PERHITUNGAN GEMPA

Tahapan perhitungan

PERHITUNGAN BEBAN DAN GAYA GESER

Data : Kota Sukabumi (Wilayah Gempa 4)

Tanah= Keras

Daktail Penuh

L1= 425 cmH1= 500 cm

L2= 425 cmH2= 400cm

L3= 500 cmH3= 350 cm

K1= 45/45 cm

P.atap= 10 cm K2= 40/40 cm

P.lantai = 14 cmK3= 30/40cm

B1= 20/50 cm

B2= 25/50 cm

B3= 30/50 cm

2.1 Perhitungan Beban

Beton tanpa dinding geser :

T = 0,0731 x H (3/4)

= 0,0731 x 16,5 (3/4)

= 0,598Dari grafik dibawah ini didapat :

T = 0,598 dan C = 0,30 = 0,501

0,598

2.1.1 Beban Plat Atap / Lantai 4 (W4)

B1

100

500

400

250B2 100

500

400

200

B3 100

500

400

300

Berat atap (t =10 cm)

q1 = 17 x 23,5 x 0,1 x 2400 =95880Kg Balok melintang

q2 = 0,25 x 0,40 x 4,25 x 2400 x 12 = 12240 = 0,20 x 0,40 x 4,25 x 2400 x 12 = 9792 = 22032 kg Balok Memanjang

q3 = 0,30 x 0,40 x 23,5 x 5 x 2400 = 33840 kg

Berat langit-langit dan gantungannya

q4= 17 x 23,5 x 18 =7191 Kg Penutup aspal dan pasir

q5 = 17 x 23,5 x 0,01 x 1400 =5593 Kg Air Hujan ( t = 5 cm)

q6= 17 x 23,5 x 0,05 x 1000 =1997Kg

Beban Kolom (1/2 k3)

q7 = 0,30 x 0,40 x H x 2400 x 30 = 0,30 x 0,40 x 3,50 x 2400 x 30 = 15120Kg

Beban Hidup

q7 = 17 x 23,5 x 100 x 0,3 = 11985Kg +

Total W4 (q )= 211616 Kg2.1.2 Beban Lantai 3 (t = 14) B1

140

500

360

250

B2

140

500

360

200

B3

140

500

360

300 Berat plat lantai (t=14 cm)

q1 = 17 x 23,5 x 0,14 x 2400 =134232Kg Balok melintang

q2 = 0,25 x 0,36 x 4,25 x 2400 x 12= 11016 = 0,20 x 0,36 x 4,25 x 2400 x12= 8812,8

= 19828,8 kg Balok Memanjang q3 = 0,30 x 0,36 x 23,5 x 5 x 2400= 30456 Kg


q4= 17 x 23,5 x 18 = 7191Kg Beban Kolom (1/2 k4)

q7 = 0,40 x 0,40 x H4 x 2400 x 30 = 0,40 x 0,40 x 3,50 x 2400 x 30= 20160 Kg


q7 = 0,40 x 0,40 x H3 x 2400 x 30 = 0,40 x 0,40 x 4 x 2400 x 30= 23040 Kg

Keramik + adukan ( t = 5 cm)

q12= 17 x 23,5 x 5 x 24 kg/m2 = 47940 Kg

Beban Hidup

q14 = (17 x 23,5 x 250 x 0,3)= 29962,5Kg

Total W3 = 312810,3 kg2.1.3 Beban Lantai 2 (T=14 cm)

B1 = B4

140

500

360

250

B2

140

500

360

200

B3

140

500

360


q1 = 17 x 23,5 x 0,14 x 2400 = 134232Kg

Balok melintang

q2 = 0,25 x 0,36 x 4,25 x 2400 x 12= 22032 = 0,20 x 0,36x 4,25 x 2400 x 12 = 8812,8

= 30844,8 kg Balok Memanjang

q3 = 0,30 x 0,36 x 23,5 x 5 x 2400=30456 Kg


q4= 17 x 23,5 x 18 =7191 Kg Beban Kolom (1/2 k3)

q7 = ,40 x 0,40 x H3 x 2400 x 30 = 0,40 x 0,40 x 4 x 2400 x 30 = 23040 Kg


q7 = 0,40 x 0,40 x H2 x 2400 x30 = 0,40 x 0,40 x 4 x 2400 x 30= 23040 Kg


q12= 17 x 23,5 x 5 x 24 kg/m2 = 47940 Kg

Beban Hidup

q14 = (17 x 23,5 x 250 x 0,3)= 29962,5Kg

Total W2 = 326706,3kg

2.1.4 Beban Lantai 1 (T=14 cm)

B1 = B4

140

500

360

250

B2

140

500

360

200

B3

140

500

360


q1 = 17 x 23,5 x 0,14 x 2400 = 134 232Kg

Balok melintang

q2 = 0,25 x 0,36 x 4,25 x 2400 x 12= 11016 = 0,20 x 0,36 x 4,25 x 2400 x 12 = 8812,8

