8/16/2019 CONTOH CENTROID PLASTIS.pdf

1/8

Diketahui :Mutu beton ; Mutu baja ;

bw = 200 mm fc ' = 25 MPa fy = 400 MPabf = 600 mm = 25 N/mm2 = 400 N/mm2h = 700 mmhf = 200 mm Modulus Elastisitas Beton Modulud Elastisitas Baja, Eyh - hf = 500 mm Ec = 4700 ( fc' ) Ey = MPa

Ec = N/mm2

Regangan beton ; Regangan baja ;,

c= ,

y, y =

D = 22

As = mm2Tulangan = 22 D 22

Centroid plastis, d"Statis Momen ke tepi atas penampang

Ac1 = 0.85 x fc x hf x bf = N Zc1 = 1/2.hf Zc1 = 100 mm Ac2 = 0.85 x fc x (h - hf) x bw = N Zc2 = hf + 1/2 ( h- hf ) Zc2 = 450 mm

As1 = 6 As = mm2 d1 = 50 mm Z1 = d1 Z1 = 50 mm As2 = 6 As = mm2 d2 = 150 mm Z2 = d2 Z2 = 150 mm As3 = 2 As = mm2 d3 = 250 mm Z3 = d3 Z3 = 250 mm As4 = 2 As = mm2 d4 = 350 mm Z4 = d4 Z4 = 350 mm As5 = 2 As = mm2 d5 = 450 mm Z5 = d5 Z5 = 450 mm As6 = 2 As = mm2 d6 = 550 mm Z6 = d6 Z6 = 550 mm As7 = 2 As = mm2 d7 = 650 mm Z7 = d7 Z7 = 650 mm

22

d " = (Ac1 x Zc1 + Ac2 x Zc2) + (As1 x fy x Z1 + As2 x fy x Z2 + As3 x fy x Z3 + As4 x fy x Z4 + As5 x fy x Z5 + As6 x fy x Z6 + As7 x fy x

d " = = mm dari tepi atas penampang kolom T

760.27760.27

380.13

0.003

0.0020

2,125,000

23500

= fy / Es

200,000

2,550,000

2,280.802,280.80

760.27

(Ac1 + Ac2) + (As1 + As2 + As3 + As4 + As5 + As6 + As7) x fy

760.27760.27

2,077,952,581.278,020,167.86

259.09

600

50 100 100 100 100 100

50

50

100

50

200

50100

50

50

150

250

350

450

550

650

By : SONDRA RAHARJA, ST Halaman 1

8/16/2019 CONTOH CENTROID PLASTIS.pdf

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Centroid plastis, d"Statis Momen ke tepi bawah penampang

Ac1 = 0.85 x fc x hf x bf = N Zc1 = 1/2.hf + (h - hf) Zc1 = 600 mm Ac2 = 0.85 x fc x (h - hf) x bw = N Zc2 = 1/2 ( h- hf ) Zc2 = 250 mm

As1 = 6 As = mm2 d1 = 50 mm Z1 = d7 Z1 = 650 mm As2 = 6 As = mm2 d2 = 150 mm Z2 = d6 Z2 = 550 mm As3 = 2 As = mm2 d3 = 250 mm Z3 = d5 Z3 = 450 mm As4 = 2 As = mm2 d4 = 350 mm Z4 = d4 Z4 = 350 mm As5 = 2 As = mm2 d5 = 450 mm Z5 = d3 Z5 = 250 mm As6 = 2 As = mm2 d6 = 550 mm Z6 = d2 Z6 = 150 mm As7 = 2 As = mm2 d7 = 650 mm Z7 = d1 Z7 = 50 mm

d " = (Ac1 x Zc1 + Ac2 x Zc2) + (As1 x fy x Z1 + As2 x fy x Z2 + As3 x fy x Z3 + As4 x fy x Z4 + As5 x fy x Z5 + As6 x fy x Z6 + As7 x fy x

d " = = mm dari tepi bawah penampang kolom T

Pembuktianh - d" = 700 - = mm dari tepi bawah penampang kolom T OK bangeets…!

d" + d" =259 + 441 = 700 0OK bangeets…!

