Fheby Shary. TOP..

psoATAPLAPANGAN

40

35

30

25pers.4

kkkkkkkkkk20

pers.1

15

10pers.2

5e

800 700 600 500 400 300 200 100 0 100 200 300 400 500 600 700 800 900 1000

5pers.3

10

15

201/2 h - 80

25Diambil e = 570 mm

30

35

40

Karena daerah e maks. Tidak memenuhi >

40

psoATAP

Tumpuan40

35

30

25

20

15

10pers.2

5e

800 700 600 500 400 300 200 100 0 100 200 300 400 500 600 700 800 900 1000

5pers.3

10pers.4

15pers.1

201/2 h -80


30

35


300

40

psoLantaiLAPANGAN

40

35

30

25pers.4

20pers.1

15

10pers.2

5e

800 700 600 500 400 300 200 100 0 100 200 300 400 500 600 700 800 900 1000

5

10pers.3

15

201/2 h - 80


30

35


300

35

40

psoLantai

Tumpuan40

35

30

25

20

15

10

5pers.2

e

800 700 600 500 400 300 200 100 0 100 200 300 400 500 600 700 800 900 1000

5pers.3

10pers.4

15pers.1

201/2 h -80


30


300

35

40

4 m

4 m

37

m

B B D D

A A C C

PO

T D

- D

Ka

be

l Te

nd

on

PO

T C

- C

Ka

be

l Te

nd

on

PO

T B

- B

PO

T A

- A

150

cm

100

cm

100

cm

57

cm

130

cm

57

cm

90

cm9

0 cm

57

cm

Ga

ris N

etr

al

Ka

be

l Te

nd

on

Ga

ris N

etr

al

Ka

be

l Te

nd

on

BA

LO

K L

AN

TA

I

BA

LO

K A

TA

P

37

m

130

cm

1

50 c

m

E=

57

E=

67

Struktur Beton Gedung Lanjutan

Maarifal/062103018 Bandit Studio 06 Aswar Guzasi/062103006

PERHITUNGAN JARAK TENDON

BALOK ATAP

TAHAP AWAL

### KNm q1 = 19.8 ### KNm

C D

44400.000

22200.0000 KN 22200.000 KN

x

30 m

Lihat Perhitungan Momen Berat Sendiri.!

Mx = ### X - ### - 9.9000 X²

Pso = 187483409 N

Fci = 28 Mpa

As = b . h

= 500 . 1000

= 500000

Ic = 1/12 . b.

= 1/12 . 500 . 1000 ³

= 41666666666.7

ATAS

0.25 . √ fci ≥ - Pso + Pso . e . Ya - Mbs x . Ya

As Ic - Ic

0.25 . 1.3229 ≥ -187483409 + 187483409 e 325 - Mbs x . 325

500000 4.166667E+10 4.1667E+10

0.33071891 ≥ -374.966819 + 1.462371E+00 e - 7.8E-09 Mbs x

375.297537445 ≥ 1.462371E+00 e - 0.0000000078000 . Mbs x

e ≥ 7.8000E-09 Mbs x + 375.297537445

h³

mm4



1.462371E+00

X Mbs x ex≤

0 -129841931234.157 -4.359151706E+02

1000 -107651831234.157 -317.557497829483

2000 -85481531234.157 -199.305434423762

3000 -63331031234.157 -81.1589803627688

4000 -41200331234.157 36.8818643534959

5000 -19089431234.157 154.817099725032

6000 3001668765.843 272.64672575184

7000 25072968765.843 390.370742433919

8000 47124468765.843 507.98914977127

9000 69156168765.843 625.501947763892

10000 91168068765.843 742.909136411786

11000 113160168765.843 860.210715714951

12000 135132468765.843 977.406685673389

13000 157084968765.843 1094.4970462871

14000 179017668765.843 1.2114818E+03

15000 200930568765.843 1.328361E+03

BAWAH

-0.6 . Fci ≥ - Pso - Pso e Yb + Mbs x . Yb

As Ic Ic

-0.6 . 28 ≥ 187483409 - 187483409 e 325 + Mbs x . 325

500000 41666666666.6667 41666666666.7

-16.8000 ≥ 374.966819 - 1.46237059 e + 0.00000000780000 Mbs x

-391.766819 ≥ -1.46237059 e + 0.00000000780000 Mbs x

e ≤ 0.0000000078000000 Mbs x - 391.766819

1.46237059



X Mbs x

0 -129841931234.15700 -960.450032009761

1000 -107651831234.15700 -842.092359259311

2000 -85481531234.15730 -723.840295853589

3000 -63331031234.15730 -605.693841792596

4000 -41200331234.15730 -487.652997076332

5000 -19089431234.15730 -369.717761704795

6000 3001668765.84267 -251.888135677988

7000 25072968765.84270 -134.164118995909

8000 47124468765.84270 -16.5457116585577

9000 69156168765.84270 100.9670863

10000 91168068765.84270 218.374275

11000 113160168765.84300 335.675854285124

12000 135132468765.84300 452.871824243561

13000 157084968765.84300 569.962184857269

14000 179017668765.84300 686.946936126249

15000 200930568765.84300 803.826078050501

TAHAP AKHIR

-295939.232 KNm q= 3367 KN/m -295939.232 KNm

C D

Q= 101010 KN

50505 50505

x

Ps = Pso - 15% Pso

= 85% Pso

Pso = 187483409 N = 159360898

Fci = 28 Mpa

ex≤



MDLx = 232845 X - 7.762 X² - 1047000000.00

MLLx = 109650 X - 3.655 X² - 508110000.00

Mtx = MDLx + MLLx

X Mtx

0 -1555110000

1000 -1224031500

2000 -915786000

3000 -630373500

4000 -367794000

5000 -128047500

6000 88866000

7000 282946500

8000 454194000.0

9000 602608500

10000 728190000.0

11000 830938500

12000 910854000

13000 967936500

14000 1002186000

15000 1013602500

ATAS

-0.45 . Fc' ≥ -Ps + Ps e Ya - Mbs x Ya - Mtx. Ya

As Ic Ic Ic

-0.45 . 36 ≥ -159360898 + 159360898 e 325 - Mbsx 325 - Mtx 325

500000 4.166667E+10 4.1667E+10 4.1667E+10

-16.2 ≥ -318.721796 + 1.243015 e- 7.8E-09 Mbsx - 7.8E-09 Mtx

302.521796 ≥ 1.243015 e- 0.00000000780 Mbsx - 0.0000000078000 Mtx



e ≤ 0.000000007800 Mbsx + 0.000000007800 Mtx 302.521796

1.243015

X Mbs x Mt x ex≤

0 -129841931234.15700 -1555110000 -581.147551623167

1000 -107651831234.15700 -1224031500 -439.825691617368

2000 -85481531234.15730 -915786000 -298.771356459687

3000 -63331031234.15730 -630373500 -157.984546150122

4000 -41200331234.15730 -367794000 -17.4652606886744

5000 -19089431234.15730 -128047500 122.786499924656

6000 3001668765.84267 88866000 262.77073568987

7000 25072968765.84270 282946500 402.487446606967

8000 47124468765.84270 454194000.0 541.936632675947

9000 69156168765.84270 602608500 681.11829389681

10000 91168068765.84270 728190000.0 820.032430269556

11000 113160168765.84300 830938500 958.679041794185

12000 135132468765.84300 910854000 1097.0581284707

13000 157084968765.84300 967936500 1235.16969029909

14000 179017668765.84300 1002186000 1373.01372727937

15000 200930568765.84300 1013602500 1510.59023941153

BAWAH

0.5 . √ Fc' ≥ - Pso - Pso e Yb + Mbs x . Yb + Mt. Yb

As Ic Ic Ic

0.5 √ 36 ≥ -159360898 - ### e 325 + Mbsx. 325 + Mt. 325

500000 41666666666.6667 4.1667E+10 4.2E+10

3.0000 ≥ -318.721796 - 1.243015 e+ 7.8E-09 Mbsx + 7.8E-09 Mt



321.721796 ≥ -1.2430150034 e+ 7.8E-09 Mbsx + 7.8E-09 Mt

1.243015 e ≥ 7.8E-09 Mbsx + 7.8E-09 Mt -321.721796

e ≤ 7.8E-09 Mbsx + 7.8E-09 Mt -321.721796

1.243015

X Mbs x Mt x ex≤

0 -129841931234.15700 -1555110000 -1083.34872359617

1000 -107651831234.15700 -1224031500 -942.026863590374

2000 -85481531234.15730 -915786000 -800.972528432693

3000 -63331031234.15730 -630373500 -660.185718123128

4000 -41200331234.15730 -367794000 -519.66643266168

5000 -19089431234.15730 -128047500 -379.41467204835

6000 3001668765.84267 88866000 -239.430436283136

7000 25072968765.84270 282946500 -99.7137253660388

8000 47124468765.84270 454194000.0 39.7354607029411

9000 69156168765.84270 602608500 178.917121923804

10000 91168068765.84270 728190000.0 317.83125829655

11000 113160168765.84300 728190000.0 455.833116300274

12000 135132468765.84300 910854000 594.856956497691

13000 157084968765.84300 967936500 732.968518326087

14000 179017668765.84300 1002186000 870.812555306365

15000 200930568765.84300 1013602500 1008.38906743853

Resume daerah aman terhadap perletakan tendon pada balok Atap.

e AWAL AKHIR

0 -435.915170579933 -581.147551623167

15 1.328361E+03 1510.59023941153



0 -960.450032009761 -1083.34872359617

15 803.826078050501 1008.38906743853

26

AWAL AKHIR

-435.915170579933 -581.147551623167

1094.4970462871 1235.16969029909

-960.450032009761 -1083.34872359617

569.962184857269 732.968518326087

325

325



Perhitungan e dalam tinjauan setiap 1 mater mulai dari tumpuan ke lapangan.

A T A P

e= 21 32.5 cm

e= 22 32.5 cm

400 300

2600 cm

Untuk 1 meter di momen negatif

21=

400

21 ex ex 300

300 ex = 15.75 cm

400

Untuk 1 meter di momen positif

xBALOK ATAP

e (mm)

100 - 157.5

22 200 - 105

300 - 52.5

300 400 - 0

500 73.33

600 146.67



ex 700 220

800 220

200 900 220

1000 220

22=

300 1100 220

ex 200 1200 220

1300 220

ex = 14.667 cm

L A N T A I

e= 40 50 cm

e= 32 cm 50 cm

420 380

2600 cm

Untuk 1 meter di momen negatif

40=

420

40 ex ex 320

320 ex = 30.48 cm

420

Untuk 1 meter di momen positif

xBALOK ATAP

e (mm)

32 100 - 304.76

200 - 209.52

380 300 - 114.29

400 - 19.05

500 67.37

600 151.58



280 700 235.79

800 320

32=

380 900 320

ex 280 1000 320

1100 320

ex = 23.579 cm 1200 320

1300 320

Tabel perletakan tendon pada balok

xBALOK ATAP BALOK LANTAI

e (mm) e (mm)

100 157.5 304.76

200 105 209.52

300 52.5 114.29

400 0 19.05

500 73.33 67.37

600 146.67 67.37

700 220 235.79

800 220 320

900 220 320

1000 220 320

1100 220 320

1200 220 320

1300 220 320



0 √ #REF! ≥ - Ps 0.85 - Ps 0.9 e ###+

#NAME? . #REF!

