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    BAB III

    PERHITUNGAN PORTAL LANTAI 2

    A.Perhitungan Portal

    I2 I2

    I1I1

    A

    B

    C

    D

    E

    1.82

    4.00

    5.33

    h=

    f =

    S=

    10.00L=

    Gambar 3.1 Gambar Rencana Portal

    1.Data Perhitungan

    Bentang kuda kuda = 10 m

    Tinggi kolom = 4 m

    Tinggi kuda-kuda = 1,8 m

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    !i"i miring kuda-kuda = #,33 m

    $arak gording = 1,# m

    $arak antar kuda-kuda = 4 m

    %emiringan ata& = 0'

    Berat &enutu& ata& = 10 kg(m) *!eng Gelombang+

    Berat &laon dan &enggantung = 10 = 1 kg(m)

    2.Pembebanan u!a"#u!a $a%&tang'

    Balok /ang direncanakan menggunakan 3#0.3#0.10.12 = 142 cm

    = 11# kg(m

    I5 = 33300 cm4I/ = 1100 cm4

    5 = 1640 cm3

    / = 242 cm3

    a. Beban gording Berat "endiri &enutu& ata&7 4 m 5 10 kg(m5 1,# m = 20 kg Berat "endiri gording7 10 kg(m 5 4 m = 40 kg Berat "endiri kuda-kuda 7 1 ,# m 5 11# kg(m = 1,# kg

    = ,# kg

    Berat alat &en/ambung 7 10 5 Berat total = ,# kg tot = 66,# kg Berat 9idu& *P+ = 00 kg

    P tot = 466,# kg

    b.Beban merata

    q= P

    1

    2 L

    q=9 .499,75

    1

    2.10

    = 866,## kg(m

    c. Beban angin

    Beban angin untuk gedung tertutu& dengan ata& "egitiga dengan kemiringan

    : 2#o* P;I 160, 9al 0+ maka, %oei"ien angin tekan7

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    00,. < -0,4 = 0,0 5 0 0,4 = 0

    %oei"ien angin 9i"a& = -0,4>ntuk dinding ?ertikal di&i9ak angin, koei"ienn/a 0,60 dan untuk

    dibelakang angin adala9 0,4

    Pembebanan &ada ata&- ngin tekan *@t+

    t = koei"ien angin tekan 5 Aarak kuda-kuda 5 @= 0,1 5 4 m 5 # kg(m = 10 kg(m

    - ngin 9i"a& *@9+9 = koei"ien angin 9i"a& 5 Aarak kuda-kuda 5 @

    = -0,4 5 4 5 # kg(m = -40 kg(m

    Pembebanan kolom te&i- ngin tekan *@t+

    t = koei"ien angin tekan 5 Aarak kuda-kuda 5 @= 0,6 5 4 m 5 # kg(m = 60 kg(m

    - ngin 9i"a& *@9+9 = koei"ien angin 9i"a& 5 Aarak kuda-kuda 5 @

    = -0,4 5 4 5 # kg(m = -40 kg(m

    d. %ombina"i Pembebanan &ada %uda-kuda

    Pembebanan teta&Beban mati beban 9idu& = 866,## kg(m

    Pembebanan "ementaraBeban mati Beban 9idu& Beban angin

    >ntuk kombina"i &embebanan &ada &embebanan angin diuba9 menAadi beban

    ?ertikal7 = t . co" 0o= 10 co" 0o= 6,362 kg(m = 9 . co" 0o= -40 co" 0o= - 3,#84 kg(m

    = beban angint = 866,## 6,362

    = 608,642 kg(m9 = 866,## *-3,#84+

    = 821,622 kg(m

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    >ntuk &er9itungan momen, maka dari beban diata" diambil &embebanan /ang

    terbe"ar 7 *t = 608,642 kg(m+

    (. Perhitungan ga)a"ga)a !alam %a!a %ortal

    >ntuk mencari be"arn/a momen /ang terAadi &ada "truktur &ortal diata",

    digunakan rumu" menurut Ra9men ormeln %leinlogel adala9 "ebagai berikut 7

    a. %oei"ien

    k=I2

    I1.

    h

    s=

    20400

    20400. 4

    5,33=0,750 m

    =f

    h=

    1,82

    4=0,455 m

    m=1+ = 1 0,4## = 1,4## m

    B = *k 1+ m = *0,#0 1+ 1,4## = 4,6## m

    C = 1 m = 1 5 1,4## = 3,61 m

    D = B m 5 C = 4,6## 1,4## 5 3,61 = 10,24 m

    A

    B

    C

    D

    E

    10.00L=

    1.82

    4.00h=

    f =

    W

    b.Ti&e I *akibat beban dari ata& dan angin ara9 ?ertikal+

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    - Perhitungan momen beban mati