2,550,0002,125,000

2,280.802,280.80

760.27760.27760.27760.27760.27

(Ac1 + Ac2) + (As1 + As2 + As3 + As4 + As5 + As6 + As7) x fy

3,536,164,919.01 440.918,020,167.86

259.09 440.91 -

440.9090909259.0909091

600

50 100 100 100 100 100

50

50

100

50

200

50100

50

50

150

250

350

450

550

650

By : SONDRA RAHARJA, ST Halaman 2

8/16/2019 CONTOH CENTROID PLASTIS.pdf

3/8

Diketahui :Mutu beton ; Mutu baja ;

bw = 200 mm fc ' = 25 MPa fy = 400 MPabf = 600 mm = 25 N/mm2 = 400 N/mm2h = 700 mm

hf = 200 mm Modulus Elastisitas Beton Modulud Elastisitas Baja, Eyh - hf = 500 mm Ec = 4700 ( fc' ) Ey = MPa

Ec = N/mm2

Regangan beton ; Regangan baja ;, c = , y

, y =

D = 22 As = mm2Tulangan = 22 D 22

Centroid plastis, d"Statis Momen ke tepi atas penampang

Ac1 = 0.85 x fc x hf x bf = N Zc1 = 1/2.hf Zc1 = 100 mm Ac2 = 0.85 x fc x (h - hf) x bw = N Zc2 = hf + 1/2 ( h- hf ) Zc2 = 450 mm

As1 = 6 As = mm2 d1 = 50 mm Z1 = d1 Z1 = 50 mm As2 = 6 As = mm2 d2 = 150 mm Z2 = d2 Z2 = 150 mm As3 = 2 As = mm2 d3 = 250 mm Z3 = d3 Z3 = 250 mm As4 = 2 As = mm2 d4 = 350 mm Z4 = d4 Z4 = 350 mm As5 = 2 As = mm2 d5 = 450 mm Z5 = d5 Z5 = 450 mm As6 = 2 As = mm2 d6 = 550 mm Z6 = d6 Z6 = 550 mm As7 = 3 As = mm2 d7 = 650 mm Z7 = d7 Z7 = 650 mm

d " = (Ac1 x Zc1 + Ac2 x Zc2) + (As1 x fy x Z1 + As2 x fy x Z2 + As3 x fy x Z3 + As4 x fy x Z4 + As5 x fy x Z5 + As6 x fy x Z6 + As7 x fy x

d " = = mm dari tepi atas penampang kolom T

Centroid plastis, d"Statis Momen ke tepi bawah penampang

Ac1 = 0.85 x fc x hf x bf = N Zc1 = 1/2.hf + (h - hf) Zc1 = 600 mm Ac2 = 0.85 x fc x (h - hf) x bw = N Zc2 = 1/2 ( h- hf ) Zc2 = 250 mm

As1 = 6 As = mm2 d1 = 50 mm Z1 = d7 Z1 = 650 mm As2 = 6 As = mm2 d2 = 150 mm Z2 = d6 Z2 = 550 mm As3 = 2 As = mm2 d3 = 250 mm Z3 = d5 Z3 = 450 mm As4 = 2 As = mm2 d4 = 350 mm Z4 = d4 Z4 = 350 mm As5 = 2 As = mm2 d5 = 450 mm Z5 = d3 Z5 = 250 mm As6 = 2 As = mm2 d6 = 550 mm Z6 = d2 Z6 = 150 mm As7 = 3 As = mm2 d7 = 650 mm Z7 = d1 Z7 = 50 mm

d " = (Ac1 x Zc1 + Ac2 x Zc2) + (As1 x fy x Z1 + As2 x fy x Z2 + As3 x fy x Z3 + As4 x fy x Z4 + As5 x fy x Z5 + As6 x fy x Z6 + As7 x fy x

d " = = mm dari tepi bawah penampang kolom T

Pembuktianh - d" = 700 - = mm dari tepi bawah penampang kolom T OK bangeets…!

d" + d" =266 + 434 = 700 0OK bangeets…!

