BAB IV

PERHITUNGAN KONTRUKSI

4.1 Data Perencanaan

Jarak antar portal : 3 m

Jumlah trave : 11 Trave

Fungsi bangunan : Gedung Kuliah

Kuat tekan beton ( fc’) : K-225 = 22.5 Mpa

Tegangan Leleh Tulangan Polos : 240 Mpa

4.2 Perhitungan Dimensi balok

Menentukan dimensi balok dengan rumus pendekatan :

Balok Memanjang

Bentang : 3,5 m = 350 cm

hmax =

hmin =

dipakai h = 40 cm

bmax =

bmin =

dipakai b = 30 cm → ( dilapangan dipakai 30 / 40 )

Balok Melintang

Bentang : 8 m = 800cm

hmax =

hmin =

38

dipakai h = 60 cm

bmax =

bmin =

dipakai b = 30 cm → ( dilapangan dipakai 30 / 60 )

Bentang : 4 m = 400cm

hmax =

hmin =

dipakai h = 40 cm

bmax =

bmin =

dipakai b = 30 cm → ( dilapangan dipakai 30 / 40 )

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4.3. Perencanaan Plat Lantai

●► Perhitungan Tebal Plat

- Plat LantaiTipe A

F’c = 22,5 Mpa ; dimensi balok induk memanjang = 25/40

Fy = 240 Mpa ; dimensi balok induk melintang = 30/60

Lx = 300 cm

Ly = 800 cm

Ln = Ly – b

= 800 – 2 ( ½ * 30 )

= 770 cm = 7700 mm

Sn = Lx – b

= 300 – 2 ( ½ * 30 )

= 270 cm = 2700 mm

β = = = 2.857 > 2 , Termasuk Plat 1 Arah

o K balok =

K plat =

α balok =

40

Ly = 800 cm

Lx = 300 cm

30\40

30\60

o K balok =

K plat =

α balok =

αm =

untuk αm > 2,0 menurut SNI 03 – 2847 – 2002 pasal 11.5.3.3, maka tebal plat minimum :

h min =

=

= 119,88 mm

Dan tidak boleh kurang dari 90 mm;

Maka tebal plat dipakai 120 mm.

- Plat Lantai Tipe H

F’c = 22,5 Mpa ; dimensi balok induk memanjang = 30/40

Fy = 240 Mpa ; dimensi balok induk melintang = 30/40

Lx = 400 cm

Ly = 400 cm

41

Ly = 400 cm

Lx = 400 cm

30\40

30\40

Ln = Ly – b

= 400 – 2 ( ½ * 30 )

= 370 cm = 3700 mm

Sn = Lx – b

= 400 – 2 ( ½ * 30 )

= 370 cm = 3700 mm

β = = = 1 < 2 , Termasuk Plat 2 Arah

o K balok =

K plat =

α balok =

o K balok =

K plat =

α balok = =

αm =

untuk αm > 2,0 menurut SNI 03 – 2847 – 2002 pasal 11.5.3.3, maka tebal plat minimum :

h min =

=

= 78,93 mm

Dan tidak boleh kurang dari 90 mm;

Maka tebal plat dipakai 120 mm.

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- Plat Lantai Tipe C

F’c = 22,5 Mpa ; dimensi balok induk memanjang = 30/60

Fy = 240 Mpa ; dimensi balok induk melintang = 30/40

Lx = 800 cm

Ly = 400 cm

Ln = Ly – b

= 400 – 2 ( ½ * 30 )

= 370 cm = 3700 mm

Sn = Lx – b

= 800 – 2 ( ½ * 30 )

= 770 cm = 7700 mm

β = = = 0,481 < 2 , Termasuk Plat 2 Arah

o K balok =

K plat =

α balok =

o K balok =

43

Ly = 400 cm

Lx = 800 cm

30\60

25\40

K plat =

α balok = =

αm =

untuk αm > 2,0 menurut SNI 03 – 2847 – 2002 pasal 11.5.3.3, maka tebal plat minimum :

h min =

=

= 88,076 mm

Dan tidak boleh kurang dari 90 mm;

Maka tebal plat dipakai 120 mm.

