 = 5 cm

    h3 = yb cm

    = 16.9 cm

  • 8/17/2019 Statis Momen

    7/160

    >k'au : > = 1.2

    = 1200 k

    >k'au : / = 2

    2000 k

    =

    = C CC

    = 225 cm+

    >k'au : = 7.2 .m

    720000 k.cm

    = 1523.71 cm³

    = 724.385 cm³

    a

    b1.

    1  b

    2.

    2

    C C

    -?%

    -,-D

  • 8/17/2019 Statis Momen

    8/160 ?A ?A. A%AR

    8

    14

    13,5792,716

  • 8/17/2019 Statis Momen

    9/160

    C = 600 ( 200 = 120000 mm2

    CC = 200 ( 500 = 100000 mm2

    y1 = 200 * 2 = 100 cm

    y2 = 500 200 = 450 cm

    2

    ya = C.y1 CC.y2 = 259.091 cm

    C CC

    yb = )205! ya = 440.909 cm

     

    600

    5010 0 1 00 1 00 1 00 1 00

    50

    50

    100

    50

    200

    50100

      50

    50

    150

    250

    350

    450

    550

    650

  • 8/17/2019 Statis Momen

    10/160

  • 8/17/2019 Statis Momen

    11/160

  • 8/17/2019 Statis Momen

    12/160 ?A. #A/?UR ?A. /BR#

    993,946

    472,5328,889

    14

    3,579

  • 8/17/2019 Statis Momen

    13/160

  • 8/17/2019 Statis Momen

    14/160

  • 8/17/2019 Statis Momen

    15/160

  • 8/17/2019 Statis Momen

    16/160

  • 8/17/2019 Statis Momen

    17/160

    b = 250 fc' = 25 N/mm2

    h = 500 fy = 400 N/mm2

    d' = 50 D = 19 mm

    As tul = 2!"52# mm2

    d = h $ d'

    d = 450 As = 50"5%2As' = 50"5%2

    d $ h/2 = 200

    d $ d' = 400

    0"5 & fc' & h & b & d $ h/2( ) As' & fy & d $ d'( %%#,!4!,#9!"#5 200"00

    0"5 & fc' & h & b ) As ) As'( & fy !!!%#1"9%#%#55

    b = 250 fc' = 25 N/mm2

    h = %00 fy = 400 N/mm2

    d' = 50 D = 19 mm

    As tul = 2!"52# mm2

    d = h $ d'

    d = 550 As = 50"5%2As' = 50"5%2

    d $ h/2 = 250

    d $ d' = 500

    0"5 & fc' & h & b & d $ h/2( ) As' & fy & d $ d'( 9%%,992,242"19 250"00

    0"5 & fc' & h & b ) As ) As'( & fy !%#9%"9%#%#55

  • 8/17/2019 Statis Momen

    18/160

    b = 250 fc' = 25 N/mm2

    h = 500 fy = 400 N/mm2

    d' = 40 D = 19 mm

    As tul = 2!"52# mm2

    d = h $ d'

    d = 4%0 As = 50"5%2

    As' = 50"5%2

    d $ h/2 = 210

    d $ d' = 420

    0"5 & fc' & h & b & d $ h/2( ) As' & fy & d $ d'( #00,#10,9!"44 210"00

    0"5 & fc' & h & b ) As ) As'( & fy !!!%#1"9%#%#55

    b = 250 fc' = 25 N/mm2

    h = 500 fy = 400 N/mm2

    d' = 50 D = 19 mm

    As tul = 2!"52# mm2

    d = h $ d'

    d = 450 As = 11!4"115   ==>PERHATAN JIKA TULAAs' = 50"5%2

    d $ h/2 = 200

    d $ d' = 400

    0"5 & fc' & h & b & d $ h/2( ) As' & fy & d $ d'( %%#,!4!,#9!"#5 19!"4!

    0"5 & fc' & h & b ) As ) As'( & fy !4501!0"4%!5%214

  • 8/17/2019 Statis Momen

    19/160

    b = 250 fc' = 25 N/mm2

    h = %00 fy = 400 N/mm2

    d' = 40 D = 19 mm

    As tul = 2!"52# mm2

    d = h $ d'

    d = 5%0 As = 11!4"115

    As' = 50"5%2

    d $ h/2 = 2%0

    d $ d' = 520

    0"5 & fc' & h & b & d $ h/2( ) As' & fy & d $ d'( 1,005,%#1,9!1" 252"59

    0"5 & fc' & h & b ) As ) As'( & fy !91!0"4%!5%214

  • 8/17/2019 Statis Momen

    20/160

  • 8/17/2019 Statis Momen

    21/160

    NGAN TIDAK SERAGAM

    ACER:,ARA%AR @A RD ?U#// E/ #A,CD ,/E@  UNTUKMENCAPAI KESEIMBANGAN(LEBIH DEKAT KE AS YANGBESAR)

  • 8/17/2019 Statis Momen

    22/160

  • 8/17/2019 Statis Momen

    23/160

    b = 250 mm fc' = 2# N/mm2

    h = %00 mm fy = 400 N/mm2

    d' = 50 mm D = 1% mmAs tul = 201"0%192929# mm2

    d = h $ d'

    d = 550 mm As = ! D 1% %0!"15#9492

    As' = ! D 1% %0!"15#9492

    Statis Momen terhadap t!an"an tari#$ As %

    d $ h/2 = 250 mm

    d $ d' = 500 mm

    d * = 0"5 & fc' & h & b & d $ h/2( ) As' & fy & d $ d'( = 91,2%2,15#"90 =

    0"5 & fc' & h & b ) As ) As'( & fy !,925,04"%!

    Statis Momen terhadap tepi atas &!o# te"' Te#an &eton %

    d * = 0"5 & fc' & h & b & h/2( ) As' & fy & d'( ) As & fy & d( 11##51459"4##42 =

    0"5 & fc' & h & b ) As ) As'( & fy !,925,04"%!

    Statis Momen terhadap t!an"an te#an$ As( %

    h/2 $ d' = 250 mm

    d $ d' = 500 mm

    d * = 0"5 & fc' & h & b & h/2 $ d'( ) As & fy & d $ d'( = 91,2%2,15#"90 =

    0"5 & fc' & h & b ) As ) As'( & fy !,925,04"%!

  • 8/17/2019 Statis Momen

    24/160

    Statis Momen terhadap titi# ) %

    & = 125 mm d+- .+-s t+l +m+. bt 3 3++

    1 = & 1 = 125 mm

    2 = h/2 $ d' $ & 2 = 125 mm

    ! = d $ d' $ 2 ! = !#5 mm

    d * = 0"5 & fc' & h & b & 1( $ As' & fy & 2( ) As & fy & !( 490,%!1,0#"95 =

    0"5 & fc' & h & b ) As ) As'( & fy !,925,04"%!

    Statis Momen terhadap "aris netra! penampan" &eton %

    1 = & 1 = 0 mm

  • 8/17/2019 Statis Momen

    25/160

    2 = h/2 $ d' 2 = 250 mm

    ! = d $ h/2 ! = 250 mm

    d * = 0"5 & fc' & h & b & 1( $ As' & fy & 2( ) As & fy & !( $ =

    0"5 & fc' & h & b ) As ) As'( & fy !,925,04"%!

  • 8/17/2019 Statis Momen

    26/160

    mm2

    mm2

      250"00 mm d+- tul+.+ t+-3

      !00"00 mm d+- t- +t+s bl3 t." T3+ bt

      250"00 mm d+- tul+.+ t3+

  • 8/17/2019 Statis Momen

    27/160

      125"00 mm d+- t-t-3 &

  • 8/17/2019 Statis Momen

    28/160

      $ mm d+- d+- .+-s t+l +m+.