200,00023500

0.003 = fy / Es

0.0020

380.13

2,550,0002,125,000

2,280.802,280.80

760.27760.27760.27760.27

1,140.40

(Ac1 + Ac2) + (As1 + As2 + As3 + As4 + As5 + As6 + As7) x fy

2,176,787,086.15 266.368,172,220.94

2,550,0002,125,000

2,280.802,280.80

760.27760.27760.27760.27

1,140.40

(Ac1 + Ac2) + (As1 + As2 + As3 + As4 + As5 + As6 + As7) x fy

3,543,767,573.23 433.648,172,220.94

266.36 433.64 -

By : SONDRA RAHARJA, ST Halaman 3

8/16/2019 CONTOH CENTROID PLASTIS.pdf

4/8

Diketahui :Mutu beton ; Mutu baja ;

bw = 200 mm fc ' = 25 MPa fy = 400 MPabf = 600 mm = 25 N/mm2 = 400 N/mm2h = 700 mmhf = 200 mm Modulus Elastisitas Beton Modulud Elastisitas Baja, Eyh - hf = 500 mm Ec = 4700 ( fc' ) Ey = MPa

Ec = N/mm2

Regangan beton ; Regangan baja ;, c = , y

, y =

D = 22 As = mm2Tulangan = 22 D 22

Centroid plastis, d"Statis Momen ke tepi atas penampang

Ac1 = 0.85 x fc x hf x bf = N Zc1 = 1/2.hf Zc1 = 100 mm Ac2 = 0.85 x fc x (h - hf) x bw = N Zc2 = hf + 1/2 ( h- hf ) Zc2 = 450 mm

As1 = 11 As = mm2 d1 = 50 mm Z1 = d1 Z1 = 50 mm As2 = 6 As = mm2 d2 = 150 mm Z2 = d2 Z2 = 150 mm As3 = 2 As = mm2 d3 = 250 mm Z3 = d3 Z3 = 250 mm As4 = 2 As = mm2 d4 = 350 mm Z4 = d4 Z4 = 350 mm As5 = 2 As = mm2 d5 = 450 mm Z5 = d5 Z5 = 450 mm As6 = 2 As = mm2 d6 = 550 mm Z6 = d6 Z6 = 550 mm As7 = 3 As = mm2 d7 = 650 mm Z7 = d7 Z7 = 650 mm

d " = (Ac1 x Zc1 + Ac2 x Zc2) + (As1 x fy x Z1 + As2 x fy x Z2 + As3 x fy x Z3 + As4 x fy x Z4 + As5 x fy x Z5 + As6 x fy x Z6 + As7 x fy x

d " = = mm dari tepi atas penampang kolom T

200,00023500

0.003 = fy / Es

0.0020

380.13

2,550,0002,125,000

4,181.462,280.80

760.27760.27760.27760.27

1,140.40

(Ac1 + Ac2) + (As1 + As2 + As3 + As4 + As5 + As6 + As7) x fy

2,214,800,357.26 247.958,932,486.36

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

By : SONDRA RAHARJA, ST Halaman 4

8/16/2019 CONTOH CENTROID PLASTIS.pdf

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Centroid plastis, d"Statis Momen ke tepi bawah penampang

Ac1 = 0.85 x fc x hf x bf = N Zc1 = 1/2.hf + (h - hf) Zc1 = 600 mm Ac2 = 0.85 x fc x (h - hf) x bw = N Zc2 = 1/2 ( h- hf ) Zc2 = 250 mm