    @ = t = 608,642 kg(m

    ;B = ;E =w L2(3+5 . m )

    16N=

    908,946 x 102(3+5 . 1,455)16 .10,64

    = -#482,03 kgm

    ;C =w L

    2

    8+m MB =

    908,946x102

    8 1,4## 5 *-#482,03+

    = 11321,8 *-68,31+

    = 336,#1 kgm

    - Reaksiakhir

    F= F=

    w , L

    2 =

    908,946 .10

    2 = 4#44,3 kg

    H = H=MB

    h=

    (5486,03)4

    = 131,#1 kg

    - Perhitungan momen beban hidup

    P = 00 kg

    m = . P. J = . 00 kg . 10 m = #00 kgm

    = 8. mL

    2 = 8.50010

    2 = 40 kg(m

    ;B = ;E =w L2(3+5 . m)

    16N=

    40x102(3+5 .1,455)16 .10,64

    = -41,4 kgm

    ;C =w L

    2

    8+m MB =

    40x102

    81,4## 5 *-41,4+

    = #00 *-3#1,22+

    Gambar 3. Pembebanan ra9 Fertikal

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    = 148,34 kgm

    - Reaksi akhir

    F= F=w , L

    2=

    40 .10

    2= 00 kg

    H = H=MB

    h=

    (241,42)4

    = 20,3## kg

    - Perhitungan momen beban angin

    t = 60 kgm

    @ = t 5 0,#

    = 60 kgm 5 0,# = 4#

    ;B = ;E =w L2(3+5 . m )

    16N=

    45x102(3+5 . 1,455)16 . 10,64

    = -1,20 kgm

    ;C =w L

    2

    8+m MB =

    45x102

    81,4## 5 *-1,20+

    = #2,# *-36#,1+

    = 12,3 kgm

    - Reaksiakhir

    F= F=w , L

    2=

    45 .10

    2= # kg

    H = H=

    MBh =

    (271.60)4 = 2,6 kg

    Eari &er9itungan diata" dida&atkan 9a"il 7

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    HE

    B

    C

    D

    VA

    HE

    VE

    ME

    --

    HA

    -

    +

    -

    +

    S/2

    wf16

    MA

    A E

    ;B = ;E = -#482,03 kgm

    ;C = 336,#1 kgm

    F = F = 4#44,3 kg

    H = H= 131,#1 kg

    N=VA sin+HA cos=4544,73sin200+1371,51cos200=2843,18kg

    = VA co" < = 4544,73cos20o = 40,24 kg

    Gambar3.3 Eiagram ;omen, Ga/a Jintangdan Ga/a Dormal

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    E = co"< D "in < = 40,24 co" 0o 843,18 "in 0o = 468#,#1 kg

    c. Ti&e II *akibat beban angin ara9 9oriKontal+

    = t . co" #o= 10 co" 0o= 6,362 kg(m = 9 . co" #o= -40 co" 0o= - 3,#86 kg(m

    A

    B

    C

    D

    E

    10.00L=

    1.82

    4.00h=

    f =

    Ei&akai nilai /ang terbe"ar = 6,362 kg(m

    - Perhitungan momen primer

    Gambar 3.4 Pembebanan ngin Pada ta& ra9 HoriKontal

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    L=w f

    2(C+m)8.N

    =9,396 x 1,82

    2(3,91+1,455)8 . 10,64

    = 1,0 kgm

    ;B= L wfh2

    = 1,0 9,396 .1,82 . 42

    = 1,0 34,0

    = 3#, kgm

    ;C= -w f

    2

    4 mL = - 9,396 .1,82

    2

    4 1,4## 5 3#,

    = -,8 #1,3

    = -43,#4 kgm

    ;E = L - wfh

    2 = 1,0

    9.396 .1,82 . 4

    2

    = 1,0 34,0

    = -33,13 kgm

    - Reaksi akhir

    F=-F= -wfh(1+m)

