Perhitungan Gempa Arah Melintang

8/2/2019 Perhitungan Gempa Arah Melintang

1/50

Dosen : Drs.Budi Kudwadi

Tugas Terstuktur Teknik Gempa

TUGAS MATA KULIAH TEKNIK GEMPA

140

550

550

550

550

140

140 550 250 550 140

DENAH

140 550 250 550 140

q2 = 1,2

25/50 25/45 25/50

400 K2 =35/35 K2 K2 35/35 atapq1 = 2,2

25/50 25/45 25/50400 K2 K2 K2 35/35

lantai 4q1 = 2,2

25/50 25/45 25/50

400 K1=45/45 K1 K1 45/45lantai 3q1 2,2

25/50 25/45 25/50400 K1 K1 K1 45/45

lantai 2q1 = 2,2

25/50 25/45 25/50K1=45/45 K1 K1 45/45

lantai 1550 q1 = 2,2

POTONGAN PORTAL MELINTANG

Nuki Saeful/020191/S1 Teknik Sipil 1


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Peruntukan : Perkantoran

Letak : Jakarta

Keadaan tanah : Jelek

Dinding : Partisi

langit-langit : Eternit

Penutup Lantai : Keramik

Atap : Pelat beton ditutup aspal + pasir

PENYELESAIAN :

0.2 wilayah 3

0.1

0.07 lunakkeras

0.05

0.5 1 2 3Waktu getar

Beton tanpa dinding getar

T = 0,06 H 3/4

= 0.06 (21,5)3/4 = 0,60

Dari Grafik

T = 0,60 C = 0,05

Beton Bertulang, k = 1

Cd= C . I .k

= 0,05 .1 . 1 =0,05

V = Cd . Wt

= C . I .k . Wt

KETERANGAN :



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l1

(m)

l2

(m)

l3

(m)

L2

(m)

h1

(m)

h2

(m)

q1

kN/m2

q2

kN/m2

b1

(cm)

b2

(cm)

k1

(cm)

k2

(cm)

1,4 5,5 2,5 5,5 5,5 4 2,2 1,2 25/50 25/45 45/45 35/35

LANGKAH-LANGKAH PERHITUNGAN

Perhitungan Pembebanan

15

35 50

25

15

4530

25

1. Pelat Atap (tebal 15 cm)

Berat Atap

q1 = 24,8 m x 16,3 m x 0,15 m x 2400 kg/m3 =

145526,4 kg

Balok Melintang

q2 = 10 x0,35 x0,25 x 5,5 x 2400 +5 x 0,30 x 0,25 x 2,5 x

2400

= 11550 + 2250 = 13800 kg

Balok Memanjangq3 = 16 x 0,35 x 0,25 x 5,5 x 2400 =

18480 kg

Berat Langit-Langit dan Gantungan

q4 = 22 x 13,5 x 18 = 5346 kg

Penutup aspal + pasir ( + = 1 cm)

q5 = 24,8 m x 16,3 m x 0,01 x 1400 =

5659,36 kg



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Berat air hujan tinggi 5 cmq6 = 24,8 m x 16,3 m x 0,05 x 1000 =

20212 kg

Beban hidup

q7 = 24,8 m x 16,3 m x 120 x 0,3

=14552,64 kg

Total Q5 =223576,4kg

18

50

32

25

1845

27

25

2. lantai tingkat 4 (tebal 18 cm)

Berat Pelatq1 = 24,8 m x 16,3 m x 0,18 x 2400 =

174631,68 kg

Berat Balok Melintang

q2 = 10 x 0,25 x 0,32 x 5,5 x 2400 +5,5 x 0,25 x 0,27 x 2,5

x 2400

= 10560 + 2227,5 =

12787,5 kg



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Berat balok memanjang

q3 = 16 x 0,25 x 0,27 x 5,5 x 2400 =14256 kg

Berat plapond

q4 = 22 x 13,5 x 18 = 5346 kg

Keramik + adukan 5 cm

q5 = 22 x 13,5 x 0,05 x 24 = 356,4 kg

Total Q4=207377,58 kg

Berat Kolom

q6 = 20 x 0,35 x 0,35 x 4 x 2400 = 5880

kg

Beban hidup

q7 = 22 x 13,5 x 220 x 0,3 = 19602 kg

Total Q4 =

232859,58 kg

3. Lantai Tingkat 3

Total Q3 = Total Q4 = 232859,58 kg

4. Lantai Tingkat 2

Q2 = Q4= 207377,58 kg

Kolom

q1 = 20 x 0,45 m x 0,45 m x 4 m x 2400 kg/m3= 38880 kg

Beban hidup

q2 = 22 x 13,5 x 220 x 0,3 = 19602 kg

Total Q2 =

265859,58kg

5. Lantai Tingkat 1



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Total Q1 = Q2 = 265859,58 kg

6. Lantai Dasar

Kolom

q16 = 20 x 0,45 m x 0,45 m x 5,5 m x 2400 kg/m3 =

53460 kg

Total Q0 = 53460

kg

Lantai Wi hi (m) Wi.hi

atap 223576,4kg 21,5 4806892,6

4232859,58

kg 17,5 4075042,65

3232859,58

kg 13,5 3143604,33

2 265859,58kg 9,5 2525666,01

1 265859,58kg 5,5 1462227,69

0 53460 kg 0 0

Wi = Wt=1274474,

72 Wi.hi

=16013433

,28

Vt = Cd . Wt = 0,05 x 1274474,72= 63723,736 kg

(Setiap portal menerima gaya V sebanyakn

Vt, n = jumlah

portal)

Beban Horizontal terpusat pada masing-masing lantai,

vhiWi

hiWiFi

.

