perhitungan balok anak

FAKULTAS TEKNIK SIPIL DANPERENCANAAN

UNIVERSITAS KRISTEN PETRA

TUGAS STRUKTUR BETON Halaman:

BAGIAN STRUKTUR: NO. GAMBAR:

BALOK ANAKNRP: 21411012

21411174

PERHITUNGAN

BAB VI

BALOK ANAK

V.1. Spesifikasi Balok Anak

Balok anak memakai dimensi 250 x 350

Tulangan lentur D16 mm, fy = 400 MPa

Tulangan sengkang 10 mm, fy = 240 MPa

fc’ 30 MPa

V.2. Perhitungan Balok Anak BA-1

Gambar V.1. Pembebanan Balok Anak BA-1

Beban Pelat :

qD = 410,8 kg/m2

qD eq = = 542,256 kg/m’

MDL = 542,256 x 62 / 8 = 1694,55 kgm

MDT = 542,256 x 62 / 24 = 564,85 kgm

qL = 250 kg/m2

qL eq = = 330 kg/m’

MLL = 330 x 62 / 8 = 1031,25 kgm

MLT = 330 x 62 / 24 = 343,75 kgm

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Bs. Balok Anak :

qD = 2400 x 0,25 x 0,35 = 210 kg/m’

MDL = 210 x 62 / 8 = 656,25 kgm

MDT = 210 x 62 / 24 = 218.75 kgm

Momen Ultimate Lapangan :

1,4D : Mu = 1,4 x (1694,55 + 656,25) = 3291,12 kgm

1,2D + 1,6L : Mu = 1,2 x (1694,55 + 656,25) + 1,6 x 1031,25 = 4470,96 kgm

Jadi, Mu = 4470,96 kgm = 44,71 kNm

Momen Ultimate Tumpuan :

1,4D : Mu = 1,4 x (564,85 + 218.75) = 1097,04 kgm

1,2D + 1,6L : Mu = 1,2 x (564,85 + 218.75) + 1,6 x 343,75 = 1490,32 kgm

Jadi, Mu = 1490,32 kgm = 14,9 kNm

Geser Ultimate :

1,4D : Vu = 1,4 x (542,256 x 6 / 2 + 210 x 6 / 2) = 2632,896 kg

1,2D + 1,6L : Vu = 1,2 x (542,256 x 6 / 2 + 210 x 6 / 2) + 1,6 x 330 x 5 / 2

= 3576,768 kg

Jadi, Vu = 3576,768 kg = 35,768 kN

Tabel 6.1 Penulangan Lentur Balok Anak

Segmen Mu Mu/bd2 ρ As n tultul.

pasang

Tumpuan 14,9 699 0,0039 284,7 1,416 2D16

Lapangan 44,71 2097,485 0,0117 854,1 4,247 5D16

Tulangan tumpuan :

d = 350 – 40 – 10 – 0,5 x 16 = 292 mm

Mu/bd2 = 699 kg/m2

ρ = 0,0039

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PERHITUNGAN

As = ρ x b x d = 0,0039 x 250 x 292 = 284,7 mm2

As 1 D16 = 201,062 mm2

n tulangan = 284,7 / 201,062 = 1,416 (pakai 2 tulangan)

Jadi, tulangan tumpuan atas terpasang 2D16

Tulangan lapangan :

Mu/bd2 = 44,71 / (0,25 x 0,2922) = 2097,485 kg/m2

ρ = 0,0117 (dari tabel 5.1.c CUR IV)

As = ρ x b x d = 0,0117 x 250 x 292 = 854,1mm2

As 1 D16 = 201,062 mm2

n tulangan = 854,1/ 201,062 = 4,247 (pakai 5 tulangan)

Jadi, tulangan lapangan terpasang 5D16

Tabel 6.3 Penulangan Geser Balok Anak

Vu Vc Vu < Vc ?

S hitung S maxS terpakai

(kN) (kN) (mm) (mm)

35,768 45,625 YES 452,389 146 10 – 120

Vu kombinasi maks = 35,768 kN

Vc = 0,75 x 1/6 x x bw x d

= 0,75 x 1/6 x x 250 x 292/1000

= 45,625 kN

S = Avmin x 1200 x fy/(75 bw)

= 2 x 1/4 π x 102 x 1200 x 240/(75 x x 250)

= 482,549 mm

atau

S = Avmin x 3fy/bw

= 2 x ¼π x 102 x 3 x 240/250

= 452,389 mm

S max = d/2 atau 600 mm

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PERHITUNGAN

= 292/2 atau 600 mm

= 146 mm

s terpasang 10 – 120



Beban Pelat :

qD = 410,8 kg/m2

qD eq = = 684,67 kg/m’