  • 8/17/2019 Statis Momen

    29/160

    MENGHITUNG d( *+ENTR,ID PLASTIS-

    D = 19 mm

    fc' = 2# N/mm2 As = 2!"52# mm2

    fy = 400 N/mm2

    As1 = 141#"%44 mm2

    b = 400 mm As2 = 5%#"05#5 mm2

    h = 400 mm As! = 5%#"05#5 mm2+ = h, As4 = 5%#"05#5 mm2

      + = 400 mm As5 = 141#"%44 mm2

    d' = 50 mm

    d = h $ d'

    d = !50 mm

    . Statis Momen terhadap "aris netra! penampan" &eton %

    50

    50mm

    125 mm

    200 mm

    2#5 mm

    !50 mm

    c = h/2 $ +/2 c = 0 mm

    1 = h/2 $ d1 1 = 150 mm

    2 = h/2 $ d2 2 = #5 mm

    ! = h/2 $ d! ! = 0 mm

    4 = d4 $ h/2 4 = #5 mm

    5 = d5 $ h/2 5 = 150 mm

    d* = 0"5 & fc' & h & b & c( ) As1& fy & 1( ) As2& fy & 2( ) As!& fy & !( $ As4& fy & 4( $ As5& fy & 5(

    0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy

    0 =   - mm dari garis netral 

      5,4%,5!"92

    d- = d

    c ) - $ 1( h $ 2d

    c( / N $ 1(

    dc= d' d

    c=

    d1=

    d2=

    d! =

    d4 =

    d5 =

     h = 400

     b = 400

     6s5  6s4  6s!  6s2  6s1

     6c

    d1

    d2

    d!

    d4

    d5

    1

    24

    5

  • 8/17/2019 Statis Momen

    30/160

    / Statis Momen terhadap tepi atas &!o# te"an"an te#an &eton %

    50mm

    125 mm

    200 mm

    2#5 mm

    !50 mm

    c = h/2 c = 200 mm

    1 = d1 1 = 50 mm

    2 = d2 2 = 125 mm

    ! = d! ! = 200 mm

    4 = d4 4 = 2#5 mm

    5 = d5 5 = !50 mm

    d* = 0"5 & fc' & h & b & c( ) As1& fy & 1 ) As2& fy & 2( ) As!& fy & !( ) As4& fy & 4( ) As5& fy & 5(0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy

    109#!1%#!"! =   200.00 mm dari tepi atas blok tegangan tekan beton

      5,4%,5!"92

    d1=

    d2=

    d! =

    d4 =

    d5 =

     h = 400

     b = 400

     6s5  6s4  6s!  6s2  6s1

     6c

    d1d2

    d!

    d4

    d5

    1

    2

    ! = c

    4

    5

  • 8/17/2019 Statis Momen

    31/160

    0 Statis Momen terhadap As1 %

    50mm

    125 mm200 mm

    2#5 mm

    !50 mm

    c = d $ h/2 c = 150 mm

    1 = d $ d1 1 = !00 mm

    2 = d $ d2 2 = 225 mm

    ! = d $ d! ! = 150 mm

    4 = d $ d4 4 = #5 mm

    5 = d $ d 5 = 0 mm

    d* = 0"5 & fc' & h & b & c( ) As1& fy & 1( ) As2& fy & 2( ) As!& fy & !( ) As4& fy & 4( ) As5& fy & 5

    0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy

    229#5#"51 =   150.00 mm dari As5 

      5,4%,5!"92

    d1=

    d2 =d

    ! =

    d4 =

    d5 =

     h = 400

     b = 400

     6s5  6s4  6s!  6s2  6s1

     6c

    4

    d1

    d2

    d!

    d4

    d5

    ! = c

    2

    1

  • 8/17/2019 Statis Momen

    32/160

    2 Statis Momen terhadap As2 %

    50mm

    125 mm200 mm

    2#5 mm

    !50 mm

    c = d4 $ h/2 c = #5 mm

    1 = d4 $ d1 1 = 225 mm

    2 = d4 $ d2 2 = 150 mm

    ! = d4 $ d! ! = #5 mm

    4 = d4 $ d4 4 = 0 mm

    5 = d5 $ d4 5 = #5 mm

    d* = 0"5 & fc' & h & b & c( ) As1& fy & 1( ) As2& fy & 2( ) As!& fy & !( ) As4& fy & 4( $ As5& fy &

    0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy

    41149!#9!"#5 =   75.00 mm dari As4

      5,4%,5!"92

    d1=

    d2 =d

    ! =

    d4 =

    d5 =

     h = 400

     b = 400

     6s5  6s4  6s!  6s2  6s1

     6c

    d1

    d2

    d!

    d4

    d5

    1

    2

    ! = c5

  • 8/17/2019 Statis Momen

    33/160

    1 Statis Momen terhadap As0 %

    50mm

    125 mm200 mm

    2#5 mm

    !50 mm

    c = d! $ h/2 c = 0 mm

    1 = d! $ d1 1 = 150 mm

    2 = d! $ d2 2 = #5 mm

    ! = d! $ d! ! = 0 mm

    4 = d4 $ d! 4 = #5 mm

    5 = d5 $ d! 5 = 150 mm

    d* = 0"5 & fc' & h & b & c( ) As1& fy & 1( ) As2& fy & 2( ) As!& fy & !( $ As4& fy & 4( $ As5& fy & 5(

    0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy

    0 =   - mm dari As3

      5,4%,5!"92

    d1=

    d2 =d

    ! =

    d4 =

    d5 =

     h = 400

     b = 400

     6s5  6s4  6s!  6s2  6s1

     6c

    d1

    d2

    d!

    d4

    d5

    1

    24

    5

  • 8/17/2019 Statis Momen

    34/160

    3 Statis Momen terhadap As/ %

    50mm

    125 mm

    200 mm

    2#5 mm

    !50 mm

    c = h/2 $ d2 c = #5 mm

    1 = d2 $ d1 1 = #5 mm

    2 = d2 $ d2 2 = 0 mm

    ! = d! $ d2 ! = #5 mm

    4 = d4 $ d2 4 = 150 mm

    5 = d5 $ d2 5 = 225 mm

    d* = $ 0"5 & fc' & h & b & c( ) As1& fy & 1( ) As2& fy & 2( $ As!& fy & !( $ As4& fy & 4( $ As5& fy & 5(

    0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy

    $41149!#9!"#5 =   (75.00) mm dari As2

      5,4%,5!"92

    ATA7

    d* = 0"5 & fc' & h & b & c( $ As1& fy & 1( $As2& fy & 2( ) As!& fy & !( ) As4& fy & 4( ) As5& fy & 5(

    0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy

    41149!#9!"#5 =   75.00 mm dari As2  5,4%,5!"92

    d1=

    d2=

    d! =

    d4 =

    d5 =

     h = 400

     b = 400

     6s5  6s4  6s!  6s2  6s1

     6c

    d1d2

    d!

    d4

    d5

    1!

    4

    5

  • 8/17/2019 Statis Momen

    35/160

    4 Statis Momen terhadap As. %

    50mm

    125 mm

    200 mm

    2#5 mm

    !50 mm

    c = h/2 $ d1 c = 150 mm

    1 = d1 $ d1 1 = 0 mm

    2 = d2 $ d1 2 = #5 mm

    ! = d! $ d1 ! = 150 mm

    4 = d4 $ d1 4 = 225 mm

    5 = d5 $ d1 5 = !00 mm

    d* = $ 0"5 & fc' & h & b & c( ) As1& fy & 1( $ As2& fy & 2( $ As!& fy & !( $ As4& fy & 4( $ As5& fy & 5(

    0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy

    $229#5#"51 =   (150.00) mm dari As2

      5,4%,5!"92

    ATA7

    d* = 0"5 & fc' & h & b & c( $ As1& fy & 1( ) As2& fy & 2( ) As!& fy & !( ) As4& fy & 4( ) As5& fy & 5(

    0"5 & fc' & h & b( ) As1) As2 ) As! ) As4 ) As5( & fy

    229#5#"51 =   150.00 mm dari As2

      5,4%,5!"92

    d1=

    d2=

    d! =

    d4 =

    d5 =

     h = 400

     b = 400

     6s5  6s4  6s!  6s2  6s1

     6c

    d1

    d2

    d!

    d4

    d5

    !