As1 = 11 As = mm2 d1 = 50 mm Z1 = d7 Z1 = 650 mm As2 = 6 As = mm2 d2 = 150 mm Z2 = d6 Z2 = 550 mm As3 = 2 As = mm2 d3 = 250 mm Z3 = d5 Z3 = 450 mm As4 = 2 As = mm2 d4 = 350 mm Z4 = d4 Z4 = 350 mm As5 = 2 As = mm2 d5 = 450 mm Z5 = d3 Z5 = 250 mm As6 = 2 As = mm2 d6 = 550 mm Z6 = d2 Z6 = 150 mm As7 = 3 As = mm2 d7 = 650 mm Z7 = d1 Z7 = 50 mm

d " = (Ac1 x Zc1 + Ac2 x Zc2) + (As1 x fy x Z1 + As2 x fy x Z2 + As3 x fy x Z3 + As4 x fy x Z4 + As5 x fy x Z5 + As6 x fy x Z6 + As7 x fy x

d " = = mm dari tepi bawah penampang kolom T

Pembuktianh - d" = 700 - = mm dari tepi bawah penampang kolom T OK bangeets…!

d" + d" =248 + 452 = 700 0OK bangeets…!

2,550,0002,125,000

4,181.462,280.80760.27760.27760.27

247.95 452.05 -

760.271,140.40

(Ac1 + Ac2) + (As1 + As2 + As3 + As4 + As5 + As6 + As7) x fy

4,037,940,097.64 452.058,932,486.36

By : SONDRA RAHARJA, ST Halaman 5

8/16/2019 CONTOH CENTROID PLASTIS.pdf

6/8

A.I = 12 x 40 = cm2 A.II = 28 x 12 = cm2

cm2

Koordinat :x1 = 12/2 x1 = 6 cm

x2 =12 + 28/2 x2 = 26 cm

Titik berat penampang total

xa = x1.A I + x2. A II

xa = cm

xb = (12 + 28) - xa

xb = cm

Mutu beton ; Mutu baja ; D = 16fc ' = 200 Kg/cm2 fy = 4000 Kg/cm2 As = mm2

= 200 Kg/cm2 = 4000 Kg/cm2 cm2

Modulus Elastisitas Beton Modulus Elastisitas Baja, EsEc = 4700 ( fc' ) Ey = Kg/cm2Ec = N/mm2

Regangan beton ; Regangan baja ;, c = , y

, y =

Centroid plastis, d"Statis Momen ke tepi kiri penampang

Ac1 = 0.85 x fc x 12 x 40 = kg.cm Zc1 = 1/2 x 12 Zc1 = cm Ac2 = 0.85 x fc x 28 x 12 = kg.cm Zc2 = 12 + 28/2 Zc2 = cm

kg.cm

As1 = 5 As = cm2 d1 = 3 cm Z1 = 3 cm As2 = 5 As = cm2 d2 = 9 cm Z2 = 9 cm As3 = 2 As = cm2 d3 = 15 cm Z3 = 15 cm As4 = 2 As = cm2 d4 = 26 cm Z4 = 26 cm As5 = 2 As = cm2 d5 = 37 cm Z5 = 37 cm

d" = (Ac1 x Zc1 + Ac2 x Zc2) + fy x ( As1 x Z1 + As2 x Z2 + As3 x Z3 + As4 x Z4 + As5 x Z5)

d" = = cm diukur dari tepi kiri penampang

26

816

A I + A II

(Ac1 + Ac2) + fy x (As1 + As2 + As3 + As4 + As5)

3,711,895.07267,399.64

2.0106

13.8814515

480336

10.053104.02124

2,100,000

201.06

14.2352941

25.7647059

6

= fy / Es

0.0019

8160057120138720

4.02124

10.05310

4.02124

210190.38988

0.003

90

150

260

370

400

120

120

280

30

By : SONDRA RAHARJA, ST Halaman 6

8/16/2019 CONTOH CENTROID PLASTIS.pdf

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Centroid plastis, d"Statis Momen ke Tulangan 1 (As1)