MDL = 684,67 x 2,52 / 8 = 534,898 kgm

MDT = 684,67 x 2,52 / 24 = 178,3 kgm

qL = 250 kg/m2

qL eq = = 416,67 kg/m’

MLL = 416,67 x 2,52 / 8 = 325,523 kgm

MLT = 416,67 x 2,52 / 24 = 108,51 kgm

Bs. Balok Anak :

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21411174

PERHITUNGAN

qD = 2400 x 0,25 x 0,35 = 210 kg/m’

MDL = 210 x 2,52 / 8 = 164,062 kgm

MDT = 210 x 2,52 / 24 = 54,687 kgm

Reaksi Perletakkan :

RD = 684,67 x 2,5 / 2 + 210 x 2,5 / 2 = 1118,338 kg

RL = 416,67 x 2,5 / 2 = 520,838 kg


1,4D : Mu = 1,4 x (534,898 + 164,062) = 978,544 kgm

1,2D + 1,6L : Mu = 1,2 x (534,898 + 164,062) + 1,6 x 325,523 = 1359,58 kgm

Jadi, Mu = 1359,58 kgm = 13,596 kNm


1,4D : Mu = 1,4 x (178,3 + 54,687) = 326.18 kgm

1,2D + 1,6L : Mu = 1,2 x (178,3 + 54,687) + 1,6 x 108,51 = 453,2 kgm

Jadi, Mu = 453,2 kgm = 4,532 kNm

Geser Ultimate :

1,4D : Vu = 1,4 x (684,67 x 2,5 / 2 + 210 x 2,5 / 2) = 1565,67 kg

1,2D + 1,6L : Vu = 1,2 x (684,67 x 2,5 / 2 + 210 x 2,5 / 2) + 1,6 x 416,67 x 2,5 / 2

= 2175,345 kg

Jadi, Vu = 2175,345 kg = 21,753 kN



pasang

Tumpuan 4,532 212,61 0,0025 182,5 0,908 2D16

Lapangan 13,596 637,83 0,0039 284,7 1,415 2D16

Tulangan tumpuan :

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21411174

PERHITUNGAN

d = 350 – 40 – 10 – 0,5 x 16 = 292 mm

Mu/bd2 = 212,61

ρ = 0,0025

As = ρ x b x d = 0,0025 x 250 x 292 = 182,5 mm2

As 1 D16 = 201,062 mm2



Tulangan lapangan :

Mu/bd2 = 13,596 / (0,25 x 0,2922) = 637,83 kg/m2


As = ρ x b x d = 0,0039 x 250 x 292 = 284,7 mm2

As 1 D16 = 201,062 mm2




Vu Vc Vu < Vc ?


(kN) (kN) (mm) (mm)

21,753 45,625 YES 452,389 146 10 – 120


Vc = 0,75 x 1/6 x x bw x d

= 0,75 x 1/6 x x 250 x 292/1000

= 45,625 kN


= 2 x 1/4 π x 102 x 1200 x 240/(75 x x 250)

= 482,549 mm

atau

S = Avmin x 3fy/bw

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PERHITUNGAN

= 2 x ¼π x 102 x 3 x 240/250

= 452,389 mm


= 292/2 atau 600 mm

= 146 mm




Beban Pelat :

qD = 410,8 kg/m2

qD segitiga eq = = 513.4 kg/m’

qD trapesium eq = = 470,708 kg/m’

MDL = (513,5 + 470,708) x 652 / 8 = 3075,65 kgm

MDT = (513,5 + 470,708) x 62 / 24 = 1025,22 kgm

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PERHITUNGAN

qL = 250 kg/m2

qL segitiga eq = = 312,5 kg/m’

qL trapesium eq = = 286,458 kg/m’

MLL = (312,5 + 286,458) x 62 / 8 = 1871,744 kgm

MLT = (312,5 + 286,458) x 62 / 24 = 623,915 kgm

Beban Balok BA-2 :

RD = 1118,338 kg

MD = 1118,338 x 5 / 2 = 2795,845 kgm

RL = 520,838 kg

ML = 520,838 x 5 / 2 = 1302,095 kgm

Bs. Balok Anak :

qD = 2400 x 0,25 x 0,35 = 210 kg/m’

MDL = 210 x 2,52 / 8 = 164,062 kgm

MDT = 210 x 2,52 / 24 = 54,687 kgm


1,4D : Mu = 1,4 x (3075,65 + 2795,845 +164,062) = 8449,78 kgm

1,2D + 1,6L : Mu = 1,2 x (3075,65 + 2795,845 +164,062) + 1,6 x (1871,744 +

1302,095)

= 12320,811 kgm

Jadi, Mu = 12320,811 kgm = 123,21 kNm


1,4D : Mu = 1,4 x (1025,22 + 2795,845 +54,687) = 5426,053 kgm

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PERHITUNGAN

1,2D + 1,6L : Mu = 1,2 x (1025,22 + 2795,845 +54,687) + 1,6 x (623,915 +

1302,095)