0 0 0



LAPANGAN BENTANGAN CD (ATAP)

AWAL

ATAS

0.25 . √ Fci ≥ - Pso + Pso . e . Ya - Mbs . Ya

As Ic Ic

0.25 √ 28 ≥ - Pso + Pso e 500-

7.6E+10 . 500

500000 41666666667 4.1667E+10

1.3229 ≥ -0.000002 Pso + 1.200000E-08 Pso e - 9.0610E+02

e <1.3229 - -2.0000E-06 Pso + 9.0610E+02

1.200000E-08 Pso

e <907.4197

- -1.666667E+02Persamaan 1

1.200000E-08 Pso

Pso <907.4197

( e -1.666667E+02 ). 1.200000E-08

pso= 0 e = 1.666667E+02 mm

e= 0 1/Pso = -4.537099E+08

Pso = -2.204052E-09 N

BAWAH

-0.6 fci ≥ - Pso - Pso e Yb + Mbs x . Yb

As Ic Ic

-0.6 28 ≥ - Pso - Pso e 500 + 7.6E+10 . 500

500000 4.166667E+10 41666666666.7

-16.8 ≥ -0.000002 - - 1.200000E-08 Pso e + 9.0610E+02

e ≥ -16.8 - -0.000002 - - 9.0610E+02

-1.200000E-08 Pso

e <-9.2290E+02

- 1.666667E+02Persamaan 2



e <-1.200000E-08 Pso

- 1.666667E+02

Pso <-922.8968

(e + 1.666667E+02 ). -1.200000E-08

pso= 0 e = -1.666667E+02 mm

e= 0 1/Pso = 461448412.595

Pso = 2.1670895E-09 N

AKHIR

ATAS

-0.45 . Fc' ≥ 0.85 -Ps Ps e Ya - Mt Ya

As + Ic Ic

-0.45 . 36 ≥ 0.85 -Ps + 0.85 Ps e 500 - 2E+11 500

500000 41666666667 4.1667E+10

-16.2 ≥ -0.0000017 Ps + 0.0000000102 e Ps - 2054.78422

e < -16.2 - -0.0000017 Ps + 2054.78422181

0.0000000102 Ps

e <2038.584

- -166.666667persamaan 3

0.0000000102 Ps

Pso <2038.5842

(e + -1.66667E+02 ) 1.020000E-08

pso= 0 e = 1.666667E+02 mm

e= 0 1/Ps = -1199167189.3

Ps = -8.3391208E-10

BAWAH

0.5 . √ Fci ≥ - Pso - Pso e Yb + Mt. Yb

As Ic Ic

0.5 √ 36 ≥ - Pso 0.85 - Pso 0.9 e 500+

1.7E+11 . 500

500000 41666666667 41666666667



3.0000 ≥ -0.0000017 Ps - 1.02E-08 e Ps + 2054.78422

e < 3.0000 - -0.0000017 Ps - 2054.78422

-0.0000000102 Ps

e < -2051.7842- 166.666666667

persamaan 4

-1.02E-08 Ps

Pso <-2051.7842

(e + 1.66667E+02 ) -1.020000E-08

pso= 0 e = -1.666667E+02 mm

e= 0 1/Ps = 1206931895.18

Ps = 8.2854716E-10 N

TUMPUAN

AWAL

ATAS


As Ic Ic

0.25 √ 28 ≥ Pso + Pso e 500-

1.3E+11 . 500

500000 4.166667E+10 4.1667E+10

1.3229 ≥ -0.000002 Pso + 1.200000E-08 Pso e - 1.5581E+03

e < 1.3229 - -0.000002 Pso + 1.5581E+03

1.200000E-08 Pso

e < 1559.4261- -1.666667E+02

Persamaan 1

1.200000E-08 Pso

Pso <1559.4261

(e + -1.66667E+02 ) 1.200000E-08



pso= 0 e = 1.666667E+02 mm

e= 0 1/Pso = -779713025.23

Pso = -1.2825231E-09 N

BAWAH


As Ic Ic

-0.6 28 ≥ - Pso - Pso e 500 + 1.3E+11 . 500

500000 4.166667E+10 41666666666.7

-16.8 ≥ -0.000002 Pso - 1.200000E-08 Pso e + 1.558E+03

e ≥ -16.8 - -0.000002 Pso - 1.5581E+03

-1.200000E-08 Pso

e <-1.5749E+03


-1.200000E-08 Pso

Pso <-1574.9032

(e + 1.66667E+02 ) -1.200000E-08

pso= 0 e = -1.666667E+02 mm

e= 0 1/Pso = 787451587.405

Pso = 1.2699193E-09 N

AKHIR

ATAS

-0.45 . Fci ≥ 0.85 -Ps Ps e Ya - Mt Ya

As + Ic Ic

-0.45 . 36 ≥ 0.85 -Ps + 0.85 Ps e 500 - 2.9594E+11 500

500000 + 41666666667 4.1667E+10

-16.2 ≥ -0.0000017 Ps + 0.0000000102 e Ps - 3551.27078

e < -16.2 - -0.0000017 Ps + 3551.27077819



0.0000000102 Ps

e <3535.071

- -166.666667persamaan 3

0.0000000102 Ps

Pso 03535.0708

(e + -1.66667E+02 ) 1.020000E-08

pso= 0 e = 1.666667E+02 mm

e= 0 1/Ps = -2079453398.9

Ps = -4.808956E-10 N

BAWAH


As Ic Ic

0.5 √ 36 ≥ - Pso 0.85 - Pso 0.9 e 500+

3E+11 . 500

500000 41666666667 41666666667

3.0000 ≥ -0.0000017 Ps - 1.02E-08 e Ps + 3551.27078

e < 3.0000 - -0.0000017 Ps - 3551.27078

-0.0000000102 Ps

e < -3548.2708- 166.666666667

persamaan 4

-1.02E-08 Ps

Pso <-3548.2708

(e + 1.66667E+02 ) -1.020000E-08

pso= 0 e = -1.666667E+02 mm

e= 0 1/Ps = 2087218104.82

Ps = 4.7910661E-10 N

BENTANGAN BE (LANTAI)

LAPANGAN

AWAL



ATAS


As Ic Ic

0.25 √ 28 ≥ - Pso + Pso e 725-

1.6E+11 . 725

1051250 1.841878E+11 1.8419E+11

1.3229 ≥ -9.5125E-07 Pso + 3.936201E-09 Pso e - 6.1452E+02

e < 1.3229 - -9.5124851E-07 Pso + 6.1452E+02

3.936201E-09 Pso

e< 615.8398

- -2.416667E+02Persamaan 1

3.936201E-09 Pso

Pso <615.8398

( e -2.416667E+02 ) 3.936201E-09

pso= 0 e = 2.416667E+02 mm

e= 0 1/Pso = -6.474016E+08

Pso = -1.544636E-09 N

BAWAH


As Ic Ic

-0.6 28 ≥ - Pso - Pso e 725 + 1.6E+11 . 725

1051250 1.841878E+11 184187760417

-16.8 ≥ -9.5125E-07 - - 3.936201E-09 Pso e + 6.1452E+02

e ≥ -16.8 - -9.5125E-07 - - 6.1452E+02

-3.936201E-09 Pso

e <-6.3132E+02


-3.936201E-09 Pso



Pso <-631.3169

(e + 2.416667E+02 ) -3.936201E-09

pso= 0 e = -2.416667E+02 mm

e= 0 1/Pso = 663671886.703

Pso = 1.5067687E-09 N

AKHIR

ATAS

-0.45 . Fci ≥ 0.85 -Ps Ps e Ya - Mt Ya

As + Ic Ic

-0.45 . 28 ≥ 0.85 -Ps + 0.85 Ps e 725 - 4E+11 725

1051250 184187760417 1.8419E+11

-12.6 ≥ -8.0856E-07 Ps + 3.3457706E-09 e Ps - 1446.78628

e < -12.6 - -8.0856E-07 Ps + 1446.78628367

3.3457706E-09 Ps

e <1434.186

- -241.666667persamaan 3

3.3457706E-09 Ps

Pso <1434.1863

(e + -2.41667E+02 ) 3.345771E-09

pso= 0 e = 2.416667E+02 mm

e= 0 1/Pso = -1773750977.3

Pso = -5.63777E-10 N

BAWAH


As Ic Ic

0.5 √ 28 ≥ - Pso 0.85 - Pso 0.9 e 725+

3.7E+11 . 725

1051250 184187760417 184187760417

2.6458 ≥ -8.0856E-07 Ps - 3.34577E-09 e Ps + 1446.78628



e < 2.6458 - -8.0856E-07 Ps - 1446.78628

-3.3457706E-09 Ps

e < -1444.1405- 241.666666667

persamaan 4

-3.3458E-09 Ps

Pso <-1444.1405

(e + 2.41667E+02 ) -3.345771E-09

pso= 0 e = -2.416667E+02 mm

e= 0 1/Ps = 1786062040.76

Ps = 5.5989097E-10 N

TUMPUAN

AWAL

ATAS


As Ic Ic

0.25 √ 28 ≥ Pso + Pso e 725-

2.8E+11 . 725

1051250 1.841878E+11 1.8419E+11

1.3229 ≥ -9.5124851E-07 Pso + 3.936201E-09 Pso e - 1.0849E+03

e < 1.3229 - -9.5124851E-07 Pso + 1.0849E+03

3.936201E-09 Pso

e < 1086.2543- -2.416667E+02

Persamaan 1



3.936201E-09 Pso- -2.416667E+02

Pso <1086.2543

(e + -2.41667E+02 ) 3.936201E-09

pso= 0 e = 2.416667E+02 mm

e= 0 1/Pso = -1141924786.3

Pso = -8.7571442E-10 N

BAWAH


As Ic Ic

-0.6 28 ≥ - Pso - Pso e 725 + 2.8E+11 . 725

1051250 1.841878E+11 184187760417

-16.8 ≥ -9.5125E-07 Pso - 3.936201E-09 Pso e + 1.0849E+03

e ≥ -16.8 - -9.5125E-07 Pso - 1.0849E+03

-3.936201E-09 Pso

e <-1.1017E+03


-3.936201E-09 Pso

Pso <-1101.7314

(e + 2.41667E+02 ) -3.936201E-09

pso= 0 e = -2.416667E+02 mm

e= 0 1/Pso = 1158195113.3

Pso = 8.6341238E-10 N

AKHIR

ATAS

-0.45 . Fci ≥ 0.85 -Ps Ps e Ya - Mt Ya



As + Ic Ic

-0.45 . 28 ≥ 0.85 -Ps + 0.85 Ps e 725 - 6.482E+11 725

1051250 184187760417 1.8419E+11

-12.6 ≥ -8.0856E-07 Ps + 3.3457706E-09 e Ps - 2551.46385

e < -12.6 - -8.0856E-07 Ps + 2551.46384548

3.3457706E-09 Ps

e <2538.864

- -241.666667persamaan 3

3.3457706E-09 Ps

Pso <2538.8638

(e + -2.41667E+02 ) 3.345771E-09

pso= 0 e = 2.416667E+02 mm

e= 0 1/Ps = -3139977197.1

Ps = -3.1847365E-10 N

BAWAH


As Ic Ic

0.5 √ 28 ≥ - Pso 0.85 - Pso 0.9 e 725+

6.5E+11 . 725

1051250 184187760417 184187760417

2.6458 ≥ -8.0856E-07 Ps - 3.34577E-09 e Ps + 2551.46385

e < 2.6458 - -8.0856E-07 Ps - 2551.46385

-3.3457706E-09 Ps

e < -2548.8181- 241.666666667

persamaan 4

-3.3458E-09 Ps

Pso <-2548.8181

(e + 2.41667E+02 ) -3.345771E-09



pso= 0 e = -2.416667E+02 mm

e= 0 1/Ps = 3152288260.59

Ps = 3.1722987E-10 N

KONTROL

BALOK ATAP

LAPANGAN

Persamaan 1

e= 570 1/Pso = 1.874834E+08

Persamaan 2 = 5.333805E-09

e= 570 1/Pso = 104400093.347

Persamaan 3 = 1.874834E+08 Diambil Pso terkecil = 1.874834E+08 N

e= 570 1/Ps = 495523631.941

Persamaan 4 = 2.0180672E-09

e= 570 1/Ps = 273061514.747

= 3.6621785E-09

TUMPUAN

Persamaan 1

e= 570 1/Pso = 322195464.972

Persamaan 2 = 3.103706E-09

e= 570 1/Pso = 178156467.739

Persamaan 3 = 5.6130435E-09 Diambil Pso terkecil = 178156467.738675 N

e= 570 1/Ps = 859278264.024

Persamaan 4 = 1.1637674E-09

e= 570 1/Ps = 472221290.683

= 2.1176512E-09

Diambil Pso terkecil= 187483409.265629 N



BALOK LANTAI

LAPANGAN

Persamaan 1

e= 670 1/Pso = 365265471.446

Persamaan 2 = 2.7377348E-09

e= 670 1/Pso = 175927648.212


e= 670 1/Ps = 1000754442.45

Persamaan 4 = 9.9924613E-10

e= 670 1/Ps = 473453374.608

= 2.1121404E-09

TUMPUAN

Persamaan 1

e= 670 1/Pso = 644276630.419

Persamaan 2 = 1.5521283E-09

e= 670 1/Pso = 307016986.157


e= 670 1/Ps = 1771582465.31

Persamaan 4 = 5.6446709E-10

e= 670 1/Ps = 835615718.071

= 1.1967223E-09

Diambil Pso terkecil = 365265471.446 N

ATAP

Menghitung banyak tendon

1 Strand = 98.7 mm2

Pso = 187483409.266 N

Aps = 2073

Besarnya gaya pratekan untuk 1strand=

= 0.74 . 18.75

= 13.875 t

= 138750 N

mm2



Jumlah Strand

= Pso

138750

= 1351.232 Dipakai 2 tendontipe 19 dng kwt untaian 15 (Lihat tabel VSL)

Maka besar Aps= 2962 Diameter masing-masing = 73 mm

LANTAI

Menghitung banyak tendon

1 Strand = 98.7 mm2

Pso = 365265471.446 N

Aps = 2 x 1481

Besarnya gaya pratekan untuk 1 strand=

= 0.74 . 18.75

= 13.875 t

= 138750 N

Jumlah Strand (Lihat tabel VSL)

= Pso

138750 1316.27196918

= 2632.544 Dipakai 2 tendontipe 19 dng kwt untaian 16

Maka besar Aps= 3158 Diameter masing-masing = 78 mm

mm2

mm2

mm2



KONTROL GARIS ELASTIS


AWAL

ATAS

- Pso + Pso . e . Ya - Mbs . Ya

As Ic Ic

- 187483409.266 + 187483409 570 500-

7.6E+10 . 500

500000 41666666667 4.1667E+10

-374.966819 + 1.282387E+03 - 9.0610E+02

1.3229 ( AMAN)

AWAL

BAWAH

- Pso-

Pso . e . Yb+

Mbs . Yb

As Ic Ic

- 187483409.266-

187483409 570 500+

7.6E+10 . 500

500000 4.166667E+10 4.1667E+10

-374.966819 + 1.282387E+03 - 9.0610E+02

-751.2565 ( AMAN)



AKHIR

ATAS

Mencari nilai Ps ( kehilangan gaya pratekan)

Ps = Pso - Pso . 20 %

Ps = 1.9E+08 - 1.9E+08 . 20 %

Ps = 149986727.413

0.85 ps+

Ps . e . Ya-

Mt Ya

As Ic Ic

0.85 -149986727+

149986727 570 500-

2E+11 . 500

500000 4.166667E+10 4.166667E+10

-254.977437 + 1.025909E+03 - 2.0548E+03

-1.283852E+03 ( AMAN)

AKHIR

BAWAH

- Ps - Ps e Yb + Mt. Yb

As Ic Ic

-149986727.41-

-149986727.41 570 500+

2E+11 . 500

500000 4.166667E+10 4.166667E+10

-299.973455 - -1.025909E+03 + 2.0548E+03

2.780720E+03 ( AMAN)

TUMPUAN

AWAL

ATAS

- Pso + Pso . e . Ya - Mbs . Ya

As Ic Ic

- 0 + 0 0 --

0 . -

0 0.000000E+00 0.0000E+00

#DIV/0! + #VALUE! - #VALUE!