- Plat Lantai Tipe D

F’c = 22,5 Mpa ; dimensi balok induk memanjang = 30/40

Fy = 240 Mpa ; dimensi balok induk melintang = 30/40

Lx = 500 cm

Ly = 300 cm

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Ln = Ly – b

= 300 – 2 ( ½ * 30 )

= 270 cm = 2700 mm

Sn = Lx – b

= 500 – 2 ( ½ * 30 )

= 470 cm = 4700 mm

β = = = 0,574 < 2 , Termasuk Plat 2 Arah

o K balok =

K plat =

α balok =

o K balok =

K plat =

α balok = =

αm =

45

Ly = 300 cm

Lx = 500 cm

30\40

30\40

untuk αm > 2,0 menurut SNI 03 – 2847 – 2002 pasal 11.5.3.3, maka tebal plat minimum :

h min =

=

= 62,965 mm

Dan tidak boleh kurang dari 90 mm;

Maka tebal plat dipakai 120 mm.

- Plat Lantai Tipe E

F’c = 22,5 Mpa ; dimensi balok induk memanjang = 30/40

Fy = 240 Mpa ; dimensi balok induk melintang = 30/40

Lx = 500 cm

Ly = 400 cm

Ln = Ly – b

= 400 – 2 ( ½ * 30 )

= 370 cm = 3700 mm

Sn = Lx – b

= 500 – 2 ( ½ * 30 )

= 470 cm = 4700 mm

β = = = 0,787 < 2 , Termasuk Plat 2 Arah

o K balok =

46

Ly = 400 cm

Lx = 500 cm

25\40

25\40

K plat =

α balok =

o K balok =

K plat =

α balok = =

αm =

untuk αm > 2,0 menurut SNI 03 – 2847 – 2002 pasal 11.5.3.3, maka tebal plat minimum :

h min =

=

= 82,446 mm

Dan tidak boleh kurang dari 90 mm;

Maka tebal plat dipakai 120 mm.

- Plat Lantai Tipe F

F’c = 22,5 Mpa ; dimensi balok induk memanjang = 30/60

Fy = 240 Mpa ; dimensi balok induk melintang = 30/40

Lx = 800 cm

Ly = 200 cm

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Ln = Ly – b

= 200 – 2 ( ½ * 30 )

= 170 cm = 1700 mm

Sn = Lx – b

= 800 – 2 ( ½ * 30 )

= 770 cm = 7700 mm

β = = = 0,221 < 2 , Termasuk Plat 2 Arah

o K balok =

K plat =

α balok =

o K balok =

K plat =

α balok = =

αm =

48

Ly = 200 cm

Lx = 800 cm

30\60

25\40

Ly = 250 cm

Lx = 300 cm

30\40

30\60

untuk αm > 2,0 menurut SNI 03 – 2847 – 2002 pasal 11.5.3.3, maka tebal plat minimum :

h min =

=

= 42,960 mm

Dan tidak boleh kurang dari 90 mm;

Maka tebal plat dipakai 120 mm.

- Plat Lantai Tipe B

F’c = 22,5 Mpa ; dimensi balok induk memanjang = 30/40

Fy = 240 Mpa ; dimensi balok induk melintang = 30/60 & 30/30

Lx = 300 cm

Ly = 250 cm

Ln = Ly – b

= 250 – 2 ( ½ * 30 )

= 220 cm = 2200 mm

Sn = Lx – b

= 300 – ( ½ * 30 + ½ * 30)

= 270 cm = 2700 mm

β = = = 0,815 < 2 , Termasuk Plat 2 Arah

o K balok =

K plat =

49

α balok =

o K balok =

K plat =

α balok =

αm =

untuk αm > 2,0 menurut SNI 03 – 2847 – 2002 pasal 11.5.3.3, maka tebal plat minimum :

h min =

=

= 48,737 mm

Dan tidak boleh kurang dari 90 mm;

Maka tebal plat dipakai 120 mm.