    5

    4

    2

  • 8/17/2019 Statis Momen

    36/160

    D-3t+hu- 8

    utu bt : utu b+;+ :

    b< = 200 mm fc ' = 25 + fy = 400 +

    bf = %00 mm = 25 N/mm2 = 400 N/mm2

    h = #00 mm

    hf = 200 mm dulus >l+st-s-t+s ?t dulud >l+st-s-t+s ?+;+, >y

    h $ hf = 500 mm >c = >y = 200,000 +>c = 2!500 N/mm2

    R.+.+ bt : R.+.+ b+;+ :

    = 0"00! = fy / >s

    = 0"0020

    D = 22

    As = !0"1! mm2

    Tul+.+ = 22 D 22

    Centroid plastis, d"St+t-s m 3 t- +t+s +m+.

    Ac1 = 0"5 & fc & hf & bf = 2,550,000 N c1 = 1/2"hf c1 = 100 mm

    Ac2 = 0"5 & fc & h $ hf( & b< = 2,125,000 N c2 = hf ) 1/2 h$ hf ( c2 = 450 mm

    As1 = % As = 2,20"0 mm2 d1 = 50 mm 1 = d1 1 = 50 mm

    As2 = % As = 2,20"0 mm2 d2 = 150 mm 2 = d2 2 = 150 mm

    As! = 2 As = #%0"2# mm2 d! = 250 mm ! = d! ! = 250 mm

    As4 = 2 As = #%0"2# mm2 d4 = !50 mm 4 = d4 4 = !50 mm

    As5 = 2 As = #%0"2# mm2 d5 = 450 mm 5 = d5 5 = 450 mmAs% = 2 As = #%0"2# mm2 d% = 550 mm % = d% % = 550 mm

    As# = 2 As = #%0"2# mm2 d# = %50 mm # = d# # = %50 mm

    4#00 √ fc' (

    @c

    @y

    @y

    600

    5010 0 1 00 1 00 1 00 1 00

    50

    50

    100

    50

    200

    50100

      50

    50

    150

    250

    350

    450

    550

    650

  • 8/17/2019 Statis Momen

    37/160

    Ac1 ) Ac2( ) As1 ) As2 ) As! ) As4 ) As5 ) As% ) As#( & fy

    d * = 2,0##,952,51"2# = 259"091 mm d+- t- +t+s +m+. 3lm T

      ,020,1%#"%

    d * = Ac1 & c1 ) Ac2 & c2( ) As1 & fy & 1 ) As2 & fy & 2 ) As! & fy & ! ) As4 & fy & 4 ) As5 & fy & 5 ) As% & fy & % ) As# & fy &

  • 8/17/2019 Statis Momen

    38/160

    Centroid plastis, d"St+t-s m 3 t- b+

  • 8/17/2019 Statis Momen

    39/160

    hf = 200 mm dulus >l+st-s-t+s ?t dulud >l+st-s-t+s ?+;+, >y

    h $ hf = 500 mm >c = >y = 200,000 +

    >c = 2!500 N/mm2

    R.+.+ bt : R.+.+ b+;+ :

    = 0"00! = fy / >s

    = 0"0020

    4#00 √ fc' (

    @c

    @y

    @y

  • 8/17/2019 Statis Momen

    40/160

    D = 22

    As = !0"1! mm2

    Tul+.+ = 22 D 22

    Centroid plastis, d"

    St+t-s m 3 t- 3-- +m+.

    Ac1 = 0"5 & fc & hf & bf = 2,550,000 N c1 = 1/2"bf c1 = !00 mm

    Ac2 = 0"5 & fc & h $ hf( & b< = 2,125,000 N c2 = 1/2"bf c2 = !00 mm

    As1 = 2 As = #%0"2# mm2 d1 = 50 mm 1 = d1 1 = 50 mm

    As2 = 2 As = #%0"2# mm2 d2 = 150 mm 2 = d2 2 = 150 mm

    As! = # As = 2,%%0"9! mm2 d! = 250 mm ! = d! ! = 250 mm

    As4 = # As = 2,%%0"9! mm2 d4 = !50 mm 4 = d4 4 = !50 mm

    As5 = 2 As = #%0"2# mm2 d5 = 450 mm 5 = d5 5 = 450 mm

    As% = 2 As = #%0"2# mm2 d% = 550 mm % = d% % = 550 mm

    As# = 0 As = $ mm2 d# = 0 mm # = d# # = 0 mm

    22 b+t+. D-+"22

    Ac1 ) Ac2( ) As1 ) As2 ) As! ) As4 ) As5 ) As% ) As#( & fy

    d * = 2,40%,050,!5#"2% = !00 mm d+- t- 3-- +m+. 3lm T

      ,020,1%#"%

    d * = Ac1 & c1 ) Ac2 & c2( ) As1 & fy & 1 ) As2 & fy & 2 ) As! & fy & ! ) As4 & fy & 4 ) As5 & fy & 5 ) As% & fy & % ) As# & fy &

  • 8/17/2019 Statis Momen

    41/160

    D-3t+hu- 8

    utu bt : utu b+;+ :

    b< = 200 mm fc ' = 25 + fy = 400 +

    bf = %00 mm = 25 N/mm2 = 400 N/mm2

    h = #00 mm

    hf = 200 mm dulus >l+st-s-t+s ?t dulud >l+st-s-t+s ?+;+, >y

    h $ hf = 500 mm >c = >y = 200,000 +>c = 2!500 N/mm2

    R.+.+ bt : R.+.+ b+;+ :

    = 0"00! = fy / >s

    = 0"0020

    D = 22

    As = !0"1! mm2

    Tul+.+ = 22 D 22

    Centroid plastis, d"St+t-s m 3 t- +t+s +m+.

    Ac1 = 0"5 & fc & hf & bf = 2,550,000 N c1 = 1/2"hf c1 = 100 mm

    Ac2 = 0"5 & fc & h $ hf( & b< = 2,125,000 N c2 = hf ) 1/2 h$ hf ( c2 = 450 mm

    As1 = % As = 2,20"0 mm2 d1 = 50 mm 1 = d1 1 = 50 mm

    As2 = % As = 2,20"0 mm2 d2 = 150 mm 2 = d2 2 = 150 mm

    As! = 2 As = #%0"2# mm2 d! = 250 mm ! = d! ! = 250 mm

    As4 = 2 As = #%0"2# mm2 d4 = !50 mm 4 = d4 4 = !50 mm

    As5 = 2 As = #%0"2# mm2 d5 = 450 mm 5 = d5 5 = 450 mmAs% = 2 As = #%0"2# mm2 d% = 550 mm % = d% % = 550 mm

    As# = 2 As = #%0"2# mm2 d# = %50 mm # = d# # = %50 mm

    4#00 √ fc' (

    @c

    @y

    @y

    600

    5010 0 1 00 1 00 1 00 1 00

    50

    50

    100

    50

    200

    50100

      50

    50

    150

    250

    350

    450

    550

    650

  • 8/17/2019 Statis Momen

    42/160

    Ac1 ) Ac2( ) As1 ) As2 ) As! ) As4 ) As5 ) As% ) As#( & fy

    d * = 2,0##,952,51"2# = 259"091 mm d+- t- +t+s +m+. 3lm T

      ,020,1%#"%

    Centroid plastis, d"St+t-s m 3 t- b+

  • 8/17/2019 Statis Momen

    43/160

  • 8/17/2019 Statis Momen

    44/160

    & #(

    & #(

  • 8/17/2019 Statis Momen

    45/160

    D-3t+hu- 8

    utu bt : utu b+;+ :

    b< = 200 mm fc ' = 25 + fy = 400 +

    bf = %00 mm = 25 N/mm2 = 400 N/mm2

    h = #00 mm

    hf = 200 mm dulus >l+st-s-t+s ?t dulud >l+st-s-t+s ?+;+, >y

    h $ hf = 500 mm >c = >y = 200,000 +>c = 2!500 N/mm2

    R.+.+ bt : R.+.+ b+;+ :

    = 0"00! = fy / >s

    = 0"0020

    D = 22

    As = !0"1! mm2

    Tul+.+ = 22 D 22

    Centroid plastis, d"St+t-s m 3 t- +t+s +m+.