#DIV/0! ( AMAN)

AWAL



BAWAH

- Pso-

Pso . e . Yb+

Mbs . Yb

As Ic Ic

- 0-

0 = -+

0 . -

0 0.000000E+00 0.0000E+00


#DIV/0! ( AMAN)

AKHIR

ATAS


Ps = Pso - Pso . 20 %

Ps = 0 - 0 . 20 %

Ps = 0

0.85 ps+

Ps . e . Ya-

Mt Ya

As Ic Ic

0.85 0+

0 = --

0E+00 . -

0 0.000000E+00 0.000000E+00


#DIV/0! ( AMAN)

AKHIR

BAWAH

- Ps - Ps e Yb + Mt. Yb

As Ic Ic

0-

0 = -+

0E+00 . -

0 0.000000E+00 0.000000E+00

#DIV/0! - #VALUE! + #VALUE!

#DIV/0! ( AMAN)

LAPANGAN BENTANGAN BE (LANTAI)

AWAL

ATAS




As Ic Ic

0.25 √ 28 ≥ - 365265471.446 + 365265471 670 725-

1.6E+11 . 725

1051250 1.841878E+11 1.8419E+11

1.3229 ≥ -347.458237 + 9.632980E+02 - 6.1452E+02

1.3229 ≥ 1.3229 ( AMAN)

AWAL

BAWAH

-0.6 . Fci ≥ - Pso-

Pso . e . Yb+

Mbs . Yb

As Ic Ic

-0.6 28 ≥ - 365265471.446-

365265471 670 725+

1.6E+11 . 725

1051250 1.841878E+11 1.8419E+11

-16.8000 ≥ -347.458237 + 9.632980E+02 - 6.1452E+02

-16.8000 ≥ -696.2393 ( AMAN)

AKHIR

ATAS


Ps = Pso - Pso . 20 %

Ps = 3.7E+08 - 3.7E+08 . 20 %

Ps = 292212377.157

-0.45 . Fc' ≥0.85 ps

+Ps . e . Ya

-Mt Ya

As Ic Ic

-0.45 . 38 ≥0.85 -292212377

+292212377 670 725

-4E+11 . 725

1051250 1.841878E+11 1.841878E+11

-17.1 ≥ -236.271601 + 7.706384E+02 - 1.4468E+03

-17.1 ≥ -9.124195E+02 ( AMAN)

AKHIR

BAWAH

0.5 . √ Fci ≥ - Ps - Ps e Yb + Mt. Yb



0.5 . √ Fci ≥As Ic Ic

0.5 . √ 28 ≥-292212377.16

--292212377.16 670 725

+4E+11 . 725

1051250 1.841878E+11 1.841878E+11

2.6458 ≥ -277.966589 - -7.706384E+02 + 1.4468E+03

2.6458 ≥ 1.939458E+03 ( AMAN)



KONTROL

BATANG CD ( ATAP )

Mn = Aps . fps . ( dp - 0.5 a )a =

Aps . fps

Mn = 2962 1669.604 ( 900 - 113.1075 ) 0.85 . fc' . b



Mn = 3891471508a =

2962 . 1669.604

0.85 . 36 . 500

Mn . Ø ≥ Mu = 323.226527

3891471508 . 0.8 ≥ 2175994574

3113177207 Nmm ≥ 2175994574 Nmm ( AMAN )

BATANG BE ( LANTAI )

Mn = Aps . fps . ( dp - 0.5 a )a =

Aps . fps

Mn = 3158 1750.761 ( 1305 - 116.8752 ) 0.85 . fc' . b

Mn = 6569026635a =

3158 . 1750.761

0.85 . 36 . 725

Mn . Ø ≥ Mu = 249.218076

6569026635 . 0.8 ≥ 4711061664

5255221308 Nmm ≥ 4711061664 Nmm ( AMAN )















BALOK LANTAI

TAHAP AWAL

2347.0800 q = 33.6 2347.0800

B E

1008

504 504

x

Lihat Perhitungan Momen Berat Sendiri untuk lantai !

Mx = 504000 X - 2347080000 - 16.8000 X²

Pso = 365265471

Fci = 28 Mpa

fc' = 40 Mpa

Ac = b . h

= 725 . 1450

= 1051250

Ic = 1/12 . b .

= 1/12 . 725 .( 1450

= 1/12 . 2210253125000.00

= 184187760416.67

ATAS

0.25 . √ Fci ≥ - Pso

+Pso . e . Ya

-Mbs x . Ya

Ac Ic Ic

0.25 .√ 28 ≥-365265471

+365265471 e 725 - Mbs x . 725

1051250 184187760416.67 184187760416.667

1.32287566 ≥ -347.458237 + 1.43775822128 e - 3.936201E-09 Mbs x

348.781112 ≥ 1.43775822128247 e - 0.0000000039362 Mbs x

e ≥ 0.000000003936 Mbs x + 348.781112465

h3

)3



1.43775822128

X Mbs x ex≤

0 -2347080000.0 236.161080070273

1000 -1859880000.0 237.494904474947

2000 -1406280000.0 238.736740989643

3000 -986280000.0 239.886589614362

4000 -599880000.0 240.944450349103

5000 -247080000.0 241.910323193867

6000 72120000.0 242.784208148654

7000 357720000.0 243.566105213463

8000 609720000.0 244.256014388294

9000 828120000.0 244.853935673148

10000 1012920000.0 245.359869068024

11000 1164120000.0 245.773814572923

12000 1281720000.0 246.095772187844

13000 1365720000.0 246.325741912788

14000 1416120000.0 246.463723747754

15000 1432920000.0 246.509717692743

BAWAH

-0.6 . Fci ≥ - Pso - Pso e Yb + Mbs x . Yb

As Ic Ic

-0.6 . 28 ≥ -365265471 - 365265471 e 725 + Mbs x . 725

1051250 184187760416.667 184187760417

-16.8000 ≥ -347.458237 - 1.43775822 e + 0.000000003936 Mbs x

330.658237 ≥ -1.43775822 e + 0.0000000039362 Mbs x

e ≤ 0.000000003936201 Mbs x - -330.658237

1.43775822



X Mbs x

0 -2347080000.0 223.556126478446

1000 -1859880000.0 224.88995088312

2000 -1406280000.0 226.131787397817

3000 -986280000.0 227.281636022536

4000 -599880000.0 228.339496757277

5000 -247080000.0 229.305369602041

6000 72120000.0 230.179254556827

7000 357720000.0 230.961151621636

8000 609720000.0 231.651060796468

9000 828120000.0 232.248982081321

10000 1012920000.0 232.754915476198

11000 1164120000.0 233.168860981097

12000 1281720000.0 233.490818596018

13000 1365720000.0 233.720788320962

14000 1416120000.0 233.858770155928

15000 1432920000.0 233.904764100917

TAHAP AKHIR

5507.5735 q= 0.08778667 KN/m 5507.5735

B E

Q= 2370.24

1185.12 1185.12

x

Ps = Pso - 15% Pso

= 85% Pso

Ps = 365265471 = 310475651

ex≤



Fci = 28 Mpa

MLLx = 270900 X - 9.03 X² - 1251870000.00

MDLx = 410220 X - 13.674 X² - 1908630000.00

Mtx = MDLx + MLLx

0 - 15000

X Mtx

0 -3160500000

1000 -2502084000

2000 -1889076000

3000 -1321476000

4000 -799284000

5000 -322500000

6000 108876000

7000 494844000

8000 835404000.0

9000 1130556000

10000 1380300000.0

11000 1584636000

12000 1743564000

13000 1857084000

14000 1938870000

15000 1947900000

ATAS

-0.45 . Fc' ≥ -Pso + Pso. e Ya - Mbs x Ya - Mtx. Ya

As Ic Ic Ic

-0.45 . 40 ≥ -310475651 + 310475651 e 725 - Mbsx 725 - Mtx 725

1051250 184187760416.667 184187760417 184187760416.7

-18 ≥ -295.339501 + 1.22209449 e- 3.936201E-09 Mbsx - 3.9362E-09 Mtx

277.339501 ≥ 1.22209449 e- 0.00000000394 Mbsx - 0.00000000394 Mtx



e ≤ 0.000000003936 Mbsx + 0.000000003936 Mtx 277.339501

1.22209449

X Mbs x Mt x ex≤

0 -2347080000.0 -3160500000 209.19868575958

1000 -1859880000.0 -2502084000 212.888559658896

2000 -1406280000.0 -1889076000 216.323959496191

3000 -986280000.0 -1321476000 219.504885271464

4000 -599880000.0 -799284000 222.431336984715

5000 -247080000.0 -322500000 225.103314635944

6000 72120000.0 108876000 227.520818225151

7000 357720000.0 494844000 229.683847752337

8000 609720000.0 835404000.0 231.592403217501

9000 828120000.0 1130556000 233.246484620642

10000 1012920000.0 1380300000.0 234.646091961763

11000 1164120000.0 1584636000 235.791225240861

12000 1281720000.0 1743564000 236.681884457937

13000 1365720000.0 1857084000 237.318069612992

14000 1416120000.0 1938870000 237.743822807129

15000 1432920000.0 1947900000 237.827017737035

BAWAH

0.5 . √ Fci ≥ - Pso - Pso e Yb + Mbs x . Yb + Mt. Yb

As Ic Ic Ic

0.5 √ 40 ≥ -310475651 - ### e 725 + Mbsx. 725 + Mt. 725

1051250 184187760416.667 184187760416.66700 1.8E+11

3.1623 ≥ -295.339501 - 1.22209449 e+ 3.9362E-09 Mbsx + 3.9362E-09 Mt



298.501779 ≥ -1.2220944881 e+ 3.9362E-09 Mbsx + 3.9362E-09 Mt

1.22209449 e ≥ 3.9362E-09 Mbsx + 3.9362E-09 Mt -298.501779

e ≤ 3.9362E-09 Mbsx + 3.9362E-09 Mt -298.501779

1.22209449

X Mbs x Mt x ex≤

0 -2347080000.0 -3160500000 -261.993424055906

1000 -1859880000.0 -2502084000 -258.30355015659

2000 -1406280000.0 -1889076000 -254.868150319295

3000 -986280000.0 -1321476000 -251.687224544022

4000 -599880000.0 -799284000 -248.760772830771

5000 -247080000.0 -322500000 -246.088795179542

6000 72120000.0 108876000 -243.671291590334

7000 357720000.0 494844000 -241.508262063149

8000 609720000.0 835404000.0 -239.599706597985

9000 828120000.0 1130556000 -237.945625194843

10000 1012920000.0 1380300000.0 -236.546017853723

11000 1164120000.0 1584636000 -235.400884574625

12000 1281720000.0 1743564000 -234.510225357548

13000 1365720000 1857084000 -233.874040202494

14000 1416120000.0 1938870000 -233.448287008356

15000 1432920000.0 1947900000 -233.36509207845

Resume daerah aman terhadap perletakan tendon pada balok Lantai

e AWAL AKHIR

0 236.161080070273 209.19868575958

15 246.509717692743 237.827017737035

0 223.556126478446 -261.993424055906



15 233.904764100917 -233.36509207845

500

500

26

AWAL AKHIR

0= 236.16108 0= 209.19868575958

13= 246.325742 13= 237.318069612992

0= 223.556126 0= -261.993424055906

13= 233.720788 13= -233.874040202494



Karena pada penggambaran tendon memiliki e tumpuan terlalu kecil yang mengakibatkan

posisi tendon ketika dari tumpuan melewati 1/4 L digaris netral terlalu jauh sebelum

mencapai e lapangan. Yakni melewati 1/2 dari bentangan dan bahkan panjang bentangan.