= 198 288 kg Balok Memanjang

q3 = 0,30 x 0,36 x 23,5 x 5 x 2400= 30456 Kg


q4= 17 x 23,5 x 18 = 7191 Kg Beban Kolom (1/2 k2)q7 = 0,40 x 0,40 x H2x 2400 x30 = 0,40 x 0,40 x 4 x 2400 x 30= 23040 Kg


q7 = 0,45 x 0,45 x H1 x 2400 x 30 = 0,45 x 0,45 x 5 x 2400 x 30= 36450 Kg


q12= 17 x 23,5 x 5 x 24 kg/m2 = 47940 Kg

Beban Hidup

q14 = (17 x 23,5 x 250 x 0,3 )= 29962,5 Kg

Total W1 = 507559,5kg

LantaiWi (kg)hi(m)Wi x hi

4211.616,016,53.491.664

3312.810,30134.066.534

2326.706,3092.940.357

1507.559,5052.537.798

wi = Wt1.358.692wi x hi13.036.352

Setiap Portal menerima gaya V sebanyak (Melintang) :

2.2 Perhitungan Beban Horizontal Terpusat Melintang

Total = F1 + F2 + F3 + F4 = 13354,94 KgKontrol :

F = V 13354,94 = 13354,94 .. OK

2.3 Perhitungan gaya geser tingkat (Qi)

Gbr 2-6 pembagian gaya geserQ4 = F4 = 3576,99 Kg

Q3 = Q4 + F3 = 3576,99 + 4165,91 = 7742,91KgQ2 = Q3 + F2 = 7742,91 + 3012,21 = 10755,12Kg Q1 = Q2 + F1 = 10755,12 + 2599,82 = 13354,94Kg2.4 Perhitungan Beban Horizontal Terpusat Memanjang

Setiap Portal menerima gaya V sebanyak (Memanjang) :

lantaiWi (kg)hi(m)Wi x hi

4211.616,016,53.491.664

3312.810,30134.066.534

2326.706,3092.940.357

1507.559,5052.537.798

wi = Wt1.358.692wi x hi13.036.352

Setiap Portal menerima gaya V sebanyak (Memanjang) :

Total = F1 + F2 + F3 + F4 = 16025,92 KgKontrol :

F = V 16025,92 = 16025,92 .. OK

2.3 Perhitungan gaya geser tingkat (Qi)

Q4 = F4 = 4292,39Kg

Q3 = Q4 + F3 = 4292,39 + 4999,09 = 9291,49KgQ2 = Q3 + F2 = 9291,49+ 3614,66 = 12906,14Kg Q1 = Q2 + F1 = 12906,14 + 3119,78 = 16025,92 KgPERHITUNGAN D -VALUE PORTAL MELINTANG3.1 Tingkat Satu

3.1.1 Kolom pinggir

= 2450,98 E

= 2733,75 E

D1.1 = D1.5= 0,482 . 2733,75 E = 1318,06 E

3.1.2 Kolom Tengah 1

= 2450,98 E

= 1960,78 E

= 2733,75 E

D1.2 = D1.4 = 0,58 . 2733,75 = 1.599,04E 3.1.2 Kolom Tengah 2

= 1960,78 E

= 1960,78 E

= 2733,75 E

D3 = 0,5633 . 2733,75 = 153980 E

Gaya geser setiap kolom pinggir :

Gaya geser setiap kolom tengah :

Gaya geser setiap kolom tengah 2 :