    Ac1 = 0"5 & fc & hf & bf = 2,550,000 N c1 = 1/2"hf c1 = 100 mm

    Ac2 = 0"5 & fc & h $ hf( & b< = 2,125,000 N c2 = hf ) 1/2 h$ hf ( c2 = 450 mm

    As1 = % As = 2,20"0 mm2 d1 = 50 mm 1 = d1 1 = 50 mm

    As2 = % As = 2,20"0 mm2 d2 = 150 mm 2 = d2 2 = 150 mm

    As! = 2 As = #%0"2# mm2 d! = 250 mm ! = d! ! = 250 mm

    As4 = 2 As = #%0"2# mm2 d4 = !50 mm 4 = d4 4 = !50 mm

    As5 = 2 As = #%0"2# mm2 d5 = 450 mm 5 = d5 5 = 450 mm

    As% = 2 As = #%0"2# mm2 d% = 550 mm % = d% % = 550 mm

    A # 2 A #%0 2# 2 d# %50 # d# # %50

    4#00 √ fc' (

    @c

    @y

    @y

    600

    50100 100 100 100 100

    50

    50

    100

    50

    200

    50100

      50

    50

    150

    250

    350

    450

    550

    650

  • 8/17/2019 Statis Momen

    46/160

    Ac1 ) Ac2( ) As1 ) As2 ) As! ) As4 ) As5 ) As% ) As#( & fy

    d * = 2,0##,952,51"2# = 259"091 mm d+- t- +t+s +m+. 3lm T

    d * = Ac1 & c1 ) Ac2 & c2( ) As1 & fy & 1 ) As2 & fy & 2 ) As! & fy & ! ) As4 & fy & 4 ) As5 & fy & 5 ) As% & fy & % ) As#

  • 8/17/2019 Statis Momen

    47/160

      ,020,1%#"%

  • 8/17/2019 Statis Momen

    48/160

    Centroid plastis, d"St+t-s m 3 t- b+

  • 8/17/2019 Statis Momen

    49/160

  • 8/17/2019 Statis Momen

    50/160

    D-3t+hu- 8

    utu bt : utu b+;+ :

  • 8/17/2019 Statis Momen

    51/160

    b< = 200 mm fc ' = 25 + fy = 400 +

    bf = %00 mm = 25 N/mm2 = 400 N/mm2

    h = #00 mm

    hf = 200 mm dulus >l+st-s-t+s ?t dulud >l+st-s-t+s ?+;+, >y

    h $ hf = 500 mm >c = >y = 200,000 +

    >c = 2!500 N/mm2

    R.+.+ bt : R.+.+ b+;+ :

    = 0"00! = fy / >s

    = 0"0020

    D = 22

    As = !0"1! mm2

    Tul+.+ = 22 D 22

    Centroid plastis, d"St+t-s m 3 t- +t+s +m+.

    Ac1 = 0"5 & fc & hf & bf = 2,550,000 N c1 = 1/2"hf c1 = 100 mm

    Ac2 = 0"5 & fc & h $ hf( & b< = 2,125,000 N c2 = hf ) 1/2 h$ hf ( c2 = 450 mm

    As1 = % As = 2,20"0 mm2 d1 = 50 mm 1 = d1 1 = 50 mm

    As2 = % As = 2,20"0 mm2 d2 = 150 mm 2 = d2 2 = 150 mm

    As! = 2 As = #%0"2# mm2 d! = 250 mm ! = d! ! = 250 mm

    As4 = 2 As = #%0"2# mm2 d4 = !50 mm 4 = d4 4 = !50 mm

    As5 = 2 As = #%0"2# mm2 d5 = 450 mm 5 = d5 5 = 450 mm

    As% = 2 As = #%0"2# mm2 d% = 550 mm % = d% % = 550 mm

    As# = ! As = 1,140"40 mm2 d# = %50 mm # = d# # = %50 mm

    Ac1 ) Ac2( ) As1 ) As2 ) As! ) As4 ) As5 ) As% ) As#( & fy

    d * = 2,1#%,##,0%"15 = 2%%"!%4 mm d+- t- +t+s +m+. 3lm T

      ,1#2,220"94

    Centroid plastis, d"St+t-s m 3 t- b+

  • 8/17/2019 Statis Momen

    52/160

      ,1#2,220"94

    mbu3t-+

    h $ d* = #00 $ 2%%"!%4 = 4!!"%!% mm d+- t- b+

  • 8/17/2019 Statis Momen

    53/160

  • 8/17/2019 Statis Momen

    54/160

    D-3t+hu- 8

    utu bt : utu b+;+ :

    b< = 200 mm fc ' = 25 + fy = 400 +

    bf = %00 mm = 25 N/mm2 = 400 N/mm2

    h = #00 mm

    hf = 200 mm dulus >l+st-s-t+s ?t dulud >l+st-s-t+s ?+;+, >y

    h $ hf = 500 mm >c = >y = 200,000 +>c = 2!500 N/mm2

    R.+.+ bt : R.+.+ b+;+ :

    = 0"00! = fy / >s

    = 0"0020

    D = 22

    As = !0"1! mm2

    Tul+.+ = 22 D 22

    Centroid plastis, d"St+t-s m 3 t- +t+s +m+.

    Ac1 = 0"5 & fc & hf & bf = 2,550,000 N c1 = 1/2"hf c1 = 100 mm

    Ac2 = 0"5 & fc & h $ hf( & b< = 2,125,000 N c2 = hf ) 1/2 h$ hf ( c2 = 450 mm

    As1 = 11 As = 4,11"4% mm2 d1 = 50 mm 1 = d1 1 = 50 mm

    As2 = % As = 2,20"0 mm2 d2 = 150 mm 2 = d2 2 = 150 mm

    As! = 2 As = #%0"2# mm2 d! = 250 mm ! = d! ! = 250 mm

    As4 = 2 As = #%0"2# mm2 d4 = !50 mm 4 = d4 4 = !50 mm

    As5 = 2 As = #%0"2# mm2 d5 = 450 mm 5 = d5 5 = 450 mmAs% = 2 As = #%0"2# mm2 d% = 550 mm % = d% % = 550 mm

    As# = ! As = 1,140"40 mm2 d# = %50 mm # = d# # = %50 mm

    4#00 √ fc' (

    @c

    @y

    @y

    600

    50  5050

    50

    100

    50

    200

    50100

      50

    50

    150

    250

    350

    450

    550

    650

    50   50 50 50 50 50 50 50 50

  • 8/17/2019 Statis Momen

    55/160

    Ac1 ) Ac2( ) As1 ) As2 ) As! ) As4 ) As5 ) As% ) As#( & fy

    d * = 2,214,00,!5#"2% = /24'525 mm d+- t- +t+s +m+. 3lm T

      ,9!2,4%"!%

    d * = Ac1 & c1 ) Ac2 & c2( ) As1 & fy & 1 ) As2 & fy & 2 ) As! & fy & ! ) As4 & fy & 4 ) As5 & fy & 5 ) As% & fy & % ) As#

  • 8/17/2019 Statis Momen

    56/160

    Centroid plastis, d"St+t-s m 3 t- b+

  • 8/17/2019 Statis Momen

    57/160

  • 8/17/2019 Statis Momen

    58/160

    & #(

  • 8/17/2019 Statis Momen

    59/160

  • 8/17/2019 Statis Momen

    60/160

    & #(

  • 8/17/2019 Statis Momen

    61/160

  • 8/17/2019 Statis Momen

    62/160

  • 8/17/2019 Statis Momen

    63/160

    & #(

    & #(

  • 8/17/2019 Statis Momen

    64/160

  • 8/17/2019 Statis Momen

    65/160

  • 8/17/2019 Statis Momen

    66/160

  • 8/17/2019 Statis Momen

    67/160

    & #(

  • 8/17/2019 Statis Momen

    68/160

    & #(

  • 8/17/2019 Statis Momen

    69/160

    A" = 12 & 40

    A" = 2 & 12

    Bd-+t 8

    &1 = 12/2

    &2 =12 ) 2/2

    Titi# &erat pe

    &+ = &1"A

    A

    &+ = 14"2!52

    &b = 12 ) 2

    &b = 25"#%4#

    utu bt : utu b+;+ : D = 1%

    fc ' = 200 B./cm2 fy = 4000 B./cm2 As = 201"0% mm2

    = 200 B./cm2 = 4000 B./cm2 2"010% cm2

    dulus >l+st-s-t+s ?t dulus >l+st-s-t+s ?+;+, >s

    >c = >y = 2,100,000 B./cm2

    >c = 210190"!9 N/mm2

    R.+.+ bt : R.+.+ b+;+ :

    = 0"00! = fy / >s

    = 0"0019

    Centroid plastis, d"

    St+t-s m 3 t- 3-- +m+.