Maka solusinya adalah dengan menghitung daerah aman untuk pemasangan tendon

dengan cara menghitung jarak e setiap 1 meter dari tumpuan ke lapangan (1/2 bentangan)

Sehingga nantinya detentukan letak tendon dengan bebas di daerah aman.



ATAS awal BE

0.6 . Fci ≥ - Pso + Pso . e . Ya - Mbs x . Ya

As Ic Ic

0.6 . 28 ≥ Pso + Pso e 500-

Mbs x . 500

1051250 1.841878E+11 1.8419E+11

16.8 ≥ -9.5124851E-07 Pso + 2.714621E-09 Pso e - 2.7146E-09 Mbs x

e ≥ 16.8 - -9.5124851E-07 Pso + 2.7146E-09 Mbs x

2.714621E-09 Pso

BAWAH

-0.25 . √ Fci ≥ - Pso - Pso e Yb + Mbs x . Yb

As Ic Ic

-0.25 √ 28 ≥ - Pso - Pso e 500 + Mbs x . 500

1051250 1.841878E+11 184187760417

16.8000 ≥ -9.5125E-07 Pso - 2.714621E-09 Pso e + 2.7146E-09 Mbs x

e ≥ 16.8000 - -9.5125E-07 Pso - 2.7146E-09 Mbs x

-2.714621E-09 Pso

ATAS Akhir BE

0.45 . Fci ≥ -Ps + Ps e Ya - Mbs x Ya - Mtx. Ya

As Ic Ic Ic

0.45 . 28 ≥ -Ps + Ps e 500 - Mbsx 500 - Mtx 500

1051250 184187760417 1.8419E+11 1.8419E+11

12.6 ≥ -9.5125E-07 Ps + 2.7146212E-09 e Ps - 2.71462E-09 Mbsx - 2.71462E-09 Mtx

e ≥ 12.6 - -9.5125E-07 Ps + 2.7146212E-09 Mbsx + 2.71462E-09 Mtx

2.7146212E-09 Ps



BAWAH

0.5 . √ Fci ≥ - Pso - Pso e Yb + Mbs x . Yb + Mt. Yb

As Ic Ic Ic

0.5 √ 28 ≥ - Pso - Pso e 500 + Mbsx. 500 + Mt. 500

1051250 184187760417 1.8419E+11 1.8419E+11

-16.8000 ≥ -9.5125E-07 Ps - 2.71462E-09 e Ps + 2.71462E-09 Mbsx + 2.71462E-09 Mt.

e ≥ -16.8000 - -9.5125E-07 Ps - 2.71462E-09 Mbsx - 2.71462E-09 Mt.

-2.7146212E-09 Ps

MOEZLEM ZTUDIO ZIVIL- ZTRUCTURE

Soal 2

Diketahui balok CD adalah balok pretensioning dengan penampang I sbb;

bf

tfBalok CD Nim Genap Nim Genap

bf 60 cm 65 cm

tf 15 cm 17 cm

bw 15 cm 15 cm

bw h h 90 cm 85 cm

Mbs 4 KNm 4.2 KNm

e 35 cm 30 cm

Aps 1800 1900

Transfer gaya pratekan terjadi pada 48 jam setelah penarikan. Mutu kabel G 270.

Kabel ditarik sampai 0.75 fpu , dengan fpy = 0.85 fpu.

Diminta kehilangan gaya pratekan pada saat kabel ditarik sampai transfer gaya pratekan?

(Akibat Relaksasi dan Elastic shortening)

Jawaban;

Diketahui;

t = 48 jam = 2 hari

G = 270

fpy = 0.85 fpu

Ac = bf .( tf . 2 ) + ( h - tf -tf ) . bw

= 60 ( 15 2 ) + ( 90 - 15 - 15 ) 15

= 2700

Akibat Relaksasi

σst = 0.75 ( 270000 x 0.07 ) = 14175

= 0.85 ( 270000 x 0.07 ) = 16065

untuk stress relieved cable

RET = σst( log 24 t - log 24 t )

(σst

- 0.55 )10 σpy

RET = 14175 ( log 48 - log 1 ) 14175

- 0.5510 16065

= 792.05

mm2 mm2

cm2

kg/cm2

σpy kg/cm2

kg/cm2


a.2

Elastic shortening pada saat transfer : ES

Ib

= 1-

1(

12 12

= 160 90

3 -

1( 60 - 15 ) ( 90 - 30

12 12

= 3645000 - 3.75 . 216000

= 2835000

MG = 4000 kgm = 400000 kgcm

= 400000 . 35

2835000

= 4.93827

Ditaksir/ dicoba Es = 800

Saat Transfer ;

= σst - RET - Es Pi = σsi . Aps

= 14175 - 792.05 - 800 = 12582.95 . 18

= 12582.95 = 226493.1 kg

Tegangan pada lokasi kabel ;

Akibat gaya pratekan ( pada e = 35 cm )

σc =-226493.1

-226493.1 . 35

2700 2835000

= -83.8863333 - 2.796211111

= -86.68254444444 ( Tekan )

bh3 b - tf ) ( h - 2 tf)3

)3

cm4

σc

kg/ cm2

kg/cm2

σsi

kg/cm2

kg/cm2


Akibat beban mati ;

σc = 4.93827 ( Tarik )

σc total pada lokasi kabel = 4.938271605 - 86.68254444

= -81.7442728

Elastic shortening :

Es = n . σc

= 8.96 . 81.74427284

= 732.4286846

Karena Es yang didapatkan lebih kecil dari perkiraan ( (= 800 ) …………………….OK

Total Loss / kehilangan ;

Tl = RET + Es

= 792.05 + 732.4286846

= 1524.478685

Jadi besar kehilangan gaya pratekan pada saat kabel ditarik = 1524.478685 Kg/cm2

Tegangan kabel ;

σst = σst - Tl

= 14175 - 1524.478685

= 12650.52132

kg/cm2

kg/cm2

kg/ cm2

Kg/cm2

kg/cm2


Soal 2

Diketahui balok CD adalah balok pretensioning dengan penampang I sbb;

bf

tfBalok CD Nim Ganjil Nim Ganjil

bf 65 cm 65 cm

tf 17 cm 17 cm

bw 15 cm 15 cm

bw h h 85 cm 85 cm

Mbs 4.2 KNm 4.2 KNm

e 30 cm 30 cm

Aps 1900 1900

Transfer gaya pratekan terjadi pada 48 jam setelah penarikan. Mutu kabel G 270.

Kabel ditarik sampai 0.75 fpu , dengan fpy = 0.85 fpu.

Diminta kehilangan gaya pratekan pada saat kabel ditarik sampai transfer gaya pratekan?

(Akibat Relaksasi dan Elastic shortening)

Jawaban;

Diketahui;

t = 48 jam = 2 hari

G = 270

fpy = 0.85 fpu

Ac = bf .( tf . 2 ) + ( h - tf -tf ) . bw

= 65 ( 17 2 ) + ( 85 - 17 - 17 ) 15

= 2975

Akibat Relaksasi

σst = 0.75 ( 270000 x 0.07 ) = 14175

= 0.85 ( 270000 x 0.07 ) = 16065

untuk stress relieved cable

RET = σst( log 24 t - log 24 t )

(σst

- 0.55 )10 σpy

RET = 14175 ( log 48 - log 1 ) 14175

- 0.5510 16065

= 792.05

mm2 mm2

cm2

kg/cm2

σpy kg/cm2

kg/cm2


a.2 Elastic shortening pada saat transfer : ES

Ib

= 1-

1(

12 12

= 165 85

3 -

1( 65 - 17 ) ( 85 - 34

12 12

= 3326510.417 - 4 . 132651

= 2795906.417

MG = 4200 kgm = 420000 kgcm

= 420000 . 30

2795906.417

= 4.50659

Ditaksir/ dicoba Es = 800

Saat Transfer ;

= σst - RET - Es Pi = σsi . Aps

= 14175 - 792.05 - 800 = 12582.95 . 19

= 12582.95 = 239076.05 kg

Tegangan pada lokasi kabel ;

Akibat gaya pratekan ( pada e = 30 cm )

σc =-239076.05

-239076.05 . 30

2975 2795906.416667

= -80.3616975 - 2.565279531

= -82.92697700954 ( Tekan )

bh3 b - tf ) ( h - 2 tf)3

)3

cm4

σc

kg/ cm2

kg/cm2

σsi

kg/cm2

kg/cm2


Akibat beban mati ;

σc = 4.50659 ( Tarik )

σc total pada lokasi kabel = 4.506588606 - 82.92697701

= -78.4203884

Elastic shortening :

Es = n . σc

= 8.96 . 78.4203884

= 702.6466801

Karena Es yang didapatkan lebih kecil dari perkiraan ( (= 800 ) …………………….OK

Total Loss / kehilangan ;

Tl = RET + Es

= 792.05 + 702.6466801

= 1494.69668

Jadi besar kehilangan gaya pratekan pada saat kabel ditarik = 1494.69668 Kg/cm2

Tegangan kabel ;

σst = σst - Tl

= 14175 - 1494.69668

= 12680.30332

kg/cm2

kg/cm2

kg/ cm2

Kg/cm2

kg/cm2


UJIAN AKHIR SEMESTER GANJIL (v)

Diketahui data sebagai berikut;

Balok Lantai Nim Genap Nim Ganjil

Momen Tumpuan

- Berat sendiri 7.4 KNm 6 KNm

- Beban Mati 1 KNm 1.2 KNm

- Beban Hidup 1.8 KNm 1.4 KNm

Momen Lapangan

- Berat sendiri 3.6 KNm 3 KNm

- Beban Mati 0.55 KNm 0.66 KNm


Lebar Balok 0.6 m 0.6 m

Tinggi Balok 0.8 m 0.8 m

fci' 35 33

fc' 48 47

Pso 75 KN 68 KN

% LS 20% 22%

e Tumpuan 0.25 m 0.25 m

e Lapangan 0.25 m 0.25 m

Sistem Pratekan Pretensioning Postensioning Unbonded

Aps 1200 1000

Diminta;

a. Analisis tegangan tegangan yang terjadi pada balok lantai AB (elastis)!

b. Analisis kembali dengan menggunakan kekuatan batas !

Jawaban;

NIM GENAP

a.Analisis tegangan (elastis)

Syarat;

Awal = (+ ) Tarik = 0.25 √ fci'

( - ) Tekan = 0.6 . fci'

Akhir = (+) Tarik = 0.5 √ fc'

( - ) Tekan = 0.45 . fc'

N/mm2 N/mm2

N/mm2 N/mm2

mm2 mm2


LAPANGAN

1. Tahap Awal

fa = - Pso

+Pso . e . Ya

-Mbs . Ya

Ac Ic Ic

Ac = b .H = 600 x 800 = 480000

Ic = 1600 800

3

12

= 25600000000

fa =-75000

+75000 250 400

- 3600000 . 400

480000 25600000000 25600000000

= -0.15625 + 0.29296875 - 0.05625

= 0.08046875 Mpa ( Tarik )

= 0.08046875 Mpa < 0.25 √ fci

= 0.08046875 Mpa < 0.25 √ 35

= 0.08046875 Mpa < 1.4790199 Mpa …………. AMAN

fb = - Pso

-Pso . e . Ya

+Mbs . Ya

Ac Ic Ic

fb =-75000

-75000 250 400

+3600000 . 400

480000 25600000000 25600000000

= -0.15625 - 0.29296875 + 0.05625

= -0.39296875 Mpa (Tekan)

= -0.39296875 Mpa < 0.6 . fci'

= -0.39296875 Mpa < 0.6 . 35

= -0.39296875 Mpa < 21 Mpa ……………….AMAN

2. Tahap Akhir

Ps = Pso - 20% Pso

= 80.0% Pso

= 80.0% . 75000

= 60000 N

fa = - Ps

+Ps . e . Ya

-Mbs . Ya

-Mt . Ya

Ac Ic Ic Ic

m2

mm4


fa =-60000

+60000 250 400

- 3600000 . 400

-1400000 . 400

480000 25600000000 25600000000 25600000000

= -0.125 + 0.234375 - 0.05625 - 0.021875

= 0.03125 Mpa (Tarik)

= 0.03125 Mpa < 0.5 √ fc'

= 0.03125 Mpa < 0.5 √ 48

= 0.03125 Mpa < 3.4641016 Mpa ……………….AMAN

fb = - Ps

-Ps . e . Ya

+Mbs . Ya

+Mt . Ya

Ac Ic Ic Ic

fb =-60000

-60000 250 400

+3600000 . 400

+1400000 . 400

480000 25600000000 25600000000 25600000000

= -0.125 - 0.234375 + 0.05625 + 0.021875

= -0.28125 Mpa (Tekan)