- Plat Lantai Tipe G

F’c = 22,5 Mpa ; dimensi balok induk memanjang = 30/60

Fy = 240 Mpa ; dimensi balok induk melintang = 30/40

Lx = 800 cm

Ly = 300 cm

50

Ln = Ly – b

= 300 – 2 ( ½ * 30 )

= 270 cm = 2700 mm

Sn = Lx – b

= 800 – 2 ( ½ * 30 )

= 770 cm = 7700 mm

β = = = 0,351 < 2 , Termasuk Plat 2 Arah

o K balok =

K plat =

α balok =

o K balok =

K plat =

α balok =

51

Ly = 300 cm

Lx = 800 cm

30\60

30\40

αm =

untuk αm > 2,0 menurut SNI 03 – 2847 – 2002 pasal 11.5.3.3, maka tebal plat minimum :

h min =

=

= 66,192 mm

Dan tidak boleh kurang dari 90 mm;

Maka tebal plat dipakai 120 mm.

Pembebanan Lantai 2 Tipe Plat A

Beban mati yang bekerja pada plat

Beban mati ( qd )

B.S.plat = 0,12 x 2400 = 288 kg/m2

B.spesi + tegel = ( 21 x 3 ) + ( 2 x 24 ) = 111 kg/m2

B.plafon+penggantung = ( 11 + 7 ) = 18 kg/m 2 +

qd = 417 kg/m2

Beban hidup ( ql )

Fungsi bangunan ( pasar ) = 250 kg/m2

Beban terfaktor ( qu )

qu = 1,2 ( qd ) + 1,6 ( ql )

= 1,2 ( 417 ) + 1,6 ( 250 )

= 900,4 kg/m2

Momen yang terjadi ( lantai 2 ) ditinjau tiap 1m

β =

( dari tabel Gideon Lampiran 1 )

2,5 3,0

Clx 62 65

52

Cly 14 14

Ctx 83 83

Cty 51 49

Interpolasi untuk mendapatkan nilai C pada angka 2,667 :

Clx = = 62,002

Cly = = 14

Ctx = = 83

Cty = = 50,332

Rumus umum : Mu = 0,001 x qu x Lx2 x C

Mlx = 0,001 x 900, 4 x 3,002 x 62,002 = 502,439 kgm

Mly = 0,001 x 900, 4 x 3,002 x 14 = 113,450 kgm

Mtx = -0,001 x 900, 4 x 3,002 x 83 = -672,599 kgm

Mty = -0,001 x 900, 4 x 3,002 x 50,332 = -407,870 kgm

Perhitungan Penulangan Plat

o Penulangan lapangan Arah x

Digunakan Tulangan Ø 10 dan selimut beton 20 mm

dx = h - D - ½ Ø

= 120 – 20 – ½ .10

= 95 mm

Mlx = Mu = 502,439 kgm = 502,439 x 103 Kgmm

Mn = = = 628,049 x 103 kgmm

53

Rn = = = 0,070 Mpa

m = = = 12,549 Mpa

Rasio penulangan keseimbangan ( ρb )

ρb = x0.85x

= x0.85x

= 0.0483

ρ max = 0.75 x ρb

= 0.75 x 0.0483

= 0.0362

ρ min = = = 0.00583

ρ =

=

= 0,00029

ρ < ρ min = 0.00583 maka dipakai nilai ρ min = 0.00583

As perlu = ρ x b x dx

= 0.00583 x 1000 x 95

= 553,85 mm2

Direncanakan tulangan pokok Ø 10 mm maka,

As = ¼ π Ø 2

= ¼ π 10 2 = 78, 540 mm2

Jarak antar tulangan (S)

SPerlu =

54

= = 141,807 mm dipakai S = 140 mm

Kontrol : As ada =

=

= 561 mm2 > As perlu = 553,85 mm2

Jadi dipakai tulangan pokok Ø 10 mm – 140 mm

o Penulangan lapangan arah y

Digunakan Tulangan Ø 10 dan selimut beton 20 mm

dy = h - D – Ø - ½ Ø

= 120 – 20 –10 - ½ .10

= 85 mm

Mly = Mu = 113,450 kgm = 113,450x 103 kgmm

Mn = = = 141,813 x 103 kgmm

Rn = = = 0,020 Mpa

m = = = 12,549 Mpa

Rasio penulangan keseimbangan ( ρb )