    Ac1 = 0"5 & fc & 12 & 40 = 1%00 3."cm c1 = 1/2 & 12 c1 = %

    Ac2 = 0"5 & fc & 2 & 12 = 5#120 3."cm c2 = 12 ) 2/2 c2 = 2%

    1!#20 3."cm

    As1 = 5 As = 10"05!10 cm2 d1 = ! cm 1 = ! cm

    As2 = 5 As = 10"05!10 cm2 d2 = 9 cm 2 = 9 cm

    As! = 2 As = 4"02124 cm2 d! = 15 cm ! = 15 cm

    As4 = 2 As = 4"02124 cm2 d4 = 2% cm 4 = 2% cm

    As5 = 2 As = 4"02124 cm2 d5 = !# cm 5 = !# cm

    4#00 √ fc' (

    @c

    @y

    @y

    90

    150

    260

    370

    400

    120

    120

    280

    30

  • 8/17/2019 Statis Momen

    70/160

    d* = !,#11,95"0# = 1!"14515! cm d-u3u d+- t- 3-- +m+.

      2%#,!99"%4

  • 8/17/2019 Statis Momen

    71/160

    Centroid plastis, d"St+t-s m 3 Tul+.+ 1 As1(

  • 8/17/2019 Statis Momen

    72/160

    Ac1 = 0"5 & fc & 12 & 40 = 1%00 3."cm c1 = 1/2 & 12 $ ! c1 = ! cm

    Ac2 = 0"5 & fc & 2 & 12 = 5#120 3."cm c2 = 12 ) 2/2 $! c2 = 2! cm

    As1 = 5 As = 10"05!10 cm2 d1 = 0 cm 1 = 0 cm

    As2 = 5 As = 10"05!10 cm2 d2 = % cm 2 = % cmAs! = 2 As = 4"02124 cm2 d! = 12 cm ! = 12 cm

    As4 = 2 As = 4"02124 cm2 d4 = 2! cm 4 = 2! cm

    As5 = 2 As = 4"02124 cm2 d5 = !4 cm 5 = !4 cm

    *A7. 8 A7/- 8 *As. 8 As/ 8 As0 8 As2 8 As1-

    d* = 2,909,%9%"1%4% = 10"14515! cm d-u3u d+- Tul+.+ 1 As1(

      2%#,!99"%4

    1!"14515!0!10"14515!0!

    !

    +ARA ANDRE N,AN$ ST$ MT'

    A" = 12 & 40

    A" = 2 & 12

    Ab =

    Bd-+t 8

    &1 = 12/2

    &2 =12 ) 2/2

    Titi# &erat pe

    &+ = &1"A

    A

    &+ = 14"2!52

    &b = 12 ) 2

    &b = 25"#%4#

    d' = !

    utu bt : utu b+;+ : D = 1%

    fc ' = 200 B./cm2 fy = 4000 B./cm2 As = 201 0% mm2

    d; = *A7. )

  • 8/17/2019 Statis Momen

    73/160

    dulus >l+st-s-t+s ?t dulus >l+st-s-t+s ?+;+, >s

  • 8/17/2019 Statis Momen

    74/160

    >c = >y = 2,100,000 B./cm2

    >c = 210190"!9 N/mm2

    4#00 √ fc' (

  • 8/17/2019 Statis Momen

    75/160

    R.+.+ bt : R.+.+ b+;+ :

    = 0"00! = fy / >s

    = 0"0019

    itik Centroid plastis penampang, d"

    St+t-s m 3 t- 3-- +m+.

    Ac1 = 0"5 & fc & 12 & 40 = 1%00 3."cm c1 = 1/2 & 12 c1 = %

    Ac2 = 0"5 & fc & 2 & 12 = 5#120 3."cm c2 = 12 ) 2/2 c2 = 2%

    1!#20 3."cm

    As1 = 5 As = 10"05!10 cm2 d1 = ! cm 1 = 0 cm

    As2 = 5 As = 10"05!10 cm2 d2 = 9 cm 2 = % cm

    As! = 2 As = 4"02124 cm2 d! = 15 cm ! = 12 cm

    As4 = 2 As = 4"02124 cm2 d4 = 2% cm 4 = 2! cm

    As5 = 2 As = 4"02124 cm2 d5 = !# cm 5 = !4 cm

    Sb = 0"5"fc'"Ab" &+ $ d'(

    Sb = 1555%0 3."cm

    0"5"fc'"Ab( ) As1 ) As2 ) As! ) As4 ) As5( & fy

    ds = 2909%9%"1%4559 = 10"14515!0! mm d+- Tul+.+ 2 As2(

    2%#!99"%!50910!

    @c

    @y

    @y

    ds = 0"5"fc'"Ab"&+ $ d'( ) As1"1 ) As2"2 ) As!"! ) As4"4 ) As5"5(

  • 8/17/2019 Statis Momen

    76/160

  • 8/17/2019 Statis Momen

    77/160

  • 8/17/2019 Statis Momen

    78/160

    40 cm2

    !!% cm2

    1% cm2

    % cm

    &2 = 2% cm

    pan" tota!

      2" A

     

    cm

    cm

    cm

    cm

  • 8/17/2019 Statis Momen

    79/160

  • 8/17/2019 Statis Momen

    80/160

  • 8/17/2019 Statis Momen

    81/160

    40 cm2

    !!% cm2

    1% cm2

    % cm

    &2 = 2% cm

    pan" tota!

      2" A

     

    cm

    cm

  • 8/17/2019 Statis Momen

    82/160

  • 8/17/2019 Statis Momen

    83/160

  • 8/17/2019 Statis Momen

    84/160

    cm

    cm

  • 8/17/2019 Statis Momen

    85/160

  • 8/17/2019 Statis Momen

    86/160

  • 8/17/2019 Statis Momen

    87/160

    TUGAS 2 BETON PRESTRESS

    Suatu jembatan beton prategang dengan penampang sebagai berikut :

    Dengan data sebagai berikut :

    Panjang jembatan = 30 m

    Initial prestress = 2000 kN

    Beban hidup = 12 kN/m

    ksentrisitas !gs " !g! #e$ diketahui setelah masing"masing ttik berat !g! dan !gs diketahui!atatan : !g! = !enter gra%it& o' !on!rete #titik berat penampang beton$

    !gs = !enter gra%it& o' steel #titik berat penampang baja/besi$

    (itung tegangan :

     " )ehilangan jangka pendek = 10*

     " )ehilangan jangka panjang = +*

    ,utu beton :