.

=



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Fatap = kgx 512,19128736,63723816013433,2

4806892,6=

F4 = kgx 194,16216736,63723816013433,2

4075042,65=

F3 = kgx 635,12509736,63723816013433,2

3143604,33=

F2 = kgx 616,10050736,63723816013433,2

2525666,01=

F1 = kgx 778,5818736,63723816013433,2

1462227,69=

Gaya geser tingkat Qi

F5 Q5

Q5 = F5 = kg512,19128F4 Q4

Q4 = F5 + F4 =35344,706

F3

Q3 Q3 = Q4 + F3 =47854,341kg

F2

Q2 Q2 = Q3 + F2 = 57904,957kg

F1 Q1 Q1 = Q2 + F1 = 63723,735kg

I. Portal Melintang

1. Menghitung D Value

Tingkat 1



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Kolom Tepi

k1

kc

EkcaDD

k

ka

kc

kk

E

E

L

EIkc

E

E

L

EIk

1,1143E0,46.2485.4111

0,460,82

0,85,0

2

5,0

8,0~76,01

2485550

)45.(45.12

1.4

4

1893550

)50.(25.12

1.4

41

3

3

====

=+

+=

+

+=

==

===

===

Kolom tengah

k1 k2

kc

Ekc

E

E

L

EIk

Ek

2485

68,1380550

)45.(25.12

1.4

42

18931

3

=

===

=



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kgkgEEQ

D

DG

E

EQ

D

DG

EEDi

EkcaDD

k

ka

kc

kkk

i

65,3047735,63723.22862

4,10931..11

2121

kg3047,65kg63723,735.22862

4,10931.

.11

1111

1lantaipinggirkolomsetiappadageserGaya

228621,1143.201

4,109324850,44..3121

0,440,662

0,665,0

2

5,0

66,04970

68,3273

2

21

20

1

====

===

==

====

=+

+=

+

+=

==+

=

=

Tingkat 2

Kolom Tepi

k1

kc

k2

E

E

L

EIkc

Ek

E

E

L

EIk

19,3417400

)45.(45.12

1.4

4

18932

1893550

)50.(25.12

1.4

41

3

3

===

=

===

EkcaDD

k

ka

kc

kkk

95,785E3417,18.0,23..4212

0,236,02

0,6

2

6,0~55,038,6834

3786

2

21

====

=+

=+

=

==

+

=

Kolom tengah

k1 k2



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kck3 k4

Ekc

Ek

Ek

EkEk

19,3417

68,13604

18933

68,1360218931

=

=

=

==

kgE

EQ

D

DGG

kgE

EQ

Di

DGG

EEEDi

EkcaDDk

ka

kc

kkkkk

i

02,3369975,57904.5,18794

50,10932.

.12

223222

539,242157904,957.18794,5

95,7852.

.2

124212

5,18794)50,109395,785.(102

50,109319.E0,32.3417,..3222

0,320,952

0,95

2

95,06834,38

36,6507

2

4321

20

1

====

===

=+=

====

=

+

=

+

=

==+++

=

=

Tingkat 3

Kolom Tepi

k1

kc

k2

E

E

L

EIkc

Ek

E

E

LEIk

19,3417400

)45.(45.12

1.4

4

18932

1893550

)50.(25.

12

1.4

41

3

3

===

=

===



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EkcaDD

k

ka

kc

kkk

95,785E3417,18.0,23..4313

0,236,02

0,6

2

6,0~55,038,6834

3786

2

21

====

=+

=+

=

==+

=

Kolom tengah

k1 k2

kck3 k4

Ekc

Ek

Ek

Ek

Ek

19,3417

68,13604

18933

68,13602

18931

=

=

=

=

=

kgE

EQD

DGG

kgE

EQ

D

DGG

EEEDi

EkcaDD

k

ka

kc

kkkk

k

i

257,2784341,47854.5,18794

50,10933..13

233323

18,2001341,47854.18794,5

95,7853.

.13

134313

5,18794)50,109395,785.(103

50,109319.E0,32.3417,..3222

0,320,952

0,95

2

95,06834,38

36,6507

2

4321

20

1

====

===

=+=

====

=+

=+

=

==

+++

=

=

Tingkat 4

Kolom Tepi

k1

kc



12/50



k2

EkcaDD

k

ka

kc

kkk

E

E

L

EIkc

Ek

E

E

L

EIk

72,537E1250,52.0,43..4414

0,435,12

1,5

2

5,1~51,104,2501

3786

2

21

52,1250400

)35.(35.12

1.4

4

18932

1893550

)50.(25.121.4

41

3

3

====

=+

=+

=

==+

=

===

=

===

Kolom tengah

k1 k2

kck3 k4

52,125068,13604

18933

68,13602

18931

==

=

=

=

KcEk

Ek

Ek

Ek



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kgE

EQ

D

DGG

kgE

EQ

D

DGG

EEDi

EkcaDD

k

ka

kc

kkkkk

i

32,1999706,35344.12380

29,7004.

.14

243424

18,153535344,706.12380

72,5374.