3.2 Tingkat Dua

3.2.1 Kolom pinggir

= 2450,98E

= 2450,98E

D.2.1= D.2.5= 0,53 . 2133,33 E = 1140,58E

3.2.2 Kolom tengah

k1 = k2 = 2450,98 E

= 1960,78 E

D2.2= D2.4 = 0,51. 2133,33 E = 1085 E

3.2.2 Kolom tengah 2

= 1960,78 E

= 1960,78 E

D3.2= 0,4789. 2133,33 E = 1021,71 E




3.3 Tingkat Tiga

3.3.1 Kolom pinggir

= 2450,98E

= 2450,98E

D3.1=D3.5 = 0,53 . 2133,33 E = 1140,58E

3.3.2 Kolom tengah

= 2450,98E

k3 = k4 = 1960,78 E

D3.2= D3.4= 0,51. 2133,33 E = 1085 E


= 1960,78 E

= 1960,78 E

D3.3= 0,4789. 2133,33 E = 1021,71 E




3.4 Tingkat Empat 3.4.1 Kolom pinggir

= 2450,98E

= 2450,98E

D4.1=D4.5 = 0,40 . 1828,57 E = 733,74E

3.4.2 Kolom tengah

= 2450,98E

=1960,78 E

D4.2 =D4.4 =0,51. 1828,57 E = 1084,50 E


=1960,78 E

=1960,78 E

D4.3= 0,4789. 1828,7 E = 875,75 E




PERHITUNGAN D-VALUE PORTAL MEMANJANG

5.1 Tingkat Satu

5.1.1.Kolom Pinggir

K1

KC

5.1.2 Kolom Tengah - 1

K1

K2

KC

5.1.3 Kolom Tengah - 2

K1

K2

KC

5.1.4Gaya Geser Pada Setiap Kolom Pinggir

5.1.5 Gaya Geser Pada Setiap Kolom Tengah

5.2 Tingkat Dua

5.2.1Kolom Pinggir

K1

Kc

K2

K2 = 1960,78 E


K1 K2

Kc

K3 K4


K1 K2

Kc

K3 K4

5.2.4 Gaya Geser Pada Setiap Kolom Pinggir


5.3 Tingkat Tiga

5.3.1.Kolom Pinggir

K1

Kc

K2

K2 = 1960,78 E


K1 K2

Kc

K3 K4


K1 K2

Kc

K3 K4



5.4 Tingkat Empat

5.4.1.Kolom Pinggir

K1

Kc

K2

5.4.2 Kolom Tengah -1

K1 K2

Kc

K3 K4


K1 K2

Kc

K3 K4



PERHITUNGAN MOMEN PORTAL MELINTANG

4.1 Perhitungan Momen Ujung Kolom

Rumus dari tabel Kyoshi Muto

GAB Bekerja Pada Titik Balok AB

Ma = GAB (1 y) h

Mb = GAB (yh)

Y = y0 + y1 + y2 + y3

1. Mencari Y0 Bangunan tingkat 4:

MENCARI Yo ( dari tabel Kyosi Muto )

TingkatKolom tepikolom tengahkolom tengah

K-YoK-YoK-Yo

10,8970,651,610,571,430,579

22,2980,502,070,501,840,492

32,2980,4652,070,4541,840,45

41,3400,3672,410,4211,840,392

2. Mencari y1 Bangunan Bertingkat 4Untuk mencari nilai y1, dapat ditentukan dengan cara menginterpolasikan data yang ada pada tabel 2. Nilai y1 tergantung harga k dan kekakuan balok atas + bawahnya.

Terbawah y1=0

Jika (k1+k2) > (k3+k4), maka dan harga y1 menjadi negatif.

Tabel y1 untuk kolom tepi dan kolom tengah

MENCARI Y1 ( dari tabel Kyosi Muto )

TingkatKolom tepikolom tengahkolom tengah

K1K21Y1K1+K2K3+K41Y1K1+K2K3+K41Y1

22450,982450,98104901,964901,96109803,929803,9210

32450,982450,98104901,964901,96109803,929803,9210

42450,982450,98104901,964901,96109803,929803,9210

3. Mencari y2 Bangunan Bertingkat 4

Untuk mencari nilai y2, dapat ditentukan dengan cara menginterpolasikan data yang ada pada tabel 3. Nilai y2 tergantung harga k, perbandingan kolom atas (ha) terhadap kolom lantai itu sendiri (h). Kolom teratas , yi = 0.

ha = tinggi kolom d atasnya

1 y2 = 0



tingkatha (cm)h (cm)2kolom tepikolom tengahkolom tengah

K_y2K-YoK-Yo

14005000,80,8965601,613801,4345020

240040012,2977902,068001,8382350

33504000,8752,2977902,068001,8382350

4. Mencari y3 Bangunan Bertingkat 4

Untuk mencari nilai y3, ditentukan dengan cara menginterpolasikan data yang ada pada tabel 4 . Nilai y3 tergantung harga k, perbandingan kolom bawah (hb) terhadap kolom lantai itu sendiri (h).