    '!u = +0 N/mm2

    '!i = 30 N/mm2

    (itung tegangan"tegangan &ang terjadi

     " )ondisi trans'er 

     " )ondisi ser%i!e

    Jawaban

    1. OND!S! TRANS"ER

    #uas $ena%$ang ba&'k

    'ndisi

    trans(er 

    1000

    400

  • 8/17/2019 Statis Momen

    88/160

    b1 = -00 mm (1 = 1000 mm

    h1 = 200 mm

    b2 = 1+0 mm

    h2 = .00 mm

    b3 = -00 mm

    h3 = 200 mm

     1 = b1h1 = 0000mm2

     2 = b2h2 = 0000mm2

     3 = b3h3 = 0000mm2

      = 1 2 3 = 2+0000mm2

      = 444 mm2

    &1 = (1 " 1/2h1 = 00 mm

    &2 = 1/2h2 h3 = +00 mm

    &3 = 1/2h3 = 100 mm

    0000 5 00 0000 5 +00 0000 5 10

    2+00+

    +00 mm dari tepi ba6ah #bottom$

    7 dimana (1 = 1000mm

    +00 mm dari tepi atas #top$

    )eng*itung !nertia

    dimana 8

    = -00 mm

    = 0mm karena berhimpitan dg garis netral pe

    = -00 mm

    = 1/12 5 -00 5 200 93 0000 5 -00 92

    = 1/12 5 1+0 5 .00 93 0000 5 0 92

    )eng*itung +arak titik berat ,-entr'id dari te$i bawa* ,b'tt'% / 0b

    &b = Σ i&i/

    &b =

    &b =

    &a = (1 " &

    b

    &a =

    I = Σ#Ii

    id

    i2$

    d1 = &

    a " 1/2h

    d2 = &

    a " 1/2(1

    d3 = &

    b " 1/2h3

    I1 = 1/12#b1h13$ 1d12

    I2 = 1/12#b2h23$ 2d22

    400

    150900

    500

    100

    y1 =

    y2 =

    y! =

  • 8/17/2019 Statis Momen

    89/160

    = 1/12 5 -00 5 200 93 0000 5 -00 92

    = 444 mm-

    = 444 mm-

    = 444 mm-Inertia total = 444 mm-

    )'%en &awan ,se-ti'n %'du&us %'du&us $ena%$ang

     """ pada bagian atas

     """ pada bagian ba6ah

    = 444 = CCC mm3

    +00

    = 444 = CCC mm3

    +00

    Jarak kern ,kern distan-e

    = 444 mm

    = 444 mm

    2. OND!S! SER!3E

    #uas $ena%$ang ba&'k

    b1 = -00 mm b3 = -00 mm (2 = 1200 mm

    h1 = 200 mm h3 = 200 mm

    b2 = 1+0 mm b- = 1000 mm

    h2 = .00 mm h- = 200 mm

     1 = b1h1 = -00 5 200 = 0000mm2 2 = b2h2 = 1+0 5 .00 = 0000mm2

     3 = b3h3 = -00 5 200 = 0000mm2

     - = b-h- = 1000 5 200 = 200000mm2

      = 1 2 3 - = -+0000mm2

      = 444 mm2

    I3 = 1/12#b3h33$ 3d32

    I1 

    I2 

    I3 

    ;1 = I / &

    a

    ;2 = I / &

    b

    ;1

    ;2

    kt = ;

    2 /

    kb = ;

    1 /

    )eng*itung +arak titik berat ,-entr'id dari te$i bawa* ,b'tt'% / 0b

    400

    150900

    500

    100

    y1 =

    y2 =

    y! =

    1

    1900y1 =

    1100y4 =

  • 8/17/2019 Statis Momen

    90/160

    &1 = (1 " 1/2h1 = 00 mm

    &2 = 1/2h2 h3 = +00 mm

    &3 = 1/2h3 = 100 mm

    &- = (2 " 1/2h- = 1100 mm

    0000 5 00 0000 5 +00 0000 5 100 200000 5 110

    -+00+

    444 mm dari tepi ba6ah #bottom$

    7 dimana (2 = 1200mm

    444 mm dari tepi atas #top$

    )eng*itung !nertia

    dimana 8

     00 "

  • 8/17/2019 Statis Momen

    91/160

    )'%en &awan ,se-ti'n %'du&us %'du&us $ena%$ang

     """ pada bagian atas

     """ pada bagian ba6ah

    = 444 = CCC mm3

    444

    = 444 = CCC mm3

    444

    )eng*itung Beban

    . kN/m1

    2- kN/m3

    12 kN/m

    -kN/m "" luas penampang plat 5 1 m 5 B Beto1000 5

    >otal ser%i!e load = Berat sendiri balok beban hidup Berat plat di atas balok

    = 22 kN/m

    ,omen maksimum &ang terjadi di tengah bentang #moment at midspan$ :

    , =

    ,omen pada kondisi trans'er #moment at trans'er$ :

    ,i = . 5 30 92

    ,i = .

  • 8/17/2019 Statis Momen

    92/160

      00

    0+

    dimana7 Pi = 2000 kN

    0 5 2000 = 100 kN

    0+ 5 2000 = 1

  • 8/17/2019 Statis Momen

    93/160

    444 mm3 e =   %%%"%# mm

    #1

  • 8/17/2019 Statis Momen

    94/160

      #lass 27 post"tensioned$

    = "03. 5 +0 9 1/2

    = "2++ N/mm2

    = 033 5 +0

    = 1.+0N/mm2

    esi%$u&an

    1 Pada kondisi trans'er #at trans'er$

    >egangan &ang terjadi

    .-2 N/mm2 "1< N/mm2egangan &ang terjadi

    12

  • 8/17/2019 Statis Momen

    95/160

  • 8/17/2019 Statis Momen

    96/160

    nampang

    400

    200

    200

    1000

    150

    500

    500

    400

    400

    d1 =

    d! =

    yb =

    y+ =

    'ndisi trans(er 

  • 8/17/2019 Statis Momen

    97/160

    400

    200

    200

    1000

    150

    500

    500

    400

    400

    d1 =

    d! =

    yb =

    y+ =

    'ndisitrans(er 

    200

    1000

    200

    1000

    4!!"!!

    1!!"!!

    2%%"%#

    !!!"!!

    y+ =

    d1 =

    d2 =

    d4 =

    'ndisiser6i-e

  • 8/17/2019 Statis Momen

    98/160

     92

     92

     92

    33 92

    400

    200

    1000

    150

    0

    #%%"%#

    2%%"%#

    %%%"%#

    yb =

    d2 =

    d! =

  • 8/17/2019 Statis Momen

    99/160

    1000 mm

    109"

      00 5 1000 mm 5109" 5 2- kN/m3

  • 8/17/2019 Statis Momen

    100/160

    skala tegangan = 30

     

  • 8/17/2019 Statis Momen

    101/160

      1+ 0+3

    skala tegangan = 30

      3

  • 8/17/2019 Statis Momen

    102/160

    nan'rHad $ada

    b'umnya

  • 8/17/2019 Statis Momen

    103/160

  • 8/17/2019 Statis Momen

    104/160

  • 8/17/2019 Statis Momen

    105/160

  • 8/17/2019 Statis Momen

    106/160

  • 8/17/2019 Statis Momen

    107/160

  • 8/17/2019 Statis Momen

    108/160

    02-

    0-1.2

    0302

    02-

    0-1.2

    0302

    021-

    02..

    012+

    023++

    A 1 : 30NTUKANERAH ATAUSUAIKAN AGARBARNYAS DILIHAT

    A 1 : 30NTUKANERAH ATAUSUAIKAN AGARBARNYA

  • 8/17/2019 Statis Momen

    109/160

    0+331

    012+

    0-1.<

    0-32

    0-23+

    0-00+

     

  • 8/17/2019 Statis Momen

    110/160

  • 8/17/2019 Statis Momen

    111/160

    TUGAS 1 BETON PRESTRESS

    Suatu jembatan beton prategang dengan penampang sebagai berikut :

    (itung besaran penampang untuk kondisi trans'er dan ser%i!e berupa :

    1 @uas penampang

    2 >itik berat penampang

    3 Inertia penampang

    - ,odulus penampang #se!tion modulus$ atau momen la6an

    Ba&'k $restress diatas dua tu%$uan :

    Panjang balok = 1+ m

    Initial ga&a prestress = 1100 kN

    Beban hidup = 12 kN/m

    ksentrisitas !gs " !g! = 32+ mm

    (itung tegangan di tengah bentang

    )ehilangan jangka pendek = 10*

    )ehilangan jangka panjang = 10*

    Aimana7

    '!u = +0 N/mm2

    '!i = 30 N/mm2

    Jawaban

    'ndisi

    trans(er  1000 mm

    'ndisi ser6i-e

     

  • 8/17/2019 Statis Momen

    112/160

    1. OND!S! TRANS"ER

    #uas $ena%$ang ba&'k

    b1 = -00 mm (1 =

  • 8/17/2019 Statis Momen

    113/160

    = 1/12 5 -00 5 200 93 0000 5 2

  • 8/17/2019 Statis Momen

    114/160

      = 444 mm2

    &1 = (1 " 1/2h1 = .+0 mm&2 = 1/2h2 h3 = 3

  • 8/17/2019 Statis Momen

    115/160

    = 1/12 5 -00 5 200 93 0000 5 --......

    = 1/12 5 1+0 5 3+0 93 +2+00 5 23030303030303

    = 1/12 5 -00 5 200 93 0000 5 +0+30303030303

    = 1/12 5 1000 5 200 93 200000 5 2--.....