Ac1 = 0.85 x fc x 12 x 40 = kg.cm Zc1 = 1/2 x 12 - 3 Zc1 = 3 cm Ac2 = 0.85 x fc x 28 x 12 = kg.cm Zc2 = 12 + 28/2 -3 Zc2 = 23 cm

As1 = 5 As = cm2 d1 = 0 cm Z1 = 0 cm As2 = 5 As = cm2 d2 = 6 cm Z2 = 6 cm As3 = 2 As = cm2 d3 = 12 cm Z3 = 12 cm As4 = 2 As = cm2 d4 = 23 cm Z4 = 23 cm As5 = 2 As = cm2 d5 = 34 cm Z5 = 34 cm

d" = (Ac1 x Zc1 + Ac2 x Zc2) + fy x ( As1 x Z1 + As2 x Z2 + As3 x Z3 + As4 x Z4 + As5 x Z5)

d" = = cm diukur dari Tulangan 1 (As1)

13.8814515310.88145153

3

CARA ANDRE NOVAN, ST, MT.

A.I = 12 x 40 = cm2 A.II = 28 x 12 = cm2 Ab = cm2

Koordinat :x1 = 12/2 x1 = 6 cm

x2 =12 + 28/2 x2 = 26 cm

Titik berat penampang total

xa = x1.A I + x2. A II

xa = cm

xb = (12 + 28) - xa

xb = cm

d' = 3

Mutu beton ; Mutu baja ; D = 16fc ' = 200 Kg/cm2 fy = 4000 Kg/cm2 As = mm2

= 200 Kg/cm2 = 4000 Kg/cm2 cm2

Modulus Elastisitas Beton Modulus Elastisitas Baja, EsEc = 4700 ( fc' ) Ey = Kg/cm2Ec = N/mm2

267,399.64

8160057120

4.021244.02124

(Ac1 + Ac2) + (As1 + As2 + As3 + As4 + As5)

2,909,696.16846 10.8814515

4.02124

10.0531010.05310

480336816

A I + A II

14.2352941

25.7647059

201.062.0106

2,100,000210190.38988

90150

260

370

400

120

120

280

30

By : SONDRA RAHARJA, ST Halaman 7

8/16/2019 CONTOH CENTROID PLASTIS.pdf

8/8

Regangan beton ; Regangan baja ;, c = , y

, y =

Titik Centroid plastis penampang, d"

Statis Momen ke tepi kiri penampang

Ac1 = 0.85 x fc x 12 x 40 = kg.cm Zc1 = 1/2 x 12 Zc1 = cm Ac2 = 0.85 x fc x 28 x 12 = kg.cm Zc2 = 12 + 28/2 Zc2 = cm

kg.cm

As1 = 5 As = cm2 d1 = 3 cm Z1 = 0 cm As2 = 5 As = cm2 d2 = 9 cm Z2 = 6 cm As3 = 2 As = cm2 d3 = 15 cm Z3 = 12 cm As4 = 2 As = cm2 d4 = 26 cm Z4 = 23 cm As5 = 2 As = cm2 d5 = 37 cm Z5 = 34 cm

Sb = 0.85.fc'.Ab. (xa - d')Sb = 1558560 kg.cm

ds = 0.85.fc'.Ab.(xa - d') + (As1.Z1 + As2.Z2 + As3.Z3 + As4.Z4 + As5.Z5)

ds = = mm dari Tulangan 2 (As2)2909696.168267399.6351

10.88145153

0.003 = fy / Es

0.0019

81600 657120 26138720

10.0531010.053104.021244.021244.02124

(0.85.fc'.Ab) + (As1 + As2 + As3 + As4 + As5) x fy

By : SONDRA RAHARJA, ST Halaman 8