Kolom terbawah , y3 = 0, 1 y3 = 0



tingkathb (cm)h (cm)3kolom tepikolom tengahkolom tengah

K_y2K-YoK-Yo

25004001,252,2977902,0701,8382350

34003501,14292,29779402,0701,8382350

435035011,34002,4101,8382350

Resume y0, y1, y2 dan y3

RESUME

TingkatKolomY0Y1Y2Y3Y = Y0+Y1+Y2+Y3

1tepi0,650000,65

tengah10,570000,57

tengah20,579

2tepi0,500000,50

tengah10,500000,50

tengah20,50

3tepi0,4920000,492

tengah10,4540000,454

tengah20,450

4tepi0,3670000,367

tengah10,421

tengah20,3920000,392

4.1.1 Perhitungan Momen Ujung Kolom Lantai Satu

h = 500 cm = 5 m

Kolom Tepi

G11 = 2387,121y= 0,65Mbawah = G11 . y . h = (2387,121) . 0,65 . 5 = 7758,144 kg.m

Matas = G11 . (1 y) .h = (2387,121) . 0,35 . 5 = 4177,462 kg.m

Kolom Tengah 1G21 = 2895,995

y= 0,57

Mbawah = G21 . y . h = (2895,995). 0,57 . 5 = 8253,586kg.mMatas = G21.(1 y) . h = (2895,995) .0,43 . 5 = 6226,390kg.m

Kolom Tengah 2

G21 = 1889,102

y= 0,579

Mbawah = G21 . y . h = (1889,102). 0,579 . 5 = 8073,294kg.mMatas = G21.(1 y) . h = (1889,102) .0,421 . 5 = 5870,219kg.m4.1.2 Perhitungan Momen Ujung Kolom Lantai Dua

h = 400 cm = 4 m

Kolom Tepi

G12 = 1889,102y= 0,50Mbawah = G12 . y . h = (1889,102) . 0,50 . 4 = 3778,205kg.mMatas = G12 . (1 y) . h = (1889,102) . 0,50 . 4 = 3778,205kg.m Kolom Tengah

G22 = 1796,227y= 0,50Mbawah = G22 . y . h = (1796,227) . 0,50 . 4 = 2397,581kg.mMatas = G22 . (1 y) . h = (1796,227) . 0,50 . 4 = 2475,552kg.m

Kolom Tengah

G22 = 1218,283

y= 0,492

Mbawah = G22 . y . h = (1218,283) . 0,492 . 4 = 2397,581kg.mMatas = G22 . (1 y) . h = (1218,283) . 0,508 . 4 = 2475,552kg.m4.1.3 Perhitungan Momen Ujung Kolom Lantai Tiga

h = 400 cm = 4 m

Kolom Tepi

G13 = 1360,017y= 0,465

Mbawah = G12 . y . h = (1360,017) . 0,465 . 4 = 2529,631kg.mMatas = G12 . (1 y) . h = (1360,017) . 0,535 . 4 = 2910,436kg.m Kolom Tengah 1G23 = 1293,153y= 0,454Mbawah = G22 . y . h = (1293,153) . 0,454. 4 = 2348,366kg.mMatas = G22 . (1 y) . h = (1293,153). 0,546. 4 = 2824,246kg.m

Kolom Tengah 2

G33 = 1452,674

y= 0,45

Mbawah = G22 . y . h = (1452,674) . 0,45. 4 = 1452,674kg.mMatas = G22 . (1 y) . h = (1452,674). 0,55. 4 = 2614,814kg.m4.1.4 Perhitungan Momen Ujung Kolom Lantai Empat

h = 350 cm = 3,5 m

Kolom Tepi

G14 = 581,661 y= 0,367Mbawah = G12 . y . h = (581,661). 0,367 . 3,5 = 747,144kg.mMatas = G12 . (1 y) . h = (581,661). 0,633 . 3,5 = 1288,670 kg.m Kolom Tengah 1G24 = 859,7176y= 0,421Mbawah = G22 . y . h = (859,7176). 0,421 . 3,5 = 1266,794kg.mMatas = G22 . (1 y) . h = (859,7176). 0,579 . 3,5 = 1742,218kg.m Kolom Tengah 2

G24 = 694,2364

y= 0,392

Mbawah = G22 . y . h = (694,2364). 0,392 . 3,5 = 1266,794kg.mMatas = G22 . (1 y) . h = (694,2364). 0,608 . 3,5 = 952,492kg.m4.2 Perhitungan Momen Ujung Balok