    = 444 mm-

    = 444 mm-

    = 444 mm-

    = 444 mm-

    Inertia total = 444 mm-

    )'%en &awan ,se-ti'n %'du&us %'du&us $ena%$ang

     """ pada bagian atas

     """ pada bagian ba6ah

    = 444 = CCC mm3

    444

    = 444 = CCC mm3

    444

    )eng*itung Beban

    +1kN/m1

    2- kN/m3

    Beban hidup = 12 kN/m

    >otal ser%i!e load = Berat sendiri balok Beban hidup

    = 1

  • 8/17/2019 Statis Momen

    116/160

    ,i = 1-3-- kNm

    ,omen pada kondisi ser%is #moment at ser%i!e$ :

    1

  • 8/17/2019 Statis Momen

    117/160

    2. Pada k'ndisi ser6is ,at ser6i-e

    Aari perhitungan besaran penampang dapat diketahui :

      = 444 mm2 e =

    444 mm3 e = .0+30303030303" 1/2 5 200

    444 mm3 e =   505"!0 mm

    = 213 4   -13 5   --<

    = 2-< N/mm2

    = 213 5  

  • 8/17/2019 Statis Momen

    118/160

    Tegangan 0ang dii7inkan ,stress &i%its

    1. Pada k'ndisi trans(er ,at trans(er

      #lass 27 post"tensioned$

    = "03. 5 30 9 1/2

    = "1< N/mm2

    = 0+ 5 30

    = 1+00N/mm2

    2. Pada k'ndisi ser6is ,at ser6i-e

      #lass 27 post"tensioned$

    = "03. 5 +0 9 1/2

    = "2++ N/mm2

    = 033 5 +0

    = 1.+0N/mm2

    esi%$u&an

    1 Pada kondisi trans'er #at trans'er$

    >egangan &ang terjadi

    0 N/mm2 "1< N/mm2

    33 N/mm2 1+00 N/mm2

    2 Pada kondisi ser%is #at ser%i!e$

    >egangan &ang terjadi

    2-< N/mm2 "2++ N/mm2

    1+- N/mm2 1.+0 N/mm2

    ' tt = "03.#' 

    !i$1/2 N/mm2

    ' !t = 0+' 

    !i N/mm2 #'le5ural members$

    ' ts = "03.#' 

    !u$1/2 N/mm2

    ' !s

     = 033' !u

     N/mm2 #'le5ural members$

    ' 1t =

    ' 2t =

    ' 1s

     =

    ' 2s

     =

    ,andnkan d'

    'anan yan$'runan s'

    c.s = ct, .,+D-ty f stl

    )2"1! N/mm2 ) #"2% N/mm2

    400

    200

  • 8/17/2019 Statis Momen

    119/160

    'ndisi trans(er 

  • 8/17/2019 Statis Momen

    120/160

    nampang

    0

    200

    200

    #50

    !#5

    2#5

    2#5

    0

    yb =

    !#5y+ =

    d1 =

    d! =

  • 8/17/2019 Statis Momen

    121/160

    200

    200

    1000

    !44"#0

    44"#0

    2!0"!0

    244"#0

    y+ =

    d1 =

    d2 =

    d4 =

    'ndisi ser6i-e

  • 8/17/2019 Statis Momen

    122/160

    200

    200

    #50

    200

    %05"!0

    !44"#0

    44"#0

    2!0"!0

    244"#0

    505"!0

    yb =

    y+ =

    d1 =

    d2 =

    d! =

    d4 =

    400

    200

    200

    #50150

    %05"!0

    !44"#0

    44"#0

    2!0"!0

    244"#0

    505"!0

    yb =

    y+ =

    d1 =

    d2 =

    d! =

    d4 =

  • 8/17/2019 Statis Momen

    123/160

     92

      2

      2

    < 92

  • 8/17/2019 Statis Momen

    124/160

    skala tegangan = 30

      -.. 01. 01++3

     

  • 8/17/2019 Statis Momen

    125/160

    skala tegangan = 30

      213 00< 00

  • 8/17/2019 Statis Momen

    126/160

    nan

    'rHad $adab'umnya

    $ #"5 N/mm2

    β-

  • 8/17/2019 Statis Momen

    127/160

    UTS BETON PRESTRESS

    Suatu jembatan beton prategang dengan penampang sebagai berikut :

    Dengan data sebagai berikut :

    Panjang jembatan = 2+ m

    Initial prestress = 1+00 kN

    Beban hidup = 1+ kN/m

    ksentrisitas !gs " !g! #e$ diketahui setelah masing"masing ttik berat !g! dan !gs diketahui!atatan : !g! = !enter gra%it& o' !on!rete #titik berat penampang beton$

    !gs = !enter gra%it& o' steel #titik berat penampang baja/besi$

    (itung tegangan :

     " )ehilangan jangka pendek = 1+*

     " )ehilangan jangka panjang = 10*

    ,utu beton :

    '!u = +0 N/mm2

    '!i = 30 N/mm2

    (itung tegangan"tegangan &ang terjadi

     " )ondisi trans'er 

     " )ondisi ser%i!e

    Jawaban

    1. OND!S! TRANS"ER

    #uas $ena%$ang ba&'k

    'ndisi

    trans(er 

    1000

    400

  • 8/17/2019 Statis Momen

    128/160

    b1 = -00 mm (1 = 1000 mm

    h1 = 200 mm

    b2 = 1+0 mm

    h2 = .00 mm

    b3 = -00 mm

    h3 = 200 mm

     1 = b1h1 = 0000mm2

     2 = b2h2 = 0000mm2

     3 = b3h3 = 0000mm2

      = 1 2 3 = 2+0000mm2

      = 444 mm2

    &1 = (1 " 1/2h1 = 00 mm

    &2 = 1/2h2 h3 = +00 mm

    &3 = 1/2h3 = 100 mm

    0000 5 00 0000 5 +00 0000 5 100

    2+00+

    +00 mm dari tepi ba6ah #bottom$

    7 dimana (1 = 1000mm

    +00 mm dari tepi atas #top$

    )eng*itung !nertia

    dimana 8

    = -00 mm

    = 0 mm karena berhimpitan dg garis netral p

    = -00 mm

    = 1/12 5 -00 5 200 93 0000 5 -00 92

    = 1/12 5 1+0 5 .00 93 0000 5 0 92

    )eng*itung +arak titik berat ,-entr'id dari te$i bawa* ,b'tt'% / 0b

    &b = Σ i&i/

    &b =

    &b =

    &a = (1 " &

    b

    &a =

    I = Σ#Ii

    id

    i2$

    d1 = &

    a " 1/2h

    d2 = &

    a " 1/2(1

    d3 = &

    b " 1/2h3

    I1 = 1/12#b1h13$ 1d12

    I2 = 1/12#b2h23$ 2d22

    400

    150900

    500

    100

    y1 =

    y2 =

    y! =

  • 8/17/2019 Statis Momen

    129/160

    = 1/12 5 -00 5 200 93 0000 5 -00 92

    = 13010 mm-

    = 2)0# mm3

    +00

    Jarak kern ,kern distan-e

    = 444 mm

    = 444 mm

    2. OND!S! SER!3E

    #uas $ena%$ang ba&'k

    b1 = -00 mm b3 = -00 mm (2 = 1200 mm

    h1 = 200 mm h3 = 200 mm

    b2 = 1+0 mm b- = 1000 mm

    h2 = .00 mm h- = 200 mm

     1 = b1h1 = -00 5 200 = 0000mm2 2 = b2h2 = 1+0 5 .00 = 0000mm2

     3 = b3h3 = -00 5 200 = 0000mm2

     - = b-h- = 1000 5 200 = 200000mm2

      = 1 2 3 - = -+0000mm2

      = 444 mm2

    I3 = 1/12#b3h33$ 3d32

    I1 

    I2 

    I3 

    ;1 = I / &

    a

    ;2 = I / &

    b

    ;1

    ;2

    kt = ;

    2 /

    kb = ;