= 7732,52 kgm

Jadi, Mu = 7732,52 kgm = 77,32 kNm

Geser Ultimate :

1,4D : Vu = 1,4 x ((513,5 + 470,708 + 210) x 5 / 2 + 1118,338 / 2)

= 4962,565 kg

1,2D + 1,6L : Vu = 1,2 x ((513,5 + 470,708 + 210) x 5 / 2 + 1118,338 / 2) + 1,6 x

((312,5 + 286,458) x 5 / 2 + 528,838 / 2)

= 7072,529 kg

Jadi, Vu = 7072,529 kg = 70,725 kN



pasang

Tumpuan 77,32 3627,32 0,024 1752 8,71 9D16

Lapangan 123,21 5720,165 0,0379 2766,7 13,72 14D16

Tulangan tumpuan :

d = 350 – 40 – 10 – 0,5 x 16 = 292 mm

Mu/bd2 = 3627,32

ρ = 0,024

As = ρ x b x d = 0,024 x 250 x 292 = 1752 mm2

As 1 D16 = 201,062 mm2

n tulangan = 1752 / 201,062 =8,71 (pakai 9 tulangan)


Tulangan lapangan :

Mu/bd2 = 123,21 / (0,25 x 0,2922) = 5720,165 kg/m2

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PERHITUNGAN

ρ = 0,0379

As = ρ x b x d = 0,0379 x 250 x 292 = 2766,7 mm2

As 1 D16 = 201,062 mm2


Jadi, tulangan lapangan atas terpasang 14D16


Vu Vc Vu < Vc ?


(kN) (kN) (mm) (mm)

70,725 45,625 NO 328,928 126 10 – 125


Vc = 0,75 x 1/6 x x bw x d = 0,75 x 1/6 x x 250 x 292 / 1000 = 45,625 kN

Vs = Vu – Vc = 70,725 – 45,625 = 25,1 kN

s = x As x fy x d / Vs

= 0,75 x ( 2 x 0,25 x π x 10² ) x 240 x 292 / (25,1 x 1000)

= 328,928 mm

Vs < x ( /3 ) x bw x d

25,1 kN < 0,75 x ( / 3 ) x 250 x 252

25,1 kN < 78,75 kN


= 252/2 atau 600 mm

= 126 mm


V.3. Perhitungan Balok Bordes Tangga

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21411174

PERHITUNGAN

Gambar V.1. Pembebanan Balok Bordes Tangga

Beban Tangga :

Dari SAP2000 diperoleh Reaksi Pelat Tangga :

qu = 498,88 kg/m’

Ru kanan = 498,88 x 2.5 x 4 / 6 = 798,208 kg

Mu = 798,208 x 2.5 – 498,88 x 2.52 / 2 = 598,656 kgm

Bs. Balok Anak :

qD = 2400 x 0,25 x 0,35 = 210 kg/m’

RD = 210 x 6 / 2 = 525 kg

MD =525 x 2.5 – 210 x 2.52 / 2 = 630kgm

Momen Ultimate Total :

Mu = 1,2 x (598,656+630) = 1474,387 kgm

Jadi, Mu = 1474,387 kgm = 14,74 kNm

Geser Ultimate :

Vu = 1,2 x (525 + 798,208) = 1587,85 kg

Jadi, Vu = 1587,85 kg = 15,89 kN


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PERHITUNGAN


pasang

Tumpuan 0 0 0,0025 182,5 0,908 2D16

Lapangan 14,74 691,5 0,0036 262,8 1,307 2D16

Tulangan tumpuan :

d = 350 – 40 – 10 – 0,5 x 16 = 292 mm

Mu/bd2 = 0

ρmin = 0,0025

Asmin = ρmin x b x d = 0,0025 x 250 x 292 = 182,5 mm2

As 1 D16 = 201,062 mm2



Tulangan lapangan :

Mu/bd2 = 14,74 / (0,25 x 0,2922) = 691,499 kg/m2


As = ρ x b x d = 0,0036 x 250 x 292 = 262,8 mm2

As 1 D16 = 201,062 mm2




Vu Vc Vu < Vc ?


(kN) (kN) (mm) (mm)

15,89 45,625 YES 452,389 146 10 – 120


Vc = 0,75 x 1/6 x x bw x d

= 0,75 x 1/6 x x 250 x 292/1000

= 45,625 kN

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PERHITUNGAN


= 2 x 1/4 π x 102 x 1200 x 240/(75 x x 250)

= 482,549 mm

atau

S = Avmin x 3fy/bw

= 2 x ¼π x 102 x 3 x 240/250

= 452,389 mm


= 292/2 atau 600 mm

= 146 mm


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