4.2.1 Perhitungan Momen Ujung Balok Lantai Satu

a. Kolom Tepi

b. Kolom Tengah 1

= 4363,925 Kg.m

= 5454,918 Kg.m

c. Kolom Tengah 2

= 4133,900 Kg.m

= 4133,900 Kg.m

4.2.2 Perhitungan Momen Ujung Balok Lantai Dua

a. Kolom Tepi

b. Kolom Tengah 1

= 2640,361 Kg.m

= 3300,458Kg.m

c. Kolom Tengah 2

= 2545,183 Kg.m

= 2545,183Kg.m

4.2.3 Perhitungan Momen Ujung Balok Lantai Tiga

a. Kolom Tepi

b. Kolom Tengah 1

= 1818,238 Kg.m

= 2272,802 Kg.m

b. Kolom Tengah 2

= 2074,188 Kg.m

= 2074,188 Kg.m4.2.4 Perhitungan Momen Ujung Balok Lantai Empat

a. Kolom Tepi

b. Kolom Tengah 1

= 774,318 Kg.m

= 967,900 Kg.m

c. Kolom Tengah 2

= 738,668 Kg.m

= 738,668 Kg.m

BAB 6

PERHITUNGAN MOMEN PORTAL MEMANJANG

6.1 Perhitungan Momen Ujung Kolom

Tabel 1. Mencari Y0 Bangunan tingkat 5:

TingkatKolom tepiKolom tengah 1Kolom tengah 2

K-YoK-YoK-Yo

10.3750.80.750.650.750.65

20.5250.51.050.51.050.5

31.2820.4652.560.52.560.5

41.2820.452.560.4782.560.478

51.2820.3652.560.4282.560.428

Tabel 2

TingkatKolom tepikolom tengah 1kolom tengah 2

K1K21Y1K1+K2K3+K41Y1K1+K2K3+K41Y1

23125.003125.00106250.006250.00106250.006250.0010

33125.003125.00106250.006250.00106250.006250.0010

43125.003125.00106250.006250.00106250.006250.0010

53125.003125.00106250.006250.00106250.006250.0010

Tabel 3

tingkatha (cm)h (cm)2kolom tepikolom tengah 1kolom tengah 2

K_y2K-YoK-Yo

13506000.58330.37500.7500.750

235035010.52501.0501.050

335035011.28202.5602.560

435035011.28202.5602.560

Tabel 4

tingkathb (cm)h (cm)3kolom tepikolom tengah 1kolom tengah 2

K_y2K-YoK-Yo

25003501.42860.52501.0501.050

335035011.28202.5602.560

435035011.28202.5602.560

535035011.28202.5602.560

Kesimpulan :