    1 /

    )eng*itung +arak titik berat ,-entr'id dari te$i bawa* ,b'tt'% / 0b

    400

    150900

    500

    100

    y1 =

    y2 =

    y! =

    900y1 =

    1100y4 =

  • 8/17/2019 Statis Momen

    130/160

    &1 = (1 " 1/2h1 = 00 mm

    &2 = 1/2h2 h3 = +00 mm

    &3 = 1/2h3 = 100 mm

    &- = (2 " 1/2h- = 1100 mm

    0000 5 00 0000 5 +00 0000 5 100 200000 5 1100

    -+00+

    444 mm dari tepi ba6ah #bottom$

    7 dimana (2 = 1200mm

    444 mm dari tepi atas #top$

    )eng*itung !nertia

    dimana 8

     00 "

  • 8/17/2019 Statis Momen

    131/160

    )'%en &awan ,se-ti'n %'du&us %'du&us $ena%$ang

     """ pada bagian atas

     """ pada bagian ba6ah

    = 444 = 1"%04>)0 mm3

    444

    = 444 = 9"0%5>)0# mm3

    444

    )eng*itung Beban

    . kN/m1

    2- kN/m3

    1+ kN/m

    -kN/m "" luas penampang plat 5 1 m 5 B Beton 1000 5

    >otal ser%i!e load = Berat sendiri balok beban hidup Berat plat di atas balok

    = 2+ kN/m

    ,omen maksimum &ang terjadi di tengah bentang #moment at midspan$ :

    , =

    ,omen pada kondisi trans'er #moment at trans'er$ :

    ,i = . 5 2+ 92

    ,i = -.

  • 8/17/2019 Statis Momen

    132/160

      0+

    0

  • 8/17/2019 Statis Momen

    133/160

    444 mm3 e =   %%%"%# mm

    #112+ 5 1093 / -+0000$ "#112+ 5 1093 5 ..............< /1.03-.1+3-.

    = 2+0 4   -. 5   12+<

    = 103N/mm2

    #112+ 5 1093 / -+0000$ #112+ 5 1093 5 ..............< /0.+21

  • 8/17/2019 Statis Momen

    134/160

      #lass 27 post"tensioned$

    = "03. 5 +0 9 1/2

    = "2++ N/mm2

    = 033 5 +0

    = 1.+0N/mm2

    esi%$u&an

    1 Pada kondisi trans'er #at trans'er$

    >egangan &ang terjadi

    -3 N/mm2 "1< N/mm2+2 N/mm2 1+00 N/mm2

    2 Pada kondisi ser%is #at ser%i!e$

    >egangan &ang terjadi

    103 N/mm2 "2++ N/mm2

    "11-. N/mm2 1.+0 N/mm2

    ' ts = "03.#' 

    !u$1/2 N/mm2

    ' !s = 033' !u N/mm2 #'le5ural members$

    ' 1t =' 2t =

    ' 1s

     =

    ' 2s

     =

     

  • 8/17/2019 Statis Momen

    135/160

  • 8/17/2019 Statis Momen

    136/160

    nampang

    400

    200

    200

    1000

    150

    500

    500

    400

    400

    d1 =

    d! =

    yb =

    y+ =

    'ndisi trans(er 

  • 8/17/2019 Statis Momen

    137/160

    400

    200

    200

    1000

    150

    500

    500

    400

    400

    d1 =

    d! =

    yb =

    y+ =

    'ndisitrans(er 

    200

    1000

    200

    1000

    4!!"!!

    1!!"!!

    2%%"%#

    !!!"!!

    y+ =

    d1 =

    d2 =

    d4 =

    'ndisiser6i-e

  • 8/17/2019 Statis Momen

    138/160

     

    92

    400

    200

    1000

    150

    0

    #%%"%#

    2%%"%#

    %%%"%#

    yb =

    d2 =

    d! =

  • 8/17/2019 Statis Momen

    139/160

    1000 mm

    109"

      00 5 1000 mm 5109" 5 2- kN/m3

  • 8/17/2019 Statis Momen

    140/160

    skala tegangan = 30

      +10 01<

    # - 02

    $ 13 02<

    skala tegangan = 30

  • 8/17/2019 Statis Momen

    141/160

      12+< 0-2

    skala tegangan = 30

      2+0 00

    1+$ 201+.2+ / 1.03-.1+3-.1+$ 2< 02

    2223 0

  • 8/17/2019 Statis Momen

    142/160

     

  • 8/17/2019 Statis Momen

    143/160

  • 8/17/2019 Statis Momen

    144/160

  • 8/17/2019 Statis Momen

    145/160

  • 8/17/2019 Statis Momen

    146/160

  • 8/17/2019 Statis Momen

    147/160

  • 8/17/2019 Statis Momen

    148/160

    02-

    0-1.2

    0302

    02-

    0-1.2

    0302

    021-

    02..

    012+

    023++

     1 : 30UKANAH ATAUAIKAN AGARRNYADILIHAT

     1 : 30UKANAH ATAUAIKAN AGARRNYA

  • 8/17/2019 Statis Momen

    149/160

    0+331

    012+

    0-1.<

    0-32

    0-23+

    0-00+

     

  • 8/17/2019 Statis Momen

    150/160

  • 8/17/2019 Statis Momen

    151/160

    3ONTO8 SOA# BETON PRESTRESS

    Balok prestress diatas dua tumpuan :

    Panjang balok = 1+

    Initial ga&a prestress = 1100

    Beban hidup = 12ksentrisitas !gs " !g! = 32+

    (itung tegangan di tengah bentang

    )ehilangan jangka pendek = 10*

    )ehilangan jangka panjang = 10*

    Aimana7

    '!u = +0

    '!i = 30

    Jawaban

    #uas $ena%$ang ba&'k

    b1 = -00 mm

    h1 = 200 mm

    b2 = 1+0 mm

    h2 = 3+0 mm

    b3 = -00 mm

    h3 = 200 mm

     1 = b1h1 = 0000mm2

     2 = b2h2 = +2+00mm2

     3 = b3h3 = 0000mm2

      = 1 2 3 = 212+00mm2

      = 444 mm2

    &1 =

  • 8/17/2019 Statis Momen

    152/160

    0000 5 .+0 +2+00 5 3

  • 8/17/2019 Statis Momen

    153/160

    = 444 mm

    = 444 mm

    )eng*itung Beban

    +1kN/m1

    2- kN/m3

    Beban hidup = 12 kN/m

    >otal ser%i!e load = Berat sendiri balok Beban hidup

    = 1

  • 8/17/2019 Statis Momen

    154/160

    = -.. 4   1. 5   -0

    = "0-2 N/mm2

    = -.. 5   1. 4   -0

    =

  • 8/17/2019 Statis Momen

    155/160

    Tegangan 0ang dii7inkan ,stress &i%its

    1. Pada k'ndisi trans(er ,at trans(er

      #lass 27 post"tensioned$

    = "03. 5 30 9 1/2

    = "1< N/mm2

    = 0+ 5 30

    = 1+00N/mm2

    2. Pada k'ndisi ser6is ,at ser6i-e

      #lass 27 post"tensioned$

    = "03. 5 +0 9 1/2

    = "2++ N/mm2

    = 033 5 +0

    = 1.+0N/mm2

    esi%$u&an

    1 Pada kondisi trans'er #at trans'er$

    >egangan &ang terjadi

    "0-2 N/mm2 "1< N/mm2

    egangan &ang terjadi

    . N/mm2 "2++ N/mm2

    "1-1 N/mm2 1.+0 N/mm2

    ' tt = "03.#' 

    !i$1/2 N/mm2

    ' !t = 0+' 

    !i N/mm2 #'le5ural members$

    ' ts = "03.#' 

    !u$1/2 N/mm2

    ' !s

     = 033' !u

     N/mm2 #'le5ural members$

    ' 1t =

    ' 2t =

    ' 1s

     =

    ' 2s

     =

    ,andnkan d'

    'anan yan$'runan s'

  • 8/17/2019 Statis Momen

    156/160

    m

    kN

    kN/mmm

    N/mm2

    N/mm2

  • 8/17/2019 Statis Momen

    157/160

    yb

    a

  • 8/17/2019 Statis Momen

    158/160

  • 8/17/2019 Statis Momen

    159/160

  • 8/17/2019 Statis Momen

    160/160