= -0.28125 Mpa < 0.45 . fc'

= -0.28125 Mpa < 0.45 . 48

= -0.28125 Mpa < 21.6 Mpa ……………….AMAN

TUMPUAN

1. Tahap Awal

fa = - Pso

+Pso . - e . Ya

-- Mbs . Ya

Ac Ic Ic

Ac = b .H = 600 x 800 = 480000

Ic = 1600 800

3

12

= 25600000000

fa =-75000

+75000 -250 400

- -7400000 . 400

480000 25600000000 25600000000

= -0.15625 + -0.29296875 - -0.115625

= -0.33359375 Mpa ( Tekan )

= -0.33359375 Mpa < 0.6 . fci'

= -0.33359375 Mpa < 0.6 . 35

m2

mm4


= -0.33359375 Mpa < 21 Mpa …………. AMAN

fb = - Pso

-Pso . - e . Ya

+- Mbs . Ya

Ac Ic Ic

fb =-75000

-75000 -250 400

+-7400000 . 400

480000 25600000000 25600000000

= -0.15625 - -0.29296875 + -0.115625

= 0.02109375 Mpa (Tarik)

= 0.02109375 Mpa < 0.25 √ fci'

= 0.02109375 Mpa < 0.25 √ 35

= 0.02109375 Mpa < 1.479 Mpa ……………….AMAN

2. Tahap Akhir

Ps = Pso - 20% Pso

= 80.0% Pso

= 80.0% . 75000

= 60000 N

fa = - Ps

+Ps . e . Ya

-Mbs . Ya

-Mt . Ya

Ac Ic Ic Ic

fa =-60000

+60000 -250 400

- -7400000 . 400

--2800000 400

480000 25600000000 25600000000 25600000000

= -0.125 + -0.234375 - -0.115625 - -0.04375

= -0.2 Mpa (Tekan)

= -0.2 Mpa < 0.45 . fc'

= -0.2 Mpa < 0.45 . 48

= -0.2 Mpa < 21.6 Mpa ……………….AMAN

fb = - Ps

-Ps . e . Ya

+Mbs . Ya

+Mt . Ya

Ac Ic Ic Ic

fb =-60000

-60000 -250 400

+-7400000 . 400

+-2800000 . 400

480000 25600000000 25600000000 25600000000

= -0.125 - -0.234375 + -0.115625 + -0.04375

= -0.05 Mpa (Tekan)


= -0.05 Mpa < 0.45 . fc'

= -0.05 Mpa < 0.45 . 48

= -0.05 Mpa < 21.6 Mpa ……………….AMAN

b. Analisis dengan Kekuatan Batas

Lihat tabel VSL

fpu untuk Tendon VSL =187500

Mpaβ1 = 0.85 -( fc' - 30 ) 0.008

98.7 = 0.85 -( 48 - 30 ) 0.008

fpu = 1899.69604863 Mpa = 0.85 - 0.144

= 0.706

Menentukan Nilai Mu

Mu = 1.2 MDL + 1.6 MLL

= 1.2 . ( 1000000 + 550000 ) + 1.6 . ( 1800000 + 850000 )

= 1860000 + 4240000

= 6100000 Nmm

=Aps

=1200

= 0.0027778b . dp 600 . 720

fps = fpu ( 1 -ال p . . fpu

)β1 . fc'

fps = 1899.696 ( 1 -0.4 . 0.0027778 1899.69604863

)0.706 . 48

fps = 1899.69604863 - 118.325893046

fps = 1781.37015559 Mpa

Menentukan Momen Rancang

Mn = Aps . fps . ( dp - 0.5 a )a =

Aps . fps

Mn = 1200 1781.3702 ( 720 - 43.661033 ) 0.85 . fc' . b

Mn = 1445772060.57 Nmma =

1200 . 1781.3702

0.85 . 48 . 600

= 87.3220664503

Mn . Ø ≥ Mu

1445772060.57 . 0.8 ≥ 6100000

1156617648.45 Nmm ≥ 6100000 Nmm ……………….AMAN

ρp

ρp


UJIAN AKHIR SEMESTER GANJIL (v)

Diketahui data sebagai berikut;

Balok Lantai Nim Genap Nim Ganjil

Momen Tumpuan

- Berat sendiri 6 KNm 6 KNm



Momen Lapangan

- Berat sendiri 3 KNm 3 KNm



Lebar Balok 0.6 m 0.6 m

Tinggi Balok 0.8 m 0.8 m

fci' 33 33

fc' 47 47

Pso 68 KN 68 KN

% LS 22% 22%

e Tumpuan 0.25 m 0.25 m

e Lapangan 0.25 m 0.25 m

Sistem Pratekan Pretensioning Postensioning Unbonded

Aps 1000 1000

Diminta;

a. Analisis tegangan tegangan yang terjadi pada balok lantai AB (elastis)!

b. Analisis kembali dengan menggunakan kekuatan batas !

Jawaban;

NIM GENAP .

a.Analisis tegangan (elastis)

Syarat;

N/mm2 N/mm2

N/mm2 N/mm2

mm2 mm2


Awal = (+ ) Tarik = 0.25 √ fci'

( - ) Tekan = 0.6 . fci'

Akhir = (+) Tarik = 0.5 √ fc'

( - ) Tekan = 0.45 . fc'

LAPANGAN

1. Tahap Awal

fa = - Pso

+Pso . e . Ya

-Mbs . Ya

Ac Ic Ic

Ac = b .H = 600 x 800 = 480000

Ic = 1600 800

3

12

= 25600000000

fa =-68000

+68000 250 400

- 3000000 . 400

480000 25600000000 25600000000

= -0.1416666667 + 0.265625 - 0.046875

= 0.07708333333 Mpa ( Tarik )

= 0.07708333333 Mpa < 0.25 √ fci

= 0.07708333333 Mpa < 0.25 √ 33

= 0.07708333333 Mpa < 1.4361407 Mpa …………. AMAN

fb = - Pso

-Pso . e . Ya

+Mbs . Ya

Ac Ic Ic

fb =-68000

-68000 250 400

+3000000 . 400

480000 25600000000 25600000000

= -0.1416667 - 0.265625 + 0.046875

= -0.3604166667 Mpa (Tekan)

= -0.3604166667 Mpa < 0.6 . fci'

= -0.3604166667 Mpa < 0.6 . 33

= -0.3604166667 Mpa < 19.8 Mpa ……………….AMAN

2. Tahap Akhir

Ps = Pso - 22% Pso

= 78.0% Pso

m2

mm4


= 78.0% . 68000

= 53040 N

fa = - Ps

+Ps . e . Ya

-Mbs . Ya

-Mt . Ya

Ac Ic Ic Ic

fa =-53040

+53040 250 400

- 3000000 . 400

-1430000 . 400

480000 25600000000 25600000000 25600000000

= -0.1105 + 0.2071875 - 0.046875 - 0.02234375

= 0.0274687 Mpa (Tarik)

= 0.0274687 Mpa < 0.5 √ fc'

= 0.0274687 Mpa < 0.5 √ 47

= 0.0274687 Mpa < 3.4278273 Mpa ……………….AMAN

fb = - Ps

-Ps . e . Ya

+Mbs . Ya

+Mt . Ya

Ac Ic Ic Ic

fb =-53040

-53040 250 400

+3000000 . 400

+1430000 . 400

480000 25600000000 25600000000 25600000000

= -0.1105 - 0.2071875 + 0.046875 + 0.0223438

= -0.24846875 Mpa (Tekan)

= -0.2484688 Mpa < 0.45 . fc'

= -0.2484688 Mpa < 0.45 . 47

= -0.2484688 Mpa < 21.15 Mpa ……………….AMAN

TUMPUAN

1. Tahap Awal

fa = - Pso

+Pso . - e . Ya

-- Mbs . Ya

Ac Ic Ic

Ac = b .H = 600 x 800 = 480000

Ic = 1600 800

3

12

= 25600000000

fa =-68000

+68000 -250 400

- -6000000 . 400

480000 25600000000 25600000000

m2

mm4


= -0.1416666667 + -0.265625 - -0.09375

= -0.3135416667 Mpa ( Tekan )

= -0.3135416667 Mpa < 0.6 . fci'

= -0.3135416667 Mpa < 0.6 . 33

= -0.3135416667 Mpa < 19.8 Mpa …………. AMAN

fb = - Pso

-Pso . - e . Ya

+- Mbs . Ya

Ac Ic Ic

fb =-68000

-68000 -250 400

+-6000000 . 400

480000 25600000000 25600000000

= -0.1416667 - -0.265625 + -0.09375

= 0.03020833333 Mpa (Tarik)

= 0.03020833333 Mpa < 0.25 √ fci'

= 0.03020833333 Mpa < 0.25 √ 33

= 0.03020833333 Mpa < 1.4361 Mpa ……………….AMAN

2. Tahap Akhir

Ps = Pso - 22% Pso

= 78.0% Pso

= 78.0% . 68000

= 53040 N

fa = - Ps

+Ps . e . Ya

-Mbs . Ya

-Mt . Ya

Ac Ic Ic Ic

fa =-53040

+53040 -250 400

- -6000000 . 400

--2600000 400

480000 25600000000 25600000000 25600000000

= -0.1105 + -0.2071875 - -0.09375 - -0.040625

= -0.1833125 Mpa (Tekan)

= -0.1833125 Mpa < 0.45 . fc'

= -0.1833125 Mpa < 0.45 . 47

= -0.1833125 Mpa < 21.15 Mpa ……………….AMAN

fb = - Ps

-Ps . e . Ya

+Mbs . Ya

+Mt . Ya

Ac Ic Ic Ic


fb =-53040

-53040 -250 400

+-6000000 . 400

+-2600000 . 400

480000 25600000000 25600000000 25600000000

= -0.1105 - -0.2071875 + -0.09375 + -0.040625

= -0.0376875 Mpa (Tekan)

= -0.0376875 Mpa < 0.45 . fc'

= -0.0376875 Mpa < 0.45 . 47

= -0.0376875 Mpa < 21.15 Mpa ……………….AMAN

b. Analisis dengan Kekuatan Batas

Lihat tabel VSL


Mpaβ1 = 0.85 -( fc' - 30 ) 0.008

98.7 = 0.85 -( 47 - 30 ) 0.008

fpu = 1899.69604863 Mpa = 0.85 - 0.136

= 0.714

Menentukan Nilai Mu

Mu = 1.2 MDL + 1.6 MLL

= 1.2 . ( 1200000 + 660000 ) + 1.6 . ( 1400000 + 770000 )

= 2232000 + 3472000

= 5704000 Nmm

=Aps

=1000

= 0.0023148b . dp 600 . 720


)β1 . fc'