tingkatkolomY0Y1Y2Y3Y = Y0+Y1+Y2+Y3

1tepi0.80000.8

tengah 10.650000.65

tengah 20.650000.65

2tepi0.50000.5

tengah 10.50000.5

tengah 20.50000.5

3tepi0.4650000.465

tengah 10.50000.5

tengah 20.50000.5

4tepi0.450000.45

tengah 10.4780000.478

tengah 20.4780000.478

5tepi0.3650000.365

tengah 10.4280000.428

tengah 20.4280000.428

6.1.1 Perhitungan Momen Ujung Kolom Lantai Satu

Tingkat 1

h = 500 cm = 5 m

Kolom tepi : G11 = 9302,41Kg ; y = 0,80

Mbawah = G11 x Yh = 9302,41x 0,8 x 5 = 37209,64 Kgm

Matas = G11 x (1-Y).h = 9302,41x 0,2 x 5 = 9302,41 Kgm

Kolom tengah 1 : G21 = 11740,17 Kg ; y = 0,65

Mbawah = G21 . y . h

= 38155,54 Kgm

Matas = G21 . (1 y) . h = 20545,29 Kgm



= 38978,76 Kgm

Matas = G31 . (1 y) . h = 20988,56 Kgm

6.1.2 Perhitungan Momen Ujung Kolom Lantai Dua

Tingkat 2 h = 350 cm = 3,5 m

Kolom tepi : G12 = 7103,151 Kg ; y = 0,50

Mbawah = G12 . y . h = 12430,514 Kgm

Matas = G12 . (1 y) . h = 12430,514 Kgm

Kolom tengah 1: G22 = 12298,598 Kg ; y = 0,50


= 21522,547 Kgm

Matas = G22 . (1 y) . h = 21522,547 Kgm



= 22419,320 Kgm

Matas = G32 . (1 y) . h = 22419,320 Kgm

6.1.3 Perhitungan Momen Ujung Kolom Lantai Tiga

Kolom tepi : G13 = 7358,913 Kg ; h = 350 ; y = 0,465


= 11976,630 Kgm

Matas = G13 . (1 y) . h = 13779,564 Kgm

Kolom tengah 1: G23 = 10902,593 Kg ; y = 0,50


= 19079,538 Kgm

Matas = G23 . (1 y) . h = 19079,538 Kgm



= 19079,538 Kgm

Matas = G33 . (1 y) . h = 19079,538 Kgm

6.1.4 Perhitungan Momen Ujung Kolom Lantai Empat

Tingkat 4

h = 350 cm = 3,5 m

Kolom tepi : G14 = 6441,285 Kg ; y = 0,45


= 10145,024 Kgm

Matas = G14 . (1 y) . h = 12399,473 Kgm

Kolom tengah : G24 = 9543.083 Kg ; y = 0,478


= 15965,577 Kgm

Matas = G24 . (1 y) . h = 17435,212 Kgm



= 15965,577 Kgm

Matas = G34 . (1 y) . h = 17435,212 Kgm

6.1.5 Perhitungan Momen Ujung Kolom Lantai Lima

Tingkat 5

h = 350 cm = 3,5 m

Kolom tepi : G15 = 5256,016 Kg ; y = 0,365


= 6714,560 Kgm

Matas = G15 . (1 y) . h = 11681,495 Kgm

Kolom tengah 1: G25 =7787,048 Kg ; y = 0,428


= 11664,998 Kgm

Matas = G25 . (1 y) . h = 15589,670 Kgm



= 11664,998 Kgm

Matas = G35 . (1 y) . h = 15589,670 Kgm

6.2 Perhitungan Momen Ujung Balok

6.2 1 Perhitungan Momen Ujung Kolom Lantai Satu

a. Kolom Tepi

b. Kolom Tengah 1

=31307,115 Kgm

= 27393,714 Kgm

c. Kolom Tengah 2

=29983,660Kgm

=29983,660Kgm

6.2.2 Perhitungan Momen Ujung Kolom Lantai Dua

a. Kolom Tepi

b. Kolom Tengah 1

= 22957,39Kgm

= 20087,71 Kg.m

c. Kolom Tengah 2

= 22419,32 Kg.m

= 22419,32 Kg.m

6.2.3 Perhitungan Momen Ujung Kolom Lantai Tiga

a. Kolom Tepi

b. Kolom Tengah 1

=20351,511Kg.m

= 20351,511Kg.m

c. Kolom Tengah 2

= 17807,565Kg.m

= 20351,511Kg.m

6.2.4 Perhitungan Momen Ujung Kolom Lantai Empat

a. Kolom Tepi

b. Kolom Tengah 1

= 17813,757Kg.m

= 17813,757Kg.m

c. Kolom Tengah 2

=15587,032Kg.m

= 17813757Kg.m

6.2.5 Perhitungan Momen Ujung Kolom Lantai Lima

a. Kolom Tepi

b. Kolom Tengah 1

= 14535,83Kg.m

= 14535,83Kg.m

c. Kolom Tengah 2

=12718,84Kg.m

= 14535,83Kg.m

BAB 7

PERHITUNGAN MOMEN MAKSIMUM

7.1 Perhitungan Momen Maksimum Pada Portal Melintang

7.1.1Perhitungan Reaksi

a. Free Body EF = GH

Perhitungan reaksi perletakan

E F

MEF

MFE

q

VEF 500 VFE

VEF= 6.068,002 kgm

VFE= - VEF = -6.068,002 kN

Perhitungan Gaya Dalam

Mx =

EMBED Microsoft Equation 3.0

Mmax =

VGH q . x = 0

x =

Maka momen max =


= 6.068,002 .2,528 - . 2400 .(5)2 1184,54

= -15.842,603 kgm

Dari perhitungan diatas dapat di tuliskan sebagai berikut :