.14

144414

12380)29,70072,537.(104

29,700E1250,520,56..3424

0,562,602

2,60

2

60,204,2501

36,6507

2

4321

1

====

====

=+=

====

=+

=+

=

==+++

=

=

Tingkat 5

Kolom Tepi

k1

kc

k2

EkcaDD

k

ka

kc

kkk

E

E

L

EIkc

Ek

E

E

L

EIk

72,537E1250,52.0,43..4515

0,435,12

1,5

2

5,1~51,1

04,2501

3786

2

21

52,1250400

)35.(35.12

1.4

4

18932

1893550

)50.(25.12

1.4

41

3

3

====

=+

=+

=

==+

=

===

=

===

Kolom tengah

k1 k2



14/50



kck3 k4

52,1250

68,13604

18933

68,13602

18931

=

=

=

=

=

Kc

Ek

Ek

Ek

Ek

kgE

EQD

DGG

kgE

EQ

D

DGG

EEDi

EkcaDD

k

ka

kc

kkkk

k

i

03,1082512,19128.12380

29,7005..14

243525

84,830512,19128.12380

72,5375.

.14

144515

12380)29,70072,537.(105

29,700E1250,520,56..3424

0,562,602

2,60

2

60,204,2501

36,6507

2

4321

1

====

====

=+=

====

=+

=+

=

==

+++

=

=

Kesimpulan

Lantai G. geser kolom pinggir (kg) G. geser kolom tengah (kg)

1

2

3

4

5

3047,65

2421,539

2001,18

1535,18

830,84

3047,65

3369,02

2784,257

1999,32

1082,03

2. Menentukan Momen-Momen Ujung Kolom



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yh

A

B MB

MA

G AB h

(1-y)h

yh

GAB bekerja pada titik balok AB y0 : ( tabel 1 ) k. muto

MA = GAB ( 1-y ) h 1. jumlah tingkat bangunan

MAB = GAB ( y. h ) 2. letak kolom

Dimana y = y0 + y1 + y2 + y3 3. harga k

Mencari y0bagian tingkat 5

kkolom tepi Kolom tengah

k- y0 k- y0

1 0,8 0,65 0,66 0,70

2 0,6 0,50 0,95 0,50

3 0,6 0,45 0,95 0,45

4 1,5 0,425 2,60 0,45

5 1,5 0,375 2,60 0,375

Y1 tergantung kekakuan balok atas + bawahnya ( tabel 2 )

k1 k2 1 =43

21

kk

kk

+

+terbawah y1 = 0

kc 1 = 1 , y1 = 0

k3 k4 jika ( k1 + k2) > ( k3 + k4 ) maka 1 =21

43

kk

kk

+

+

dan harga y1menjadi

t kolom tepi Kolom tengah



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k k1+k2 k3+k4 a1 y1 k1+k2 k3+k4 a1 y1

2 3786E 3786E 1 0 3253,68E 3253,68E 1 0

3 3786E 3786E 1 0 3253,68E 3253,68E 1 04 3786E 3786E 1 0 3253,68E 3253,68E 1 0

5 3786E 3786E 1 0 3253,68E 3253,68E 1 0

harga y2, tergantung harga k

( table 3 )k. muto perbandigan tinggi kolom

_ kolom teratas y1 = 0

2 =h

ha , ha = tinggi kolom di atasnya

2 = 1, y2 = 0

t

kha h a2

kolom tepi kolom tengah

K y2 k- y2

1 400 550 0,73 0,8

-

0,175 0,66 -0,25

2 400 400 1 0,6 0 0,95 0

3 400 400 1 0,6 0 0,95 0

4 400 400 1 1,5 0 2,60 0

Harga y3 - tergantung harga k

( table 3 ) - perbandingan tinggi kolom terhadap tinggi kolom bawah,

3 =h

hb

- kolom terbawah y3 = 0

- 3 = 1, y3 = 0

t

khb h a3


k- Y3 k- Y3

2 550 400 1,38 0,6 -0,05 0,95 --0,05

3 400 400 1 0,6 0 0,95 0

4 400 400 1 1,5 0 2,60 0

5 400 400 1 1,5 0 2,60 0



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Resume

t

k klm yo Y1 y2 y3 Y

1 tp 0,65 0

-

0,175 0 0,475

tgh 0,70 0 -0,25 0 0,45

2 tp 0,50 0 0 -0,05 0,45tgh 0,50 0 0 -0,05 0,45

3tp 0,45 0 0 0 0,45

tgh 0,45 0 0 0 0,45

4tp 0,425 0 0 0 0,425

tgh 0,45 0 0 0 0,45

5tp 0,375 0 0 0 0,375

tgh 0,375 0 0 0 0,375

3. Perhitungan Momen Di Ujung KolomTingkat 1

h = 550 cm = 5,5 m

a. Kolom tepi

M bawah = G11 . y. h

= kg3047,65 x 0,475 x 5,5

= 7961,98 kg

M atas = G11 . (1-y)h= kg3047,65 x (1 - 0475) x 5,5

= 8800,09 kg

b. Kolom tengah

M bawah = G21 . y . h

= kg65,3047 x 0,45 x 5,5

= 7542,93 kg

M atas = G21 . (1-y) .h



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= kg65,3047 x (1 - 0,45) x 5,5