fps = 1899.696 ( 1 -0.4 . 0.0023148 1899.69604863

)0.714 . 47

fps = 1899.69604863 - 99.574564027

fps = 1697.81203647 Mpa

Menentukan Momen Rancang

Mn = Aps . fps . ( dp - 0.5 a )a =

Aps . fps

Mn = 1000 1697.812 ( 720 - 35.415353 ) 0.85 . fc' . b

Mn = 1162296053.18 Nmma =

1000 . 1697.812

0.85 . 47 . 600

= 70.8307065696

ρp

ρp


Mn . Ø ≥ Mu

1162296053.18 . 0.8 ≥ 5704000

929836842.543 Nmm ≥ 5704000 Nmm ……………….AMAN


0.008

0.75 x 1899.69604863 = 1424.77203647416

fps fse + 70 + fc

100 ρp

fps = 1424.77203647 + 70 + 48

100 0.00277777778

= 1667.57203647416


0.008

0.75 x 1899.69604863 = 1424.77203647416

fps fse + 70 + fc

100 ρp

fps = 1424.77203647 + 70 + 47

100 0.00231481481

= 1697.81203647416


TABEL.I DISTRIBUSI MOMEN AKIBAT BEBAN HIDUP

Titik A B C D E F

Batang AB BA BE BC CB CD DC DE ED EB EF FE

K rel 1.33 1.33 0.270 1.33 1.33 0.270 0.270 1.33 1.33 0.270 1.33 1.33

Cyc DF 0.4540 0.0920 0.4540 0.8315 0.1685 0.1685 0.8315 0.4540 0.0920 0.4540

1

MF -137995.20 -55855.20 55855.20 137995.20

BAL 62648.13 12698.94 62648.13 46441.40 9413.80 -9413.80 -46441.40 -62648.13 -12698.94 -62648.13

2

MF 31324.06 -6349.47 23220.70 31324.06 -4706.90 4706.90 -31324.06 -23220.70 6349.47 -31324.06

BAL -7659.33 -1552.57 -7659.33 -22131.13 -4486.04 4486.04 22131.13 7659.33 1552.57 7659.33

3

MF -3829.67 776.28 -11065.56 -3829.67 2243.02 -2243.02 3829.67 11065.56 -776.28 3829.67

BAL 4671.21 946.87 4671.21 1319.23 267.41 -267.41 -1319.23 -4671.21 -946.87 -4671.21

4

MF 2335.60 -473.43 659.62 2335.60 -133.71 133.71 -2335.60 -659.62 473.43 -2335.60

BAL -84.53 -17.13 -84.53 -1830.79 -371.11 371.11 1830.79 84.53 17.13 84.53

5

MF -42.26 8.57 -915.40 -42.26 185.55 -185.55 42.26 915.40 -8.57 42.26

BAL 411.69 83.45 411.69 -119.14 -24.15 24.15 119.14 -411.69 -83.45 -411.69

6

MF 205.84 -41.73 -59.57 205.84 12.08 -12.08 -205.84 59.57 41.73 -205.84

BAL 45.99 9.32 45.99 -181.19 -36.73 36.73 181.19 -45.99 -9.32 -45.99

7

MF 22.99 -4.66 -90.60 22.99 18.36 -18.36 -22.99 90.60 4.66 -22.99

BAL 43.25 8.77 43.25 -34.39 -6.97 6.97 34.39 -43.25 -8.77 -43.25

8

MF 21.62 -4.38 -17.19 21.62 3.49 -3.49 -21.62 17.19 4.38 -21.62

BAL 9.80 1.99 9.80 -20.88 -4.23 4.23 20.88 -9.80 -1.99 -9.80

9

MF 4.90 -0.99 -10.44 4.90 2.12 -2.12 -4.90 10.44 0.99 -4.90

BAL 5.19 1.05 5.19 -5.83 -1.18 1.18 5.83 -5.19 -1.05 -5.19

10

MF 2.59 -0.53 -2.92 2.59 0.59 -0.59 -2.59 2.92 0.53 -2.59

BAL 1.56 0.32 1.56 -2.65 -0.54 0.54 2.65 -1.56 -0.32 -1.56

11

MF 0.78 -0.16 -1.32 0.78 0.27 -0.27 -0.78 1.32 0.16 -0.78

BAL 0.67 0.14 0.67 -0.87 -0.18 0.18 0.87 -0.67 -0.14 -0.67

12

MF 0.34 -0.07 -0.44 0.34 0.09 -0.09 -0.34 0.44 0.07 -0.34

BAL 0.23 0.05 0.23 -0.35 -0.07 0.07 0.35 -0.23 -0.05 -0.23

13

MF 0.11 -0.02 -0.18 0.11 0.04 -0.04 -0.11 0.18 0.02 -0.11

BAL 0.09 0.02 0.09 -0.13 -0.03 0.03 0.13 -0.09 -0.02 -0.09

14

MF 0.05 -0.01 -0.06 0.05 0.01 -0.01 -0.05 0.06 0.01 -0.05

BAL 0.03 0.01 0.03 -0.05 -0.01 0.01 0.05 -0.03 -0.01 -0.03

15

MF 0.02 0.00 -0.02 0.02 0.00 0.00 -0.02 0.02 0.00 -0.02

BAL 0.01 0.00 0.01 -0.02 0.00 0.00 0.02 -0.01 0.00 -0.01

16

MF 0.01 0.00 -0.01 0.01 0.00 0.00 -0.01 0.01 0.00 -0.01

BAL 0.00 0.00 0.00 -0.01 0.00 0.00 0.01 0.00 0.00 0.00

17

MF 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

BAL 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Jumlah 30046.99 60093.99 -131904.59 71810.60 53480.21 -53480.21 53480.21 -53480.21 -71810.60 131904.59 -60093.99 -30046.99

0.0000 0.0000

TABELII. DISTRIBUSI MOMEN AKIBAT BEBAN MATI

Titik A B C D E F


K rel 1.33 1.33 0.270 1.33 1.33 0.270 0.270 1.33 1.33 0.270 1.33 1.33

Cyc DF 0.4540 0.0920 0.4540 0.8315 0.1685 0.1685 0.8315 0.4540 0.0920 0.4540

1

MF -251348.400 -118692.30 118692.30 251348.40

BAL 114109.09 23130.22 114109.09 98687.98 20004.32 -20004.32 -98687.98 -114109.09 -23130.22 -114109.09

2

MF 57054.54 -11565.11 49343.99 57054.54 -10002.16 10002.16 -57054.54 -49343.99 11565.11 -57054.54

BAL -17151.15 -3476.58 -17151.15 -39122.21 -7930.18 7930.18 39122.21 17151.15 3476.58 17151.15

3

MF -8575.57 1738.29 -19561.10 -8575.57 3965.09 -3965.09 8575.57 19561.10 -1738.29 8575.57

BAL 8091.34 1640.14 8091.34 3833.44 777.05 -777.05 -3833.44 -8091.34 -1640.14 -8091.34

4

MF 4045.67 -820.07 1916.72 4045.67 -388.52 388.52 -4045.67 -1916.72 820.07 -4045.67

BAL -497.87 -100.92 -497.87 -3040.77 -616.37 616.37 3040.77 497.87 100.92 497.87

5

MF -248.93 50.46 -1520.39 -248.93 308.19 -308.19 248.93 1520.39 -50.46 248.93

BAL 667.33 135.27 667.33 -49.27 -9.99 9.99 49.27 -667.33 -135.27 -667.33

6

MF 333.66 -67.63 -24.63 333.66 4.99 -4.99 -333.66 24.63 67.63 -333.66

BAL 41.89 8.49 41.89 -281.58 -57.08 57.08 281.58 -41.89 -8.49 -41.89

7

MF 20.94 -4.25 -140.79 20.94 28.54 -28.54 -20.94 140.79 4.25 -20.94

BAL 65.84 13.35 65.84 -41.14 -8.34 8.34 41.14 -65.84 -13.35 -65.84

8

MF 32.92 -6.67 -20.57 32.92 4.17 -4.17 -32.92 20.57 6.67 -32.92

BAL 12.37 2.51 12.37 -30.84 -6.25 6.25 30.84 -12.37 -2.51 -12.37

9

MF 6.18 -1.25 -15.42 6.18 3.13 -3.13 -6.18 15.42 1.25 -6.18

BAL 7.57 1.53 7.57 -7.74 -1.57 1.57 7.74 -7.57 -1.53 -7.57

10

MF 3.78 -0.77 -3.87 3.78 0.78 -0.78 -3.78 3.87 0.77 -3.78

BAL 2.11 0.43 2.11 -3.80 -0.77 0.77 3.80 -2.11 -0.43 -2.11

11

MF 1.05 -0.21 -1.90 1.05 0.39 -0.39 -1.05 1.90 0.21 -1.05

BAL 0.96 0.19 0.96 -1.20 -0.24 0.24 1.20 -0.96 -0.19 -0.96

12

MF 0.48 -0.10 -0.60 0.48 0.12 -0.12 -0.48 0.60 0.10 -0.48

BAL 0.32 0.06 0.32 -0.50 -0.10 0.10 0.50 -0.32 -0.06 -0.32

13

MF 0.16 -0.03 -0.25 0.16 0.05 -0.05 -0.16 0.25 0.03 -0.16

BAL 0.13 0.03 0.13 -0.17 -0.04 0.04 0.17 -0.13 -0.03 -0.13

14

MF 0.06 -0.01 -0.09 0.06 0.02 -0.02 -0.06 0.09 0.01 -0.06

BAL 0.05 0.01 0.05 -0.07 -0.01 0.01 0.07 -0.05 -0.01 -0.05

15

MF 0.02 0.00 -0.03 0.02 0.01 -0.01 -0.02 0.03 0.00 -0.02

BAL 0.02 0.00 0.02 -0.02 0.00 0.00 0.02 -0.02 0.00 -0.02

16

MF 0.01 0.00 -0.01 0.01 0.00 0.00 -0.01 0.01 0.00 -0.01

BAL 0.01 0.00 0.01 -0.01 0.00 0.00 0.01 -0.01 0.00 -0.01

17

MF 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

BAL 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Jumlah 52675.00 105349.99 -240671.04 135321.04 112617.09 -112617.09 112617.09 -112617.09 -135321.04 240671.04 -105349.99 -52675.00

0.0000 0.0000

TABELIII. DISTRIBUSI MOMEN AKIBAT BEBAN SENDIRI

Titik A B C D E F


K rel 1.33 1.33 0.27 1.33 1.33 0.27 0.27 1.33 1.33 0.27 1.33 1.33

Cyc DF 0.4540 0.0920 0.4540 0.8315 0.1685 0.1685 0.8315 0.4540 0.0920 0.4540

1

MF -287832.25 -136900.00 136900.00 287832.25

BAL 130672.31 26487.63 130672.31 113826.97 23073.03 -23073.03 -113826.97 -130672.31 -26487.63 -130672.31

2

MF 65336.15 -13243.82 56913.48 65336.15 -11536.52 11536.52 -65336.15 -56913.48 13243.82 -65336.15

BAL -19825.49 -4018.68 -19825.49 -44732.28 -9067.35 9067.35 44732.28 19825.49 4018.68 19825.49

3

MF -9912.75 2009.34 -22366.14 -9912.75 4533.68 -4533.68 9912.75 22366.14 -2009.34 9912.75

BAL 9241.74 1873.33 9241.74 4472.48 906.58 -906.58 -4472.48 -9241.74 -1873.33 -9241.74

4

MF 4620.87 -936.66 2236.24 4620.87 -453.29 453.29 -4620.87 -2236.24 936.66 -4620.87

BAL -589.99 -119.59 -589.99 -3465.18 -702.40 702.40 3465.18 589.99 119.59 589.99

5

MF -295.00 59.80 -1732.59 -295.00 351.20 -351.20 295.00 1732.59 -59.80 295.00

BAL 759.43 153.94 759.43 -46.73 -9.47 9.47 46.73 -759.43 -153.94 -759.43

6

MF 379.71 -76.97 -23.37 379.71 4.74 -4.74 -379.71 23.37 76.97 -379.71

BAL 45.55 9.23 45.55 -319.65 -64.79 64.79 319.65 -45.55 -9.23 -45.55

7

MF 22.78 -4.62 -159.83 22.78 32.40 -32.40 -22.78 159.83 4.62 -22.78

BAL 74.66 15.13 74.66 -45.87 -9.30 9.30 45.87 -74.66 -15.13 -74.66

8

MF 37.33 -7.57 -22.94 37.33 4.65 -4.65 -37.33 22.94 7.57 -37.33

BAL 13.85 2.81 13.85 -34.90 -7.07 7.07 34.90 -13.85 -2.81 -13.85

9

MF 6.92 -1.40 -17.45 6.92 3.54 -3.54 -6.92 17.45 1.40 -6.92

BAL 8.56 1.74 8.56 -8.70 -1.76 1.76 8.70 -8.56 -1.74 -8.56

10

MF 4.28 -0.87 -4.35 4.28 0.88 -0.88 -4.28 4.35 0.87 -4.28

BAL 2.37 0.48 2.37 -4.29 -0.87 0.87 4.29 -2.37 -0.48 -2.37

11

MF 1.18 -0.24 -2.15 1.18 0.43 -0.43 -1.18 2.15 0.24 -1.18

BAL 1.08 0.22 1.08 -1.35 -0.27 0.27 1.35 -1.08 -0.22 -1.08

12

MF 0.54 -0.11 -0.67 0.54 0.14 -0.14 -0.54 0.67 0.11 -0.54

BAL 0.36 0.07 0.36 -0.56 -0.11 0.11 0.56 -0.36 -0.07 -0.36

13

MF 0.18 -0.04 -0.28 0.18 0.06 -0.06 -0.18 0.28 0.04 -0.18

BAL 0.14 0.03 0.14 -0.20 -0.04 0.04 0.20 -0.14 -0.03 -0.14

14

MF 0.07 -0.01 -0.10 0.07 0.02 -0.02 -0.07 0.10 0.01 -0.07

BAL 0.05 0.01 0.05 -0.08 -0.02 0.02 0.08 -0.05 -0.01 -0.05

15

MF 0.03 -0.01 -0.04 0.03 0.01 -0.01 -0.03 0.04 0.01 -0.03

BAL 0.02 0.00 0.02 -0.03 -0.01 0.01 0.03 -0.02 0.00 -0.02

16

MF 0.01 0.00 -0.01 0.01 0.00 0.00 -0.01 0.01 0.00 -0.01

BAL 0.01 0.00 0.01 -0.01 0.00 0.00 0.01 -0.01 0.00 -0.01

17

MF 0.00 0.00 -0.01 0.00 0.00 0.00 0.00 0.01 0.00 0.00

BAL 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Jumlah 60202.32 120404.63 -275629.08 155224.44 129841.93 -129841.93 129841.93 -129841.93 -155224.44 275629.08 -120404.63 -60202.32

0.0000 0.0000


FEBRYANTI / 09 2103 026 ANDI SARIMAI / 09 2103 007

Direncanakan dari sebuah portal beton pratekan dengan data sebagai berikut :