ρb = x0.85x

= x0.85x

= 0,0483

ρ max = 0.75 x ρb

= 0.75 x 0.0483

= 0.0362

55

ρ min = = = 0.00583

ρ =

=

= 0.000083

ρ < ρ min = 0.00583 maka dipakai nilai ρ min = 0.00583

As perlu = ρ x b x dx

= 0.00583 x 1000 x 85 = 495,55 mm2

Direncanakan tulangan pokok Ø 10 mm maka,

As = ¼ π Ø 2

= ¼ π 10 2 = 78, 540 mm2

Jarak antar tulangan (S)

SPerlu =

= = 158,491 dipakai S = 150 mm

Kontrol : As ada =

= = 523,6 mm2 > As perlu = 495,55 mm2

Jadi dipakai tulangan pokok Ø 10 mm – 150 mm

o Penulangan tumpuan arah x

Digunakan Tulangan Ø 10 dan selimut beton 20 mm

dx = h - D - ½ Ø

= 120 – 20 – ½ .10

= 95 mm

Mtx = Mu = 672,599 kgm = 672,599 x 103 kgmm

56

Mn = = = 840,749 x 103 kgmm

Rn = = = 0,093 Mpa

m = = = 12,549 Mpa

Rasio penulangan keseimbangan ( ρb )

ρb = x0.85x

= x0.85x

= 0.0483

ρ max = 0.75 x ρb

= 0.75 x 0.0483

= 0.0362

ρ min = = = 0.00583

ρ =

=

= 0,000388

ρ < ρ min = 0.00583 maka dipakai nilai ρ min = 0.00583

As perlu = ρ x b x dx

= 0.00583 x 1000 x 95

= 553,85 mm2

Direncanakan tulangan pokok Ø 10 mm maka,

As = ¼ π Ø 2 = ¼ π 10 2 = 78.540 mm2

Jarak antar tulangan (S)

SPerlu =

= = 141,807 mm dipakai S = 140 mm

57

Kontrol : As ada =

=

= 561 mm2 > As perlu = 553,85 mm2

Jadi dipakai tulangan pokok Ø 10 mm – 140 mm

As. Tulangan bagi = 20 % As. Perlu

= 20% x 553,85 = 110,77 mm2

Dipakai tulangan bagi Ø 8 mm

As = ¼ π Ø 2

= ¼ π 8 2 = 50.265 mm2

Jarak antar tulangan (S)

S =

= = 453,782 mm dipakai S = 140 mm

Kontrol : As ada =

= = 359.036 mm2 > As perlu = 110,77 mm2

Dipakai tulangan bagi Ø 8 – 140 mm

58

o Penulangan tumpuan arah y

Digunakan Tulangan Ø 10 dan selimut beton 20 mm

dy = h - D - ½ Ø

= 120 – 20 – ½ .10

= 95 mm

Mty = Mu = 407,870 kg m = 407,870 x 103 kgmm

Mn = = = 509,838 x 103 kgmm

Rn = = = 0.056 Mpa

m = = = 12,549 Mpa

Rasio penulangan keseimbangan ( ρb )

ρb = x0.85x

= x0.85x

= 0,0483

ρ max = 0.75 x ρb

= 0.75 x 0.0483

= 0.0362

ρ min = = = 0.00583

ρ =

=

= 0.00023

ρ < ρ min = 0.00583 maka dipakai nilai ρ min = 0.00583

As perlu = ρ x b x dx

= 0.00583 x 1000 x 95

59

= 553,85 mm2

Direncanakan tulangan pokok Ø 10 mm maka,

As = ¼ π Ø 2

= ¼ π 10 2 = 78.540 mm2

Jarak antar tulangan (S)