= 9219,14 kgTingkat 2

h = 400 cm =4 m

a. Kolom tepi

M bawah = G12 . y .h

= kg539,2421 x 0,45 x 4

= 4358,77

M atas = G12 . (1-y). h

= 2421,539 x (1 0,45) x 4

= 5327,39

b. Kolom tengah

M bawah = G22 . y h

= kg02,3369 x 0,45 x 4

= 6064,24 kg

M atas = G22 . (1-y) .h

= kg02,3369 x (1 0,45) x 4

= 7411,84

Tingkat 3

h = 400 cm = 4 m

a. Kolom tepi


= kg18,2001 x 0,45 x 4

= 3602,12 kg

M atas = G13 . (1-y) . h

= 2001,18kg x (1 0,45) x 4

= 4402,59 kg

b. Kolom tengah


= kg257,2784 x 0,45 x 4

= 5011,66 kg



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M atas = G23 . (1-y) . h

= 2784,257 x (1 0,45) x 4

= 6125,36 kg

Tingkat 4

h = 400 cm = 4 m

a. Kolom tepi


= 18,1535 kg x 0,425 x 4

= 2609,81 kg

M atas = G14 . (1-y) .h

= 1535,18 x (1 0,425) x 4

= 3530,91

b. Kolom tengah


= kg32,1999 x 0,45 x 4

= 3598,78 kg

M atas = G24 . (1-y) . h

= 1999,32 x (1 0,45) x 4

= 4398,50 kg

Tingkat 5

h = 400 cm = 4 m

a. Kolom tepi


= kg84,830 x 0,375 x 4

= 1246,26 kg

M atas = G15 . (1-y) . h

= 830,84 kg x (1 0,375) x 4

= 2077,1 kg

b. Kolom tengah


= kg03,1082 x 0,375 x 4



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= 1623,05 kg

M atas = G25 . (1-y) . h

= 1082,03 kg x ( 1- 0,375 ) x 4

= 2705,08 kg

4. Menentukan Momen Ujung Balok

kolom

kika

kaka M

kk

kM

+= ; kolom

kika

kiki M

kk

kM

+= ; abKolom MMM +=

Mb = Kolom Atas; Ma = Kolom Bawah

Syarat Mij = 0

Balok Tepi Balok Tengah

i j = 0

MKolomkkikka

kkaMka

+=

MKolomkkakki

kkiMkb

+=

1. Tingkat 1( satu )- balok tepi

Mka= Mkolomkk

k

kika

ka +

.

= )4358,7709,8800.(1893

1893+

= 13158,86 Kg.M

Mki = 0

Nuki Saeful/020191/S1 Teknik Sipil

Kki

Mki

Kka

Mka

20


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- balok tengah

Mka= Mkolomkk

kkika

ka +

.

= )6064,2414,9219.(189368,1380

68,1380+

+

= 6445,79Kg.M

Mki = Mkolomkk

k

kika

ki +

.

= )6064,249219,14.(189368,1380

1893

++

= 8833,79 Kg.M

2. Tingkat 2( dua )

- balok tepi

Mka= Mkolomkk

k

kika

ka +

.

= )3602,125327,39.(1893

1893+

= 8929,51 Kg.M

Mki = 0

- balok tengah

Mka= Mkolomkk

k

kika

ka +

.

= )5011,667411,84.(

189368,1380

68,1380+

+

= 5292,41 Kg.M

Mki = Mkolomkk

k

kika

ki +

.

= )5011,667411,84.(189368,1380

1893+

+

= 7180,78 Kg.M

3. Tingkat 3( tiga )



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Mka= Mkolomkk

k

kika

ka +

.

= )2609,814402,59.(1893

1893+

= 8929,51 Kg.M

Mki = 0

- balok tengah

Mka= Mkolomkk

k

kika

ka +

.

= )3598,786125,36.(189368,1380

68,1380+

+

= 4142,48 Kg.M

Mki = Mkolomkk

k

kika

ki +

.

= )3598,786125,36.(189368,1380

1893+

+

= 5620,55Kg.M

4. Tingkat 4( empat )

Mka= Mkolomkk

k

kika

ka +

.

= )1246,263530,91.(1893

1893+

= 4777,17 Kg.M

Mki = 0- balok tengah

Mka= Mkolomkk

k

kika

ka +

.

= )1623,054398,50.(189368,1380

68,1380+

+

= 2565,18 Kg.M



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Mki = Mkolomkk

k

kika

ki +

.

= .189368,1380

1893

+)1623,054398,50( +

=3480,46 Kg.M

5. Tingkat 5( lima )

Mka= Mkolomkk

k

kika

ka +

.

= )2077,1.(1893

1893

= 2077,1 Kg.M

Mki = 0

- balok tengah

Mka= Mkolomkk

k

kika

ka +

.

= )2077,1.(

189368,1380

68,1380

+

= 884,84 Kg.M

Mki = Mkolomkk

k

kika

ki +

.

= )1,2077.(189368,1380

1893

+

= 1200,56 Kg.M



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5. Perhitungan Free Body Portal Melintang