- Jarak Portal : 3.6 m - Bentang ( l ) : 37 m

- Beban hidup atap : 136 Kg/m² - Tinggi ( h ) : 3.75 m

- Beban hidup lantai : 336 Kg/m² - Sisi pratekan : Postensioning

- Mutu beton (Fc) : 36 Mpa (Fci) : 30.6 Mpa

- Tendon : VSL

- Ib : 2 Ik

1. MENGHITUNG MOMEN AKIBAT BEBAN HIDUP

q1 = 489.6 Kg/m Beban hidup atap

C D q1 = 136 . 3.6

2 EI = 489.6 Kg/m

EI

Beban hidup lantai

q2 = 1209.6 Kg/m q2 = 336 . 3.6

B E = 1209.6 Kg/m

2 EI

EI

A F

37 m

A.MENGHITUNG KEKUATAN RELATIF

KAB = KBC = KDE = KEF =EI

=1 EI

.5

= 1.333H 3.75 1 EI

KBE = KCD =2 EI

=2 EI

.5

= 0.27027L 37 1 EI

B. MENGHITUNG FAKTOR DISTRIBUSI

TITIK B = TITIK E

DF BA : DF BE : DF BC =4 EI

:4 E( 2 I)

:4 EI

H L H

=4 EI

:8 EI

:4 EI

3.75 37 3.75

= 1.066667 : 0.216216 : 1.066667



DF BA = DF EF =1.066667

= 0.4539882.34955

DF BE = DF EB =0.216216

= 0.0920252.34955

DF BC = DF ED =1.066667

= 0.4539882.34955 +

Σ DF B = Σ DF E = 1.0000

TITIK C = TITIK D

DF CB : DF CD =4 EI

:4 E( 2 I )

H L

=4 EI

:8 EI

3.75 37

= 1.066667 : 0.216216

DF CB = DF DE =1.066667

= 0.8314611.282883

DF CD = DF DC =0.216216

= 0.1685391.282883 +

Σ DF C = Σ DF D = 1.0000

C. MENGHITUNG MOMEN PRIMER

BATANG CD ( ATAP)

q1 = 489.6 Kg/m MF CD = MF DC = 1/12. q l²

C D = 1/12 489.6 37 ²

= 55855.200 Kgm

37 m


q2 = 1209.6 Kg/m MF BE = MF EB = 1/12 q l²

B E = 1/12 1209.6 37 ²

= 137995.200 Kgm

37 m



FREE BODY BEBAN HIDUP

q1 = 489.6 Kg/m

C D

53480.21 53480.21

53480.212 18115.2 ###

71810.60 q2 = 1209.6 Kg/m 71810.6

B E

131905 ###

60093.99 60094

30046.99 30047

A F

BATANG CD ( ATAP )

q1 = 489.6 Kg/m

C D

53480.21 53480.21

9057.6 18115.2 9057.6

37 m

Q = q1. l = 489.6 . 37 = 18115.2 Kg

RCV = RDV =Q . 1/2 L

=18115.2 . 18.5

L 37

= 9057.6 Kg

Mencari Momen Max

X Qx = q1 . X = 489.6 X

MCD Mx = RCV . X - Qx . 1/2 X - MCD

= 9057.6 X - 244.8 X² - 53480.21

Dx =dMx

= 9057.6 - 489.6 X9057.6 Qx= 489.6 x dx

X =9057.6

= 18.5489.6

Mmax = 9057.6 X - 244.8 X² - 53480.21

= 9057.6 . ( 18.5 ) - 244.8 . ( 18.5 )²- ###

= 30302.588 Kgm

= 30.30259 tm



q2 = 1209.6 Kg/m

B E

131905 131904.592590728

44755.2 Kg

37 m

Q = q2 . l = 1209.6 . 37 = 44755.2 Kg

RBV = REV =Q . 1/2 L

=44755.2 . 18.5

L 37

= 22377.6 Kg

Mencari Momen Max

X

MBE Qx = qx . . X = 1209.6 X

Mx = RBV . X - Qx . 1/2X - MBE

= 22377.6 X - 604.8 X² - 131905

22377.6 QxDx =

dMx = 22377.6 - 1209.6 X

dx

X = 18.5

Mmax = 22377.6 . ( 18.5 )- 604.8 . ( 18.5 )² - 131905

= 75088.2074 Kgm

= 75.08821 tm

2. MENGHITUNG MOMEN AKIBAT BEBAN MATI

BATANG CD ( ATAP)

Tebal Plat = 11 cm = 0.11 m q air hujan = 25 . 3.6

q plat = 0.11 . 2400 . 3.6 = 90 Kg/m

= 950.4 Kg/m = 90 Kg/m

= 950.4 Kg/m q1 = q plat + q air hujan

q1 = 1040.4 Kg/m

Tebal plat lantai = 13 cm = 0.13 m 0

q plat = 0.13 . 2400 . 3.6 = 1123.2 Kg/m

q tegel = 24 . 3.6 = 86.4 Kg/m

q spesi = 21 . 3.6 = 75.6 Kg/m

q tembok = 0.15 . 1700 . 3.6 = 918 Kg/m +

q2 = 2203.20 Kg/m

q2 = 2203.20 kg/m





MENGHITUNG MOMEN PRIMER

BATANG CD ( ATAP)

q1 = 1040.4 Kg/m MF CD = MF DC = 1/12 q . l²

C D = 1/12 1040.4 .( 37 )²

= 118692.3 Kgm

37 m


q2 = 2203.2 Kg/m MF BE = MF EB = 1/12 q l²

B E = 1/12 ### . ( 37 )²

= 251348.400 Kgm

37 m

FREE BODY BEBAN MATI

q1 = 1040.4 Kg/m

C D

### ###

### Q1 = 38494.8 KN ###

### q2 = ### Kg/m ###

B E

240671 ###

### Q2 = 81518.4 Kg ###

52675.00 52675

A F

BATANG CD ( ATAP )

q1 = 1040.4 Kg/m

C D

### ###

19247.4 38494.8 19247.4

37 m

Q = q1. l = ### . 37 = 38494.8 Kg

RCV = RDV = Q .1/2 L = 38494.8 . 19

L 37

= 19247.40 Kg



Mencari Momen Max

X Qx = q1 . X = 1040.4 X


= 19247.40 X - 520.2 X² - ###

Dx =dMx

= 19247.4 - 1040.4 X19247.4 Qx= 1040.4 x dx

X =19247.4

= 18.51040.4

Mmax = 19247.4 X - 520.2 X² - ###

= 19247.4 . ( 18.5 ) - 520.2 . ( 18.5 )²- ### = 65421.3617 Kgm

= 65.42136 tm

240671 q2 = 2203.2 Kg/m ###

B E

240671 ###

81518.4 Kg

37 m

Q = q2 . l = 2203.2 . 37 = 81518.4 Kg


=81518.4 . 18.5

L 37

= 40759.2 Kg

Mencari Momen Max

X

MBE Qx = qx . . X = 2203.2 X


= 40759.2 X - 1101.6 X² - 240671

40759.2 QxDx =

dMx = 40759.2 - 2203.2 X

dx

X = 18.5

Mmax = 40759.2 . ( 18.5 )- 1101.6 . ( 18.5 )² - 240671 = 136351.564 Kgm

= 136.3516 tm

MOMEN TOTAL ( beban hidup + beban mati )

MOMEN BATANG CD ( ATAP )

M Total = Momen Beban Hidup + Momen Beban Mati

= 30.302588 + 65.4213617 = 95.7239497 tm

MOMEN BATANG BE ( LANTAI )

M Total = Momen Beban Hidup + Momen Beban Mati

= 75.0882074 + 136.351564 = 211.439772 tm




PERENCANAAN PENDAHULUAN

BALOK ATAP

Dianggap MBS <<< 20% - 30%

Pe =ML h = k √ ML

0.5 h = 10 √ 95.7239497181

=95.72395 = 97.83862 cm

h 0.5 . 0.978386

= 195.677234 t

= 195677.234 Kg

= 195677.234 Kg

bAc =

Pe Fcs = 0.45 . fc

0.5 .Fcs = 0.45 . 36

=195677.234 = 16.2

0.5 . 16.20

= 24157.6832 mm²

Nilai h = 97.83862 cm h = 100 cm

b = 0.5 h = 0.5 100 = 50 cm

Dari perhitungan diatas diperoleh :

h = 100 cm

b = 50 cm

100 cm

50 cm



BALOK LANTAI

Dianggap MBS <<< 20% - 30%

Pe =ML h = k √ ML

0.5 h = 10 √ 211.439771886

=211.4398 = 145.4097 cm

h 0.5 . 1.454097

= 290.819375 t

= 290819.375 Kg

= 290819.375 Kg

bAc =

Pe Fcs = 0.45 . fc

0.5 .Fcs = 0.45 . 36

=290819.375 = 16.2

0.5 . 16.20

= 35903.6265 mm²

Nilai h = 145.4097 cm h = 145 cm

b = 0.5 h = 0.5 145 = 72.5

Dari perhitungan diatas diperoleh :

h = 145 cm

b = 72.5 cm

145 cm

72.5 cm

3. MENGHITUNG MOMEN AKIBAT BEBAN SENDIRI

BATANG CD ( ATAP) q1 = b. h. ρ

q1 = 1200 KN/m = 0.5 . 1 . 2400

C D = 1200 kg/m

= 1200 Kg/m

37 m



MF CD = MF DC = 1/12 q. l²

= 1/12 . 1200 ( 37 )²

= 136900 Kgm


q2 = 2523 KN/m

B E q2 = b. h. ρ

= 0.725 . 1.45 . 2400

37 m = 2523 kg/m

= 2523 Kg/m

MF BE = MF EB = 1/12 q. l²

= 1/12 . 2523 ( 37 )²

= 287832.25 Kgm

FREE BODY BERAT SENDIRI

q1 = 1200 Kg/m

C D

### ###

### Q1 = 44400 Kg ###

### ###

q2 = 2523 Kg/m

B E

275629 ###

### Q2 = 93351 Kg ###

60202.32 60202.32

A F



BATANG CD ( ATAP )

q1 = 1200 Kg/m

C D

### ###

22200 44400 22200

37 m

Q = q1. l = 1200 . 37 = 44400 Kg

RCV = RDV =Q . 1/2 L

=44400 . 18.5

L 37

= 22200 Kg

Mencari Momen Max

X Qx = q1 . X = 1200 X


= 22200 X - 600 X² - ###

Dx =dMx

= 22200 - 1200 X22200 Qx= 1200 x dx

X =22200

= 18.51200

Mmax = 22200 X - 600 X² - ###

= 22200 . ( 18.5 ) - 600 . ( 18.5 )²- ###

= 75508.0688 Kgm

= 75.50807 tm

275629 q2 = 2523 Kg/m ###

B E

275629 ###

93351 Kg

37 m

Q = q2 . l = 2523 . 37 = 93351 Kg


=93351 . 18.5

L 37

= 46675.5 Kg




Mencari Momen Max

X

MBE Qx = qx . . X = 2523 X


= 46675.5 X - 1261.5 X² - 275629

46675.5 QxDx =

dMx = 46675.5 - 2523 X

dx

X = 18.5

Mmax = 46675.5 . ( 18.5 ) - 1261.5 . ( 18.5 )² - 275629

= 156119.298 Kgm

= 156.1193 tm

KONTROL

MBS .100% < 20%

MT

Momen Total ( MT )

ATAP ( CD ) = MLL + MDL + MBS

= 30.30259 + 65.42136 + 75.5081

= 171.232 tm

LANTAI ( BE ) = MLL + MDL + MBS

= 75.08821 + 136.3516 + 156.119

= 367.5591 tm

KONTROL BALOK ATAP

MBS .100% < 20%

MT

75.50807 .100% < 20%

171.232

44.09693 % > 20% ( TIDAK MEMENUHI )

KONTROL BALOK LANTAI

MBS .100% < 20%

MT

156.1193 .100% < 20%

367.5591

42.47461 % > 20% ( TIDAK MEMENUHI )

Karena tidak memenuhi maka digunakan langkah I



Pe =MT

0.65 . h

ATAP

Pe =171.232

= 263.433875 t = 263433.875 Kg0.65 . 1

LANTAI

Pe =367.5591

= 389.983098 t = 389983.098 Kg0.65 . 1.45

PERENCANAAN SECARA KEKUATAN BATAS

1. MENENTUKAN Mu

BATANG CD ( ATAP )

Mu = 1.2 MDL + 1.6 MLL

= 1.2 . ( 65.42136 + 75.50807 ) + 1.6 . 30.3026

= 169.1153 \ 48.48414

= 217.5995 tm = 2175.99457 KNm

= 2175994574 Kgmm


Mu = 1.2 MDL + 1.6 MLL

= 1.2 . ( 136.3516 + 156.1193 ) + 1.6 . 75.0882

= 350.965 + 120.1411 = 471.1062 tm

= 4711.06166 KNm

= 4711061664 Kgmm

2. MENENTUKAN RASIO PENULANGAN PRATEKAN ( ωp )

BATANG CD ( ATAP )

d' = 0.1 h dp = h - d'

dp = 0.1 . 100 = 100 - 10

h = 10 cm = 90 cm

d'

b

Mu = Ø .b fc' ωp .( 1 - 0.59 ωp )

2175994574 = 0.8 . 500 . 900 36 ωp .( 1 - 0.59 ωp )

2175994574 = 1.1664E+10 ωp - 6881760000 ωp²

1.1664E+10 ωp - 6881760000 ωp² - 2175994574 = 0

dp2 .