    2L= -

    9,396 .1,82 .4(1+1,455)2.10

    = -8,36 kgH=

    Xh

    w f2

    4= 1,077

    4

    9,396 .1,822

    4

    = - 0,26 ,8

    = -8,046 kg

    H =X

    h+

    w f2

    4= 1,077

    4 +

    9,369 .1,822

    4

    = -0,26 ,8

    = 8,046 kg

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    = -10,433 kg

    = VA co" < = 8,39cos20o = -,88 kg

    E = co"< D "in < = *-,88+ co" 0o *-10,433+ "in 0o

    = -10,6 kg

    d. Ti&e III *akibat beban angin ara9 kolom 9oriKontal+

    t = koei"ien angin tekan 5 Aarak kuda-kuda 5 @= 0,6 5 4 m 5 # kg(m = 60 kg(m

    A

    B

    C

    D

    E

    10.00L=

    1.82

    4.00h=

    f =

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    HA

    B D

    VA

    MA

    VE

    -+

    wf8

    2.00

    C -

    H= (whHE) = -* 5 4 8,3+ = -06, kg

    Eari &er9itungan diata" dida&atkan 9a"il 7

    ;B = 402,8 kgm

    ;C = -6#,02 kgm

    Gambar3.Eiagram ;omen, Ga/a Jintangdan Ga/a Dormal

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    ;E = -313, kgm

    F = -F = - kg

    H = -06, kg

    H= 8,3 kg

    N=VA sin+HAcos=72sin 200+(209,7)cos200

    = -1,2 kg

    = VA co" < = 72cos20o = -2,2# kg

    E = co"< D "in < = *-2,2#+ co" 0o *-1,2+ "in 0o

    = *-23,#+ *-#,81+ = 136,38 kg

    e. Tabel kombina"i &embebanan

    kibat beban

    merata

    kibat angin

    &ada ata&

    kibat angin

    &ada kolom

    Ha"il *Eiambil

    ;omen /ang

    terbe"ar +;mak" -#482,03 -43,#4 -402,8 #482,03 kgm

    D 843,18 10,43 221,67 843,18 kg 40,24 kg -,88 kg -2,2# 40,24 kgE 468#,#1 -10,6 136,38 468#,#1 kg

    ;mak" = #482,03 kgm

    D = 843,18 kg = 40,24 kg

    E = 468#,#1 kg

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    B. Perhitungan Dimen&i Penam%ang

    Eigunakan baAa ti&e 3#0.3#0.10.12 *tabel &roil baAa 9al +

    3

    0.10

    3.50

    0.16

    = 11#,0 kg(m

    = 142,0 cm

    5 = 1640 cm4

    / = 242 cm4

    I5 = 33300 cm3

    I/ = 1100 cm3

    i5 = 1#,1 cm

    i/ = 8,8 cm

    b = 3#0 mm = 3# cm

    9 =3#0 mm = 3# cm

    tb = 10mm = 1,0 cm

    t" = 12mm = 1,2 cm

    1. ontrol tegangan

    Wx

    M

    A

    N+=

    Gambar 3.8 BaAa 3#0.3#0.10.12

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    =3 1640

    03,#482

    0,142

    843,18

    cm

    kgcm

    cm

    kg+

    (1400(301, cmkgijincmkg ==

    2. ontrol tegangan ge&er

    (811400#8,0

    #8,0

    cmkgx

    ijinx

    ==

    =

    M = *b t"+ . 4.

    htbhtsh +

    = 43#.

    0,13#

    2,13#.+2,13#*

    +

    = 02,#3 cm

    = N .

    ! .Ix: *PPBBI 1684 7 #+

    2843,18 kg .706,53 cm

    2

    1,0cm .33300 cm4

    = 20,34 kg(cm : 02,#3 kg(cm *N%+

    3.50

    0.10

    3.50

    0.16

    22,301 k/!"

    60,324 k/!"

    22,301 k/!"

    (. ontrol %erubahan bentu# %enam%ang

    Gambar3.6 Eiagram Tegangan

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    PPBBI O84 7 41 *1+ 7

    h

    ! #

    35cm1,0cm

    #

    3# cm # *N%+

    ;encari &anAang tekuk "endi-"endi *PPBBI 1684 9al 1#+

    Jk = 1,0 J

    = 1,0 5 #,33 = #,33 m = #,33 cm

    L

    h. Q 1,#

    !

    s =

    5,33

    0,35>1,25 0,35

    0,016

    = 1#,3 cm Q ,34 cm *N% +

    Eari &er9itungan diata" ba9@a &enam&ang tidak beruba9 bentuk.

    *. ontrol len!utan

    *PPBBI, 168471#+ bata" lendutan mak"imum ara9 ?ertical untuk balok

    &endukung ata& adala9 J(#0.