Tingkat 5

Balok Tepi

q = 120 kg/m

A B

5,5 m

VA = ql -l

MBMA +VB = ql -

l

MBMA +

VA = 330 + (-48,28) VB = 330 + 48,28

= 281,72 kg = 378,28 kg

Mx = VA . x qx2 Mx = 281,72(2,35) (120).(2,35)2

= 662,04 331,35 = 330,69 kg.m

mq

VAx

qxVAdx

dMx

35,2120

72,281

00

===

==

Balok Tengah

q = 120 kg/m

A B

3,5 m

VA = ql -l

MBMA +VB = ql -

l

MBMA +

VA = 210 + (-75,87) VB = 210 + 75,87

= 134,13 kg = 285,87 kg



25/50



Mx = VA . x qx2 Mx = 134,13(1,12) (120).(1,12)2

= 150,23 75,26 = 74,97 kg.m

mq

VAx

qxVAdx

dMx

12,1120

13,134

00

===

==

Tingkat 4

Balok Tepi

q = 220 kg/m

A B

5,5 m

VA = ql -

l

MBMA +VB = ql -

l

MBMA +

VA = 605 + (-96,57) VB = 605 + 96,57

= 508,43 kg = 701,57 kg

Mx = VA . x qx2 Mx = 508,43(2,31) (220).(2,31)2

= 1174,47 586,97 = 587,50 kg.m

mq

VAx

qxVAdx

dMx

31,2220

43,508

00

===

==



26/50



Balok Tengah

q = 220 kg/m

A B

3,5 m

VA = ql - l

MBMA +

VB = ql - l

MBMA +

VA = 385 + (-151,75) VB = 385 + 151,75

= 233,25 kg = 536,75 kg

Mx = VA . x qx2 Mx = 233,25(1,06) (220).(1,06)2

= 247,24 123,60 = 123,64 kg.m

mq

VAx

qxVAdx

dMx

06,1220

25,233

00

===

==

Tingkat 3

Balok Tepi

q = 220 kg/m

A B

5,5 m

VA = ql -l

MBMA +VB = ql -

l

MBMA +

VA = 605 + (-156,03) VB = 605 + 156,03

= 448,97 kg = 761,03 kg



27/50



Mx = VA . x qx2 Mx = 448,97(2,04) (220).(2,04)2

= 915,50 457,78 = 458,12 kg.m

mq

VAx

qxVAdx

dMx

04,2220

97,448

00

===

==

Balok Tengah

q = 220 kg/m

A B

3,5 m

VA = ql -l

MBMA +VB = ql -

l

MBMA +

VA = 385 + (-245,19) VB = 385 + 245,19

= 139,81 kg = 630,19 kg

Mx = VA . x qx2 Mx = 139,81(0,64) (220).(0,64)2

= 89,48 45,06 = 44,42 kg.m

mq

VAx

qxVAdx

dMx

64,0220

81,139

00

===

==

Tingkat 2

Balok Tepi

q = 220 kg/m

A B

5,5 m



28/50



VA = ql -l

MBMA +VB = ql -

l

MBMA +

VA = 605 + (-215,49) VB = 605 + 215,49

= 389,51 kg = 820,49 kg

Mx = VA . x qx2 Mx = 389,51(1,77) (220).(1,77)2

= 521,49 278,091 = 243,40 kg.m

m

q

VAx

qxVAdx

dMx

77,1

220

51,389

00

===

==

Balok Tengah

q = 220 kg/m

A B

3,5 m

VA = ql -l

MBMA +VB = ql -

l

MBMA +

VA = 385 + (-338,63) VB = 385 + 338,63

= 46,37 kg = 723,63 kg

Mx = VA . x qx2 Mx = 46,37(0,22) (220).(0,22)2

= 10,20 5,32 = 4,8 kg.m

mq

VAx

qxVAdx

dMx

22,0220

37,46

00

===

==



29/50



Tingkat 1

Balok Tepi

q = 220 kg/m

A B

5,5 m

VA = ql -l

MBMA +VB = ql -

l

MBMA +

VA = 605 + (-183,17) VB = 605 + 183,17

= 421,83 kg = 788,17 kg

Mx = VA . x qx2 Mx = 421,83(1,92) (220).(1,92)2

= 809,91 405,50 = 404,41 kg.m

mq

VA

x

qxVAdx

dMx

92,1220

83,421

00

===

==

Balok Tengah

q = 220 kg/m

A B

3,5 m

VA = ql -l

MBMA +VB = ql -

l

MBMA +

VA = 385 + (-287,84) VB = 385 + 287,84

= 97,16 kg = 672,84 kg

Mx = VA . x qx2 Mx = 97,16(0,44) (220).(0,44)2

= 42,75 21,30 = 21,45 kg.m



30/50



mq

VAx

qxVAdx

dMx

44,0220

16,97

00

===

==

Resume Free Body Portal Melintang

Balok Tepi Balok Tengah Kantilever

Tingkat VA VB xMx

(kg.m) VA VB xMx

(kg.m) kg.m

5 281.72 378.28 2.35 330.69 134.13 285.87 1.12 74.97 72

4 508.43 701.57 2.31 587.5 223.25 536.75 1.06 123.64 132

3 448.97 761.03 2.04 458.12 139.81 630.19 0.64 44.42 132

2 389.51 820.49 1.77 243.4 46.37 723.63 0.22 4.8 132

1 421.83 788.17 1.92 404.41 97.16 672.84 0.44 21.45 132

I. Portal Melintang



31/50



1. Menghitung D Value

Tingkat 1

Kolom Tepi

k1

kc

EkcaDD

k

ka

kc

kk

E

E

L

EIkc

E

E

L

EIk

1,1143E0,46.2485.5111

0,460,82

0,85,0

2

5,0

8,0~76,01

2485550

)45.(45.12

1.4

4

1893

550

)50.(25.12

1.4

41

3

3

====

=+

+=

+

+=

==

===

===

Kolom tengah

k1 k2

kc

Ekc

Ek

Ek

2485

18932

18931

=

=

=



32/50



kgkgEEQ

DDGGG

E

EQ

D

DGG

EDi

EkcaDDD

k

ka

kc

kkk

i

38,3115735,63723.22365

4,10931..11

21413121

kg99,3256kg63723,735.22365

1,11431.