Menghitung Momen Maximum dan Jarak

Free Body EF = Free Body GH

q=2.400,000Kg/m

L=5,000m

MEF=1.184,540Kgm

MFE=844,530Kgm

(1/2.ql2)=30.000,000Kg

VEF=6.068,002Kg

VFE=-6.068,002Kg

x=2,528m

VEF. X=15.341,937Kgm

(1/2.qx2)=30.000,000Kg

Mmax=-15.842,603Kgm

b. Free Body FG


Free Body FG

q=2.400,000Kg/m

L=4,000m

MEF=844,530Kgm

MFE=1.184,540Kgm

(1/2.ql2)=19.200,000Kg

VEF=4.714,998Kg

VFE=-4.714,998Kg

x=1,965m

VEF. X=9.263,001Kgm

(1/2.qx2)=19.200,000Kg

Mmax=-10.781,529Kgm

c. Free Body IJ


Free Body IJ = Free Body KL

q=2.400,000Kg/m

L=5,000m

MEF=849,020Kgm

MFE=739,790Kgm

(1/2.ql2)=30.000,000Kg

VEF=6.021,846Kg

VFE=-6.021,846Kg

x=2,509m

VEF. X=15.109,429Kgm

(1/2.qx2)=30.000,000Kg

Mmax=-15.739,591Kgm

d. Free Body JK

Menghitung Momen Maksimum dan Jarak

Free Body JK

q=2.400,000Kg/m

L=4,000m

MEF=739,790Kgm

MFE=849,020Kgm

(1/2.ql2)=19.200,000Kg

VEF=4.772,693Kg

VFE=-4.772,693Kg

x=1,989m

VEF. X=9.491,081Kgm

(1/2.qx2)=19.200,000Kg

Mmax=-10.448,709Kgm

e. Free Body MN


Free Body MN = Free Body OP

q=2.400,000Kg/m

L=5,000m

MEF=684,340Kgm

MFE=591,620Kgm

(1/2.ql2)=30.000,000Kg

VEF=6.018,544Kg

VFE=-6.018,544Kg

x=2,508m

VEF. X=15.092,863Kgm

(1/2.qx2)=30.000,000Kg

Mmax=-15.591,477Kgm

f. Free Body NO


Free Body NO

q=2.400,000Kg/m

L=4,000m

MEF=591,620Kgm

MFE=684,340Kgm

(1/2.ql2)=19.200,000Kg

VEF=4.776,820Kg

VFE=-4.776,820Kg

x=1,990m

VEF. X=9.507,504Kgm

(1/2.qx2)=19.200,000Kg

Mmax=-10.284,116Kgm

g. Free Body QR


Free Body QR = Free Body ST

q=2.400,000Kg/m

L=5,000m

MEF=437,880Kgm

MFE=410,720Kgm

(1/2.ql2)=30.000,000Kg

VEF=6.005,432Kg

VFE=-6.005,432Kg

x=2,502m

VEF. X=15.027,172Kgm

(1/2.qx2)=30.000,000Kg

Mmax=-15.410,708Kgm

h. Free Body RS


Free Body RS

q=2.400,000Kg/m

L=4,000m

MEF=410,720Kgm

MFE=437,880Kgm

(1/2.ql2)=19.200,000Kg

VEF=4.793,210Kg

VFE=-4.793,210Kg

x=1,997m

VEF. X=9.572,859Kgm

(1/2.qx2)=19.200,000Kg

Mmax=-10.037,861Kgm

i. Free Body UV


Free Body UV = Free Body WX

q=1.400,000Kg/m

L=5,000m

MEF=270,690Kgm

MFE=196,980Kgm

(1/2.ql2)=17.500,000Kg

VEF=3.514,742Kg

VFE=-3.514,742Kg

x=2,511m

VEF. X=8.823,865Kgm

(1/2.qx2)=17.500,000Kg

Mmax=-8.946,825Kgm

j. Free Body VW


Free Body VW

q=1.400,000Kg/m

L=4,000m

MEF=196,980Kgm

MFE=270,690Kgm

(1/2.ql2)=11.200,000Kg

VEF=2.781,573Kg

VFE=-2.781,573Kg

x=1,987m

VEF. X=5.526,533Kgm

(1/2.qx2)=11.200,000Kg

Mmax=-5.870,477Kgm

7.2 Perhitungan Momen Maksimum Pada Portal Memanjang

a. Free Body FG = IJ

Perhitungan reaksi perletakan

F G

MFG

MGF

q

VFG 400 VGF

VFG= 4.822,775

VGF= - VFG = -4.822,775 kN

Perhitungan Gaya Dalam

Mx =


Mmax =

VFG q . x = 0

x =

Maka momen max =


= 4.822,775 .2,009 - . 2400 .(2,009)2 1011,64

= -10.520,324 kgm

Dari perhitungan diatas dapat di tuliskan sebagai berikut :