S =

= = 141,807 mm dipakai S = 140 mm

Kontrol : As ada =

= = 561 mm2 > As perlu = 553,85 mm2

Jadi dipakai tulangan pokok Ø 10 mm – 140 mm

As. Tulangan bagi = 20 % As. Perlu

= 20% x 553,85 = 110,77 mm2

Dipakai tulangan bagi Ø 8 mm

As = ¼ π Ø 2

= ¼ π 8 2 = 50.265 mm2

S =

= = 453,782 mm dipakai S = 140 mm

Kontrol : As ada =

= = 453,778 mm2 > As perlu = 110.77 mm2

Dipakai tulangan bagi Ø 8 – 140 mm

Type Plat B (Kantilever)

Fc’ = 22,5 Mpa Lx = 300 cm

Fy = 240 Mpa Ly = 250 cm

60

Balok x = 30/40

Balok y = 30/60 & 30/30

Tebal plat kantilever = 120 mm

( dari tabel Gideon Lampiran 1 ) Dengan Interpolasi didapat :

1,2

Clx 34

Cly 22

Ctx 63

Cty 54

Rumus umum : Mu = 0,001 x qu x Lx2 x C

Mlx = 0.001 x 900, 4 x 2,502 x 34 = 191,335 kgm

Mly = 0.001 x 900, 4 x 2,502 x 22 = 123,805 kgm

Mtx = -0.001 x 900, 4 x 2,502 x 63 = -354,533kgm

Mty = -0.001 x 900, 4 x 2,502 x 54 = -303,885kgm

Beban yang bekerja

Beban mati ( qd )

B.S plat = 0.12 x 2400 = 288 kg/m2

Berat Spesi = 0.01 x 21 = 0.21kg/m2

B.plafon+penggantung = ( 11 + 7 ) = 18 kg/m 2 +

Beban mati qd = 306.21 kg/m2

Beban hidup ( ql )

B.orang = 100 = 100 kg/m2

B.air hujan = 0,05 x 1000 = 50 kg/m 2 +

Beban hidup ql = 150 kg/m2

Beban terfaktor (qu)

qu = 1,2 ( qd ) + 1,6 ( ql )

61

= 1,2 ( 306.21 ) + 1,6 ( 150 )

= 607.452 kg/m2

Beban lisplank

Pu = ( 0.15 x 0.5 ) 2400 x 1

= 180 kg

Momen yang terjadi

Mu = ( ½ .qu.L2 ) + ( Pu.L )

= ( ½.607.452 x 2,5 ) + ( 180 x 2,5 )

= 1209.315 kgm = 1209.315 x 104Nmm

Perhitungan tulangan direncanakan Ø 10

d = h - D - ½ Ø

= 120 – 20 – ½ .10

= 95 mm

Mlx = Mu = 1209.315 kgm = 1209.315 x 104Nmm

Mn = = = 1511,644 x 104 Nmm

Rn = = = 1.675 Mpa

m = = = 12,549 Mpa

Rasio penulangan keseimbangan ( ρb )

ρb = x0.85x

= x0.85x = 0.0483

ρ max = 0.75 x ρb

= 0.75 x 0.0483

= 0.0362

ρ min = = = 0.00583

ρ =

62

=

= 0.00731

ρ > ρ min = 0.00583 maka dipakai nilai ρ = 0.00731

As perlu = ρ x b x dx

= 0.00731 x 1000 x 95

= 694,45 mm2

Direncanakan tulangan pokok Ø 10 mm maka,

As = ¼ π Ø 2

= ¼ π 10 2 = 78.540 mm2

Jarak antar tulangan

S =

= = 113,096 mm dipakai S = 110 mm

Kontrol : As ada =

= = 714 mm2 > As perlu = 694,45 mm2

Jadi dipakai tulangan pokok Ø 10 mm – 110 mm

As. Tulangan bagi = 20 % As. Perlu

= 20% x 694,45 = 138,89 mm2

Dipakai tulangan bagi Ø 10 mm

As. = ¼ π Ø 2

= ¼ π 8 2 = 50,265 mm2

S =

= = 361,908 mm dipakai S = 140 mm

Kontrol : As ada =

63

= = 359,036 mm2 > As perlu = 138,98 mm2

Dipakai tulangan bagi Ø 8 – 140 mm.

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