.11

115111

1lantaipinggirkolomsetiappadageserGaya

22365)4,1093(10)1,1143.(101

4,109324850,44..413121

0,440,662

0,665,0

2

5,0

66,04970

68,3273

2

21

20

1

======

====

=+=

=====

=+

+=

+

+=

==+

=

=

Tingkat 2

Kolom Tepi

k1

kc

k2

E

E

L

EIkc

Ek

E

E

L

EIk

19,3417400

)45.(45.12

1.4

4

18932

1893550

)50.(25.12

1.4

41

3

3

===

=

===

EkcaDD

k

ka

kc

kkk

95,785E3417,18.0,23..5212

0,236,02

0,6

2

6,0~55,038,6834

3786

2

21

====

=+

=+

=

==

+

=



33/50



Kolom tengah

k1 k2

kck3 k4

Ekc

Ek

Ek

Ek

Ek

19,3417

18934

18933

18932

18931

=

=

=

=

=

kgE

EQ

D

DGGG

kgE

EQ

Di

DGG

EDi

EkcaDDD

k

ka

kc

kkkkk

i

43,3355975,57904.84,20639

02,11962.

.12

22423222

98,2204975,57904.20639,84

95,7852.

.2

125212

84,20639)02,1196(12)95,785(82

02,119619.E0,35.3417,..423222

0,351,102

1,10

2

10,16834

7572

2

4321

20

1

=====

===

=+=

=====

=+

=+

=

==+++

=

=

Tingkat 3

Kolom Tepi

k1

kc

k2

E

E

L

EIkc

Ek

E

E

L

EIk

19,3417400

)45.(45.12

1.4

4

18932

1893550

)50.(25.12

1.4

41

3

3

===

=

===



34/50



EkcaDD

k

ka

kc

kkk

95,785E3417,18.0,23..5313

0,236,02

0,6

2

6,0~55,038,6834

3786

2

21

====

=+

=+

=

==+

=

Kolom tengah

k1 k2

kck3 k4

Ekc

Ek

Ek

Ek

Ek

19,3417

18934

18933

18932

18931

=

=

=

=

=

kgE

EQD

DGGG

kgE

EQ

D

DGG

Di

EkcaDDD

k

ka

kc

kkkk

k

i

02,2773341,47854.84,20639

02,11963..13

23433323

23,1822341,47854.20639,84

95,7853.

.13

135313

84,20639)02,1196.(12)95,785.(83

02,119619.E0,35.3417,..433222

0,351,102

1,10

2

10,16834,38

7572

2

4321

20

1

=====

===

=+=

=====

=+

=+

=

==

+++

=

=

Tingkat 4



35/50



Kolom Tepi

k1

kc

k2

EkcaDD

k

ka

kc

kkk

E

E

L

EIkc

Ek

E

E

L

EIk

72,537E1250,52.0,43..4414

0,435,12

1,5

2

5,1~51,104,2501

3786

2

21

52,1250400

)35.(35.12

1.4

4

18932

1893550

)50.(25.12

1.4

41

3

3

====

=+

=+

=

==+

=

===

=

===

Kolom tengah

k1 k2

kck3 k4

52,1250

18934

18933

18932

18931

=

=

=

=

=

Kc

Ek

Ek

Ek

Ek



36/50



kgE

EQ

D

DGGG

kgE

EQ

D

DGG

EEDi

EkcaDDD

k

ka

kc

kkkkk

i

13,1993706,35344.48,13305

31,7504.

.14

24443424

40,142835344,706.48,13305

72,5374.

.14

145414

48,13305)31,750.(12)72,537.(84

31,750E1250,520,60..443424

0,603,032

3,03

2

03,304,2501

7572

2

4321

1

=====

====

=+=

=====

=+

=+

=

==+++

=

=

Tingkat 5

Kolom Tepi

k1

kc

k2

EkcaDD

k

ka

kc

kkk

E

E

L

EIkc

Ek

E

E

L

EIk

72,537E1250,52.0,43..4515

0,435,12

1,5

2

5,1~51,1

04,2501

3786

2

21

52,1250400

)35.(35.12

1.4

4

18932

1893550

)50.(25.12

1.4

41

3

3

====

=+

=+

=

==+

=

===

=

===



37/50



Kolom tengah

k1 k2

kck3 k4

52,1250

18934

18933

18932

18931

=

=

=

=

=

Kc

Ek

Ek

Ek

Ek

kgE

EQ

D

DGGG

kgE

E

QD

D

GG

EEDi

EkcaDDD

k

ka

kc

kkkkk

i

68,1078512,19128.48,13305

31,7505.

.14

24453525

05,773512,19128.48,13305

72,537

5..14

14

4515

48,13305)31,750.(12)72,537.(85

31,750E1250,520,60..453424

60,03,032

3,03

2

03,304,2501

7572

2

4321

1

=====

====

=+=

=====

=+

=+

=

==+++

=

=

Kesimpulan

Lantai G. geser kolom pinggir (kg) G. geser kolom tengah (kg)