Free Body FG = Free Body IJ

q=2.400,000Kg/m

L=4,000m

MAB=1.011,640Kgm

MBA=920,540Kgm

(1/2.ql2)=19.200,000Kg

VAB=4.822,775Kg

VBA=-4.822,775Kg

x=2,009m

VAB. X=9.691,316Kgm

(1/2.qx2)=19.200,000Kg

Mmax=-10.520,324Kgm

b. Free Body BC = CD


Free Body GH = Free Body HI

q=2.400,000Kg/m

L=5,000m

MEF=920,540Kgm

MFE=1.011,640Kgm

(1/2.ql2)=30.000,000Kg

VEF=5.981,780Kg

VFE=-5.981,780Kg

x=2,492m

VEF. X=14.909,038Kgm

(1/2.qx2)=30.000,000Kg

Mmax=-16.011,502Kgm

c. Free Body FG = IJ


Free Body KL = Free Body NO

q=2.400,000Kg/m

L=4,000m

MEF=1.012,240Kgm

MFE=987,190Kgm

(1/2.ql2)=19.200,000Kg

VEF=4.806,263Kg

VFE=-4.806,263Kg

x=2,003m

VEF. X=9.625,066Kgm

(1/2.qx2)=19.200,000Kg

Mmax=-10.587,174Kgm

d. Free Body GH = HI


Free Body LM = Free Body MN

q=2.400,000Kg/m

L=5,000m

MEF=987,190Kgm

MFE=1.012,240Kgm

(1/2.ql2)=30.000,000Kg

VEF=5.994,990Kg

VFE=-5.994,990Kg

x=2,498m

VEF. X=14.974,960Kgm

(1/2.qx2)=30.000,000Kg

Mmax=-16.012,230Kgm

e. Free Body KL = NO


Free Body PQ = Free Body ST

q=2.400,000Kg/m

L=4,000m

MEF=816,720Kgm

MFE=373,520Kgm

(1/2.ql2)=19.200,000Kg

VEF=4.910,800Kg

VFE=-4.910,800Kg

x=2,046m

VEF. X=10.048,315Kgm

(1/2.qx2)=19.200,000Kg

Mmax=-9.968,405Kgm

f. Free Body LM = MN


Free Body QR = Free Body RS

q=2.400,000Kg/m

L=5,000m

MEF=373,520Kgm

MFE=816,720Kgm

(1/2.ql2)=30.000,000Kg

VEF=5.911,360Kg

VFE=-5.911,360Kg

x=2,463m

VEF. X=14.560,074Kgm

(1/2.qx2)=30.000,000Kg

Mmax=-15.813,446Kgm

g. Free Body PQ


Free Body UV = Free Body XY

q=2.400,000Kg/m

L=4,000m

MEF=531,830Kgm

MFE=498,810Kgm

(1/2.ql2)=19.200,000Kg

VEF=4.808,255Kg

VFE=-4.808,255Kg

x=2,003m

VEF. X=9.633,048Kgm

(1/2.qx2)=19.200,000Kg

Mmax=-10.098,782Kgm

h. Free Body QR


Free Body VW = Free Body WX

q=2.400,000Kg/m

L=5,000m

MEF=498,810Kgm

MFE=531,830Kgm

(1/2.ql2)=30.000,000Kg

VEF=5.993,396Kg

VFE=-5.993,396Kg

x=2,497m

VEF. X=14.966,998Kgm

(1/2.qx2)=30.000,000Kg

Mmax=-15.531,812Kgm

i. Free Body UV


Free Body Z-aa = Free Body ac-ad

q=1.400,000Kg/m

L=4,000m

MEF=257,270Kgm

MFE=197,130Kgm

(1/2.ql2)=11.200,000Kg

VEF=2.815,035Kg

VFE=-2.815,035Kg

x=2,011m

VEF. X=5.660,301Kgm

(1/2.qx2)=11.200,000Kg

Mmax=-5.796,969Kgm

j. Free Body VW


Free Body ab-ac = Free Body ac-ad

q=1.400,000Kg/m

L=5,000m

MEF=197,130Kgm

MFE=257,270Kgm

(1/2.ql2)=17.500,000Kg

VEF=3.487,972Kg

VFE=-3.487,972Kg

x=2,491m

VEF. X=8.689,963Kgm

(1/2.qx2)=17.500,000Kg

Mmax=-9.007,167Kgm

EMBED AutoCAD.Drawing.17




kc

k1

kc

k2

k1

K3

K5

K3

K3

K5

K4

K6

kc

K2

kc

k1

kc

k4

K2

K3

k1

K5

K4

K6

kc

k1

K3

K2

k4

kc

k1

kc

K2

K4

K6

kc

k1

K3

K2

k4

kc

k1

kc

K2

dari nilai momen atas (Ma) dari kolom bawah

dari nilai momen bawah (Mb) dari kolom atas

Mki

Mka

kki

kki

A

B

yh

( 1-y ) h










EMBED Equation.3



K2

K3

kc

60Analisis Gempa Statik Ekivalen / UPI / 0900759

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