    Jk = 1,0 J

    = 1,0 5 #,33

    = #,33 m

    ma5=1

    250L =

    1

    250#,33 = ,13 cm

    = 5q"L4

    348E I"

    = 5.37 .5334

    348 .2100000 .33300=0,61 cm : ma5 = ,13 cm *N%+

    +. ontrol li%at

    Ji&at "a/a&

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    *PPBBI, 168474+ &a"al . a/at 2, untuk mema"tikan ba9@a "tabilita" batang-

    batang tekan atau elemen /ang dibebani lentu rtidak terganggu ole9 ba9a/a

    li&at &erbanding anantara lebar dan tebal &elat 9aru" memenu9i 7

    !s

    #10

    $%$&

    Eimana 7 d = tegangan tekan terbe"ar /ang terAadi *9arga mutlak 1+ r = 32 kg(cm untuk &elat-&elat /ang tidak di&erkuat

    350

    16#10

    3267

    449,68'21,875 #26,95 *N%+

    Ji&at badan

    !e"uai PPBBIO84 9alaman 4 Bab 2 a/at 3, ba9@a dalam &emerik"aan ter9ada&

    ba9a/a li&at, keem&at "i"i badan itu diangga& ber"iat "endi. $ika &erbandingan

    antara tinggi dan tebal badan lebi9 kecil dari 20, &emerik"aan ter9ada& ba9a/a

    li&at dari badan tidak di&erlukan.

    Perbandingan tinggi dantebal badan7350

    10=35

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    B E

    A E

    C

    SAMB#$%A$ C &SAMB#$%A$ 'ADA

    '#$CA( (A'S)A$%*

    C

    0.2

    1.0

    1.0

    1.0

    1.0

    1.0

    0.8

    0.2

    = 3#0 L 3#0 L 10 L 12

    ,. Perhitungan

    -ambungan Pa!a Puna# a%&tang

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    Eata &er9itungan 7

    ;ma5 = #48203 kgcmEma5 = 468#,#1 kg

    D = 843,18 kgEirencanakan "ambungan menggunakan baut dan la".>ntuk tebal &elat &en/ambung /ang di&akai adala9 10 mm dan diameter

    bautn/a adala9 12 mm.

    1. Per9itungan !ambungan Baut

    Tenga9S ,# d u d

    S ,# *+ u *+

    S ## u 1#4 di&akai Aarak u = 80 mm

    8 cm di&akai Aarak u = 100 mm10 cm

    Te&iS 1,# d u1 3 dS 1,# *+ u1 3 *+S 33 u1 22 di&akai Aarak ! = #0 mm# cm

    Gambar3.10 Perletakan !ambungan

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    di&akai Aarak ! = 20 mm2 cm

    Gambar 3.11 Rencana !ambungan Baut

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    a. %ontrol tegangan tarik baut

    Plat &en/ambung tebal 10 mm, di&akai baut U 12 mm

    /1 = 2 cm /1

    = 2

    = 32 cm

    / = 14 cm / = 14 = 162 cm

    /3 = 4 cm /3 = 4 = #2 cm

    /4 = 34cm /4 = 34 = 11#2 cm

    /# = 44 cm /# = 44 = 1632 cm

    /2 = #4cm /2 = #4 = 612 cm

    V/ = 2812 cm

    D1=M " . (1

    2 (2 =

    548603 kgcm .6cm

    2" 6816 cm2 = 41,42 kg

    D=M " . (

    2

    2 (2

    =548603 kgcm .14 cm

    2" 6816 cm2 = #23,41 kg

    D3=M " . ( 3

    2 (2 =

    548603 kgcm .24cm

    2" 6816 cm2 = 62#,8#0 kg

    D4=M " . (

    4

    2 (2

    =548603 kgcm .34cm

    2" 6816 cm2 = 1328,8 kg

    D#=M " . ( 5

    2 (2 =

    548603 kgcm .44cm

    2" 6816 cm2 = 10,# kg

    D2=M " . ( 6

    2 (2

    = 548603 kgcm .54 cm2" 6816 cm

    2 = 13,123kg

    >ntuk &er9itungan kontrol tegangan tarik baut diambil nilai D /ang terAau9

    /aitu D2.

    tarikbaut=N

    1

    4. ) .