1

2

3

4

5

3256,99

2204,98

1822,23

1428,40

773,05

3115,38

3355,43

2773,02

1993,13

1078,68

2. Menentukan Momen-Momen Ujung Kolom



38/50



yh

A

B MB

MA

G AB h

(1-y)h

yh

GAB bekerja pada titik balok AB y0 : ( tabel 1 ) k. muto

MA = GAB ( 1-y ) h 1. jumlah tingkat bangunan

MAB = GAB ( y. h ) 2. letak kolom

Dimana y = y0 + y1 + y2 + y3 3. harga k

Mencari y0bagian tingkat 5

kkolom tepi Kolom tengah

k- y0 k- y0

1 0,8 0,65 0,66 0,70

2 0,6 0,50 1,10 0,50

3 0,6 0,45 1,10 0,455

4 1,5 0,425 3,03 0,452

5 1,5 0,375 3,03 0,45

Y1 tergantung kekakuan balok atas + bawahnya ( tabel 2 )

k1 k2 1 =43

21

kk

kk

+

+terbawah y1 = 0

kc 1 = 1 , y1 = 0

k3 k4 jika ( k1 + k2) > ( k3 + k4 ) maka 1 =21

43

kk

kk

+

+

dan harga y1menjadi

t

k

kolom tepi Kolom tengah

k1+k2 k3+k4 a1 y1 k1+k2 k3+k4 a1 y1

2 3786 3786 1 0 3786 3786 1 0



39/50



3 3786 3786 1 0 3786 3786 1 0

4 3786 3786 1 0 3786 3786 1 0

5 3786 3786 1 0 3786 3786 1 0

harga y2, tergantung harga k

( table 3 )k. muto perbandigan tinggi kolom

_ kolom teratas y1 = 0

2 =h

ha , ha = tinggi kolom di atasnya

2 = 1, y2 = 0

t

kha h a2


K y2 k- Y2

1 400 550 0,73 0,8

-

0,175 0,66 -0,5

2 400 400 1 0,6 0 1,10 0

3 400 400 1 0,6 0 1,10 0

4 400 400 1 1,5 0 3,03 0

Harga y3 - tergantung harga k

( table 3 ) - perbandingan tinggi kolom terhadap tinggi kolom bawah,

3 =h

hb

- kolom terbawah y3 = 0

- 3 = 1, y3 = 0

t

khb h a3


k- Y3 k- Y3

2 550 400 1,38 0,6 -0,05 1,10 0

3 400 400 1 0,6 0 1,10 0

4 400 400 1 1,5 0 3,03 0

5 400 400 1 1,5 0 3,03 0

Resume



40/50



t

k klm yo Y1 y2 y3 Y

1 tp 0,65 0

-

0,175 0 0,475

tgh 0,70 0 -0,5 0 0,20

2tp 0,50 0 0 -0,05 0,45

tgh 0,50 0 0 0 0,50

3tp 0,45 0 0 0 0,45

tgh 0,455 0 0 0 0,455

4tp 0,425 0 0 0 0,425

tgh 0,452 0 0 0 0,452

5tp 0,375 0 0 0 0,375

tgh 0,45 0 0 0 0,45

3. Perhitungan Momen Di Ujung Kolom

Tingkat 1

h = 550 cm = 5,5 m

a. Kolom tepi

M bawah = G11 . y. h

= kg99,3256 x 0,475 x 5,5

= 8508,89 kg.m

M atas = G11 . (1-y). h

= kg99,3256 x (1 0,475) x 5,5

= 9404,56 kg.m

b. Kolom tengah


= kg38,3115 x 0,20x 5,5

= 3426,92 kg.m

M atas = G21 . (1-y) .h

= kg38,3115 x (1 - 0,20) x 5,5

= 13707,67 kg.m

Tingkat 2

h = 400 cm =4 m

a. Kolom tepi




41/50



= kg98,2204 x 0,45 x 4

= 3968,96 kg.mM atas = G12 . (1-y). h

= kg98,2204 x (1 0,45) x 4

= 4850,96 kg.m

b. Kolom tengah

M bawah = G22 . y h

= kg43,3355 x 0,50 x 4

= 6710,86 kg.mM atas = G22 . (1-y) .h

= kg43,3355 x (1 0,50) x 4

= 6710,86 kg.m

Tingkat 3

h = 400 cm = 4 m

a. Kolom tepiM bawah = G13 . y . h

= kg23,1822 x 0,45 x 4

= 3280,01 kg.m

M atas = G13 . (1-y) . h

= kg23,1822 x (1 0,45) x 4

= 4008,91

b. Kolom tengah


= kg02,2773 x 0,455 x 4

= 5046,89 kg.m

M atas = G23 . (1-y) . h

= kg02,2773 x (1 0,455) x 4

= 6045,18 kg.m



42/50



Tingkat 4

h = 400 cm = 4 m

a. Kolom tepi


= kg40,1428 x 0,425 x 4

= 2428,28 kg.m

M atas = G14 . (1-y) .h

= kg40,1428 x (1 0,425) x 4

= 3285,32 kg.m

b. Kolom tengah


= kg13,1993 x 0,452 x 4

= 3603,58 kg.m

M atas = G24 . (1-y) . h

= kg13,1993 x (1 0,452) x 4

= 4368,94 kg.m

Tingkat 5

h = 400 cm = 4 m

a. Kolom tepi


= kg05,773 x 0,375 x 4

= 1159,58 kg.m

M atas = G15 . (1-y) . h

= kg05,773 x (1 0,375) x 4

= 1932,62 kg.m

b. Kolom tengah


= kg68,1078 x 0,45 x 4

= 1941,62 kg.m

M atas = G25 . (1-y) . h



43/50



= kg68,1078 x ( 1- 0,45 ) x 4

= 2373,31 kg.m

E. MENENTUKAN MOMEN UJUNG BALOK

Mka= Mkolomkk

k

kika

ka +

.

Mki= Mkolomkk

k

kika

ki +

.

1. Tingkat 1( satu )

- balok tepi

Mka= Mkolomkk

k

kika

ka +

.

= )56,396856,9404.(1893

1893+

= 13373,12 Kg.M

Mki = 0

- balok tengah

Mka= Mkolomkk

k

kika

ka +

.

= )86,671062,13707.(18931893

1893+

+

= 10209,24 Kg.M

Mki = Mkolomkk

k

kika

ki +

.



44/50



= )86,671062,13707.(18931893

1893+

+

= 10209,24 Kg.M

2. Tingkat 2( dua )

- balok tepi

Mka= Mkolomkk

k

kika

ka +

.

= )01,328096,4850.(1893

1893+

= 8130,97 Kg.M

Mki = 0

- balok tengah

Mka= Mkolomkk

k

kika

ka +

.

= )89,504686,6710.(

18931893

1893+

+= 5878,87Kg.M

Mki = Mkolomkk

k

kika

ki +

.

= )89,504686,6710.(18931893

1893+

+

= 5878,87 Kg.M

3. Tingkat 3( tiga )

Mka= Mkolomkk

k

kika

ka +

.

= )28,482891,4008.(1893

1893+

= 8867,19 Kg.M



45/50



Mki = 0

- balok tengah

Mka= Mkolomkk

k

kika

ka +

.

= )58,360318,6045.(18931893

1893+

+

= 4824,38 Kg.M

Mki = Mkolomkk

k

kika

ki

+ .

= )58,360318,6045.(18931893

1893+

+

= 4824,38 Kg.M

4. Tingkat 4( empat )

Mka= Mkolom

kk

k

kika

ka

+

.

= )58,115932,3285.(1893

1893+

= 4444,9 Kg.M

Mki = 0

- balok tengah

Mka= Mkolomkk

kkika

ka +

.

= )62,194194,4368.(18931893

1893+

+

= 3155,28 Kg.M

Mki = Mkolomkk

k

kika

ki +

.



46/50



= )62,194194,4368.(18931893

1893+

+

= 3155,28 Kg.M

5. Tingkat 5( lima )

Mka= Mkolomkk

k

kika

ka +

.

= )2077,1.(

1893

1893

= 2077,1 Kg.M

Mki = 0

- balok tengah

Mka= Mkolomkk

k

kika

ka +

.

= )2077,1.(189368,1380

68,1380

+

= 884,84 Kg.M

Mki = Mkolomkk

k

kika

ki +

.

= )1,2077.(189368,1380

1893

+

= 1200,56 Kg.M

0.028 0.06 0.009 0.071 0.071 0.0090.062 0.028

17 18 1920

0.166 0.035 0.044 0.153 0.153 0.044

0.035 0.166



47/50



13 14 1516

1.991 0.049 0.043 0.151 0.151 0.0430.049 0.199 9 1011 12

0.199 0.036 0.043 0.151 0.151 0.0430.036 0.199

5 6 7 8

0.23 0.049 0.059 0.21 0.21 0.0590.049 0.23

1 2 34

F. MENENTUKAN MOMENT MAX

1.MOMENT MAX BALOK TEPI (Tingkat 1)

Ma = -7102 Mb = 9268.9

A B

Ra 5,5 m Rb

MB = 0


q = 220 kg


48/50



L

MbMaql

Ra

MbMaqlLRa

+

=

=+

2

2

2

1

02

1

.

5,5

9,926871025,5.2202

1 2+

=Ra = 211 Kg

MV = 0

Ra + Rb (q.L) = 0Rb = (q.L) Ra

Rb = 1210 211 = 999 kg

mq

Rax

xqRa

dx

dMx

qxxRa

96.0220211

0.

0

02

1. 2

===

=

=

=

x = 0.96 m maka,

Kgm

qxxRaM

2,10196,0.220.2

196,0.211

2

1.max

2

2

=

=

2.MOMENT MAX BALOK TENGAH (Tingkat 1)

MB = 0

Nuki Saeful/020191/S1 Teknik Sipil

q = 220 kg

3,5

48


49/50



L

MbMaql

Ra

MbMaqlLRa

+

=

=+

2

2

2

1

02

1.

5,3

5,80915,80915,3.2202

1 2+

=Ra = 385 Kg

MV = 0

Ra + Rb (q.L) = 0

Rb = (q.L) Ra

Rb = 770 385 = 385 kg

mq

Ra

x

xqRa

dx

dMx

qxxRa

75,1220

385

0.

0

02

1. 2

===

=

=

=

x = 1,75 m maka,

Kgm

qxxRaM

9,33675,1.385.2

175,1.385

2

1.max

2

2

=

=

Dengan perhitungan yang sama Moment maksimun didapat, pada table ini :

FREE BODY

tingkat BALOKM balok

q L q.L

Gayavertikal x M max

ki ka RA RB

1tepi -7102 9268.9 220 5.5 1210 211 999 0.96 101.2

tengah -8091.5 8091.5 220 3.5 770 385 385 1.75 336.9

2tepi -4394.2 9108.3 220 5.5 1210 -252 1462 -1.15 144.5

tengah -7951.3 7951.3 220 3.5 770 385 385 1.75 336.9

3tepi -3650 7505.8 220 5.5 1210 -96 1306 -0.44 21

tengah -6604.7 6604.7 220 3.5 770 385 385 1.75 336.9

4tepi

-2704.9 5364 220 5.5 1210 122 1088 0.55 33.6tengah -4692.6 4692.6 220 3.5 770 385 385 1.75 336.9



50/50



5tepi 1505.4 1612.1 120 5.5 660 -237 897 -1.97 233.7

tengah -2289 2289 120 3.5 420 210 210 1.75 183.8

Perhitungan Gempa Arah Melintang

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