    2 =2173,163 kg

    1

    4. 3,14 .(2,2)2 = #1,68 kg(cm

    #1,68 kg(cm

    : 0, *1400 kg(cm

    +#1,68 kg(cm : 680 kg(cm *N%+

    b.%ontrol ge"er akibat ga/a lintang

    W=D

    1

    43,14" &

    2 =4 985,51

    1

    4. 3,14 . 2,2

    2

    = 810,0 kg(cm : 0,#8 = 81 kg(cm* N% +

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    %ombina"i tegangan ge"er X tegangan tarik /ang diAinkan

    *PPBBI O84 9al. 28+

    i =

    #2,1 +

    = +0,810*#2,168,#1 +

    = 112,2 kg(cm) : 1400 kg( cm) *N%+

    . Per9itungan !ambungan Ja"

    a. Tebal la"

    Tebal la" badan = Y 5 Z 5 4 = ,8 mm [ 3 mm

    Tebal la" "a/a& = Y 5 Z 5 6 = 2,4 mm [ 2 mm

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    b. !tati" momen la" ter9ada& la" bagian ba@a9

    Bidang $umla9 b 9 $arak Jua" ;omen !tati" bua9 cm cm cm cm cm3

    !1 1 0,00 0,20 0,30 1 3,20! 6,0 0,20 ,0 11,04 4,88!3 0,30 1,2# 10,4# 10,#6 110,4!4 6,0 0,20 16,# 11,04 1,#!# 6,0 0,20 0,8# 11,04 30,18!2 0,30 3,4# 36,## ,4 886,#

    ! 6,0 0,20 #8,30 11,04 243,23!8 1 0,00 0,20 #6,60 1 18,8

    Total 101, 83,2

    $arak titik berat &roil *"umbu 5+ akibat la" *ditinAau dari la" bagian ba@a9+7

    Lb= V!( V

    = 83,2cm3 (101, cm

    = ,68 cm *dari la" bagian ba@a9+

    $arak titik berat &roil *"umbu 5+ akibat la" *ditinAau dari la" bagian ata"+7La= 9 total &roil "etela9 dila" Lb

    = #6,60 cm ,68cm

    = 31,6 cm *dari bagian ata" la"+

    Gambar 3.1 Perencanaan !ambungan Ja"

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    I5 = 1

    12b93 J

    Bidang $umla9 b 9 $arak Jua" ;omen Iner"ia bua9 cm cm cm cm cm3

    !1 1 0,00 0,20 ,68 1 406,88! 6,0 0,20 #,8 11,04 314,11!3 0,30 1,2# 12,## 10,#6 18#2,0#!4 6,0 0,20 ,3 11,04 64,14!# 6,0 0,20 #,#3 11,04 24,01!2 0,30 3,4# 13,16# ,4 222,1! 6,0 0,20 6, 11,04 32,3!8 1 0,00 0,20 31,6 1 4#6#,1

    Total 101, ##4,36

    b =25524,39

    27,98=912,06 cm3

    a =25524,39

    31,92=799,77 cm3

    c. %ontrol tegangan la"

    kibat ;omen

    $m=M*+=548603799,77 = 28#,6# kg(cm: 1400 kg(cm *N%+

    d.kibat ga/a ge"er

    = E(= 468#,#1 (101,= 46,# kg(cm

    ;enurut PPBBI 16847#

    $i&=$2+3 ()

    2# $i,in

    $i&=685,952

    +3 ( 49,25 )2

    # $iin

    Gambar 3.13 Titik Berat !ambungan Ja"

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    $i& = 261,33 kg(cm : $iin = 0, 5 1400 kg(cm

    $i& = 261,33 kg(cm : $iin = 680 kg(cm * N%+

    3.50

    0.10

    3.50

    0.16

    4+,25 k/!"

    6+1,233 k/!"

    6+1,233 k/!"

    D. Perhitungan antile/er $O/er&te#'

    1. Per9itungan Pembebanan

    a. Pembebanan kantile?er

    Gambar 3.14 Eiagram Tegangan

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    Berat "endiri &enutu& ata&7 4 m 5 10 kg(m5 1,# m = 20 kg( m

    Berat "endiri gording7 11kg/m .4m.1!-+h

    1,50m= 6,33

    kg( mBerat "endiri kuda-kuda 7 1 ,# m 5 11# kg(m = 1 ,# kg ( m

    = 21,83 kg( mBerat alat &en/ambung 7 10 5 Berat total = 2,183 kg ( m tot = 88,013 kg( m

    Berat 9idu& *P+ = 00 kg ( mP tot = 488,013 kg( m

    b. Reak"i /ang bekerAa;mak"= Y . . J

    = Y 5 488,013 kg(m 5 *1,#+m

    = #46,014 kgm = #4601,4 kgcmF = = 5 J= 488,013 kgm 5 1,#0 m= 3,016 kg

    D = F5 "in