2 .



1.69491525 ωp - 1 ωp² - 0.31619739 = 0

ωp = -b ± √ b² - 4 a c

2 a

ωp =-1.69491525 ± √ 2.87273772 - 4 ( -1 )( -0.3162 )

-2

ωp =-1.69491525 ± √ 1.60794815

-2

ωp =-1.69491525 ± 1.26804895

-2

ωp1 = 0.2134

ωp2 = 1.4814821

= 0.2134


d' = 0.1 h dp = h - d'

dp = 0.1 . 145 = 145 - 14.5

h = 14.5 cm = 130.5 cm

d'

b

Mu = Ø .b fc' ωp .( 1 - 0.59 ωp )

4711061664 = 0.8 . 725 . 1305 36 ωp .( 1 - 0.59 ωp )

4711061664 = 3.555916E+10 ωp - 20979905580 ωp²

3.5559E+10 ωp - 2.098E+10 ωp² - 4711061664 = 0

1.69491525 ωp - 1 ωp² - 0.22455114 = 0

ωp =

-b ± √ b² - 4 a c

2 a

ωp =-1.69491525 ± √ 2.87273772 - 4 ( -1 )( -0.22455 )

-2

ωp =-1.69491525 ± √ 1.97453317

-2

ωp =-1.69491525 ± 1.40518083

-2

ωp1 = 0.14487

ωp2 = 1.550048

= 0.14487

Digunakan nilai ωp terkecil

dp2 .

2 .

Digunakan nilai ωp terkecil



3. MENENTUKAN LUAS KABEL PRATEKAN

BATANG CD ( ATAP )


Mpaβ1 = 0.85 -( fc' - 30 ) 0.008

98.7 = 0.85 -( 36 - 30 ) 0.008

fpu = 1899.69605 Mpa = 0.85 - 0.048

= 0.802

Apsωp . b . dp . fc'

= . b . dpfps ( bonded )

ωp . b . dp . fc' = . b . dp

fpu ( 1 -ال p . . fpu

)β1 . fc

0.2134 . 500 . 900 . 36 = . 500 . 900

1899.696 ( 1 -0.4 . . 1899.69605

)0.802 . 36

3457617.05 = 450000

1899.696 ( 1 -759.878419

)28.872

3457617.05 = 450000

1899.696 - 49997.8537

854863222 - 22499034147.0628 - 3457617.0451 = 0

247.240574 - 6507.09255926214 - 1 = 0

= -b ± √ b² - 4 a.c

2 a

= -247.240574 ± √ 247.240574 ² - 4 ( -6507.0926 )( -1 )

2 ( -6507.09256 )

= -247.240574 ± √ 35099.5310486

-13014.1851

= -247.240574 ± 187.348688

-13014.1851

= 0.00460205 = 0.03339351


)β1 . fc

fps = 1899.696 ( 1 -0.4 . 0.004602 1899.69605

)0.802 . 36

fps = 1899.69605 - 230.092448Aps =

ωp . b . dp . fc'

fps = 1669.6036 Mpa fps ( bonded )

Aps = 2070.92093 = 0.21343 . 500 . 900 . 36

Digunakan 1 tendon tipe unit 27 dengan untaian kawat 21 dengan Aps = 2073

ρp

ρp

ρp

ρp

ρp

ρp

ρp

ρp

ρp

ρp ρp2

ρp ρp2

ρp

ρp1 ρp2

ρp

mm2

mm2





Mpaβ1 = 0.85 -( fc' - 30 ) 0.008

98.7 = 0.85 -( 36 - 30 ) 0.008

fpu = 1899.69605 Mpa = 0.85 - 0.048

= 0.802

Aps ωp . b . dp . fc' = . b . dpfps ( bonded )

ωp . b . dp . fc' = . b . dp

fpu ( 1 -ال p . . fpu

)β1 . fc

0.14487 . 725 . 1305 . 36 = . 725 . 1305

1899.696 ( 1 -0.4 . . 1899.69605

)0.802 . 36

4934249.66 = 946125

1899.696 ( 1 -759.878419

)28.872

4934249.66 = 946125

1899.696 - 49997.8537

1797349924 - 47304219294.1995 - 4934249.6551 = 0

364.260029 - 9586.91241848016 - 1 = 0

= -b ± √ b² - 4 a.c

2 a

= -364.260029 ± √ 364.260029 ² - 4 ( -9586.9124 )( -1 )

2 ( -9586.91242 )

= -364.260029 ± √ 94337.7192832

-19173.8248

= -364.260029 ± 307.14446

-19173.8248

= 0.00297883

= 0.03501672

fps =fpu ( 1 -

ال p . . fpu)

β1 . fc

fps =1899.696 ( 1 -

0.4 . 0.002979 1899.69605 )

0.802 . 36

fps = 1899.69605 - 148.935119

fps = 1750.76093 Mpa

ρp

ρp

ρp

ρp

ρp

ρp

ρp

ρp

ρp

ρp ρp2

ρp ρp2

ρp

ρp1

ρp2

ρp



Aps =ωp . b . dp . fc'

fps ( bonded )

=0.14487 . 725 . 1305 . 36

1750.76093

Aps = 2818.34577

Digunakan 2 tendon tipe unit 19 dengan untaian kawat 15 dengan Aps = 2 x 1481

= 2962 mm2

BATANG CD ( ATAP )

baru =Aps

=2073

= 0.00460667 b . dp 500 . 900

ωp = .fps

≤ 0.36 . β1fc'

= 0.004607 .1669.6036

≤0.36 . 0.802

36

= 0.21364742 ≤ 0.28872 ( MEMENUHI )

Aps br = 2073


baru = Aps = 2962 = 0.00313066

b . dp 725 . ###

ωp = . fps ≤0.36

. β1

fc'

= 0.003131 . 1750.76093 ≤ 0.36 . 0.802

36

= 0.15225 ≤ 0.28872 ( MEMENUHI )

Aps br = 2962

5. MENENTUKAN Mn

BATANG CD ( ATAP )

Mn = Aps . fps . ( dp - 0.5 a )a =

Aps . fps

Mn = 2073 1669.604 ( 900 - 113.1075 ) 0.85 . fc' . b

Mn = 2723504536a =

2073 . 1669.604

0.85 . 36 . 500

Mn . Ø ≥ Mu = 226.214919

2723504536 . 0.80 ≥ 2175994574

2178803629 Nmm ≥ 2175994574 Nmm ( AMAN )

mm2

mm2

4. MENENTUKAN KEMBALI NILAI ωp

ρp

ρp

ρp

ρp




Mn = Aps . fps . ( dp - 0.5 a )a =

Aps . fps

Mn = 2962 1750.761 ( 1305 - 116.8752 ) 0.85 . fc' . b

Mn = 6161322639a =

2962 . 1750.761

0.85 . 36 . 725

Mn . Ø ≥ Mu = 233.750456

6161322639 . 0.8 ≥ 4711061664

4929058111 Nmm ≥ 4711061664 Nmm ( AMAN )

TABEL RESUME

DAERAHMOMEN Kg/m

HIDUP MATI SENDIRI TOTAL

ATAP

CD -53480.2120 -112617.0883 -129841.9312 -295939.231516

LAP 30302.5880 65421.3617 75508.0688 171232.0185

DC -53480.2120 -112617.0883 -129841.9312 -295939.2315

LANTAI

BE -131904.5926 -240671.0355 -275629.0774 -648204.7055

LAP 75088.2074 136351.5645 156119.2976 367559.0695

EB -131904.5926 -240671.0355 -275629.0774 -648204.7055

MOMEN LAPANGAN TUMPUAN h b AC IC

ATAPMO 755080687.66 -1298419312.3416 1000 500 500000 41666666666.7

MT 957239497.18 -1660973002.8193 1000 500 500000 41666666666.7

LANTAIMO 1561192976.20 -2756290773.8005 1450 725 1051250 184187760417

MT 2114397718.86 -3725756281.1438 1450 725 1051250 184187760417

Tahap Awal1 e ≤ 166.66666666667 mm

1/pso ≤ -1.914993 N2 e ≥ 166.66666666667 mm

81/pso ≥ 0.7293688 N

3 e ≥ -166.6666666667 mm7

1/pso ≥ 0.7592735 N a

63

51 b

2

4

3

2

1 e

-600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700

-1

-2

-3

-4

-5Tahap AkhirA e ≤ 166.66666666667 mm

-61/pso ≤ -4.93062 N

B e ≥ -166.6666666667 mm

-71/pso ≥ 0.9733399 N

C e ≥ 166.66666666667 mm

-81/pso ≥ 0.4301325 N

x 107

x 107

x 107

x 107

x 107

x 107

LAPANGAN TUMPUAN

e = 150 e = -230

Ya = 500.0 Ya = 500.0

As = 500000.0 As = 500000.0

Ic = 41666666667 Ic = 41666666667

Mo = 755080687.7 Mo = -1298419312.3

Mt = 957239497.2 Mt = -1660973002.8

Pso = 7099050.0 Pso = 7099050.0



AWAL

ATAS

- Pso + Pso . e . Ya - Mo . Ya

As Ic Ic

- 7099050.0 + 7099050.0 150.0 500.0-

755080687.7 . 500.0

500000.0 41666666666.7 41666666666.7

- 14.2 + 12.8 - 9.1

= -10.5 ≤ - 0.60 X Fci

= -10.5 ≤ -18.36 (Aman)

AWAL

BAWAH

= - Pso-

Pso . e . Yb+

Mbs . Yb

As Ic Ic

= - 7099050.0-

7099050.0 150.0 500.0+

755080687.7 . 500.0

500000.0 41666666666.7 41666666666.7

14.2 + 12.8 - 9.1

= -17.9 ≤ - 0.6 X Fci

= -17.9 ≤ -18.36 (Aman)

AKHIR

ATAS


Ps = Pso x 0.85

Ps = 7099050.0 x 0.85

Ps = 6034192.5

= -ps

+Ps . e . Ya

-Mo Ya

-Mt Ya

As Ic Ic Ic

= -6034192.5

+6034192.5 150.0 500.0

-755080687.7 . 500.0

-957239497 . 500.0

500000.0 41666666666.7 41666666666.7 41666666666.7

= - 12.1 + 10.9 - 9.1 - 11.5

= -21.8 ≤ - 0.45 x Fc

= -21.8 ≤ -16.2 (Tidak Aman)

AKHIR

BAWAH

= -Ps - Ps e Yb + Mo Yb + Mt. Yb

As Ic Ic Ic

= -6034192.5

-6034192.5 150.0 500.0

+755080687.7 . 500.0

+957239497.2 . 500.0

500000.0 41666666666.7 41666666666.7 41666666666.7

= - 12.1 - 10.9 + 9.1 + 11.5

= -2.4 ≤ - 0.45 x Fc

= -2.4 ≤ -16.2 (Aman)

TUMPUAN

AWAL

ATAS


As Ic Ic

- 7099050.0 + 7099050.0 -230.0 500.0-

-1298419312.3 . 500.0

500000.0 41666666666.7 41666666666.7

= - 14.2 + -19.6 - -15.6

= -18.2 ≤ - 0.60 X Fci

= -18.2 ≤ -18.36 (Aman)

AWAL

BAWAH

- Pso-

Pso . e . Yb+

Mbs . Yb

As Ic Ic

- 7099050.0-

7099050.0 -230.0 500.0+

-1298419312.3 . 500.0

500000.0 41666666666.7 41666666666.7

= - 14.2 + 19.6 + -15.6

= -10.2 ≤ - 0.6 X Fci

= -10.2 ≤ -18.4 (Aman)

AKHIR

ATAS


Ps = Pso x 0.85

Ps = 7099050.0 x 0.85

Ps = 6034192.5

= -ps

+Ps . e . Ya

-Mo Ya

-Mt Ya

As Ic Ic Ic

= -6034192.5

+6034192.5 -230.0 500.0

--1298419312.3 . 500.0

--1660973003 . 500.0

500000.0 41666666666.7 41666666666.7 41666666666.7

= - 12.1 + -16.7 + 15.6 + 19.9

= 6.8 ≤ 0.50 X √Fc

= 6.8 ≤ 3.0 (Tidak Aman)

AKHIR

BAWAH

= -Ps - Ps e Yb + Mt. Yb

As Ic Ic

= -6034192.5

-6034192.5 -230.0 500.0

+-1298419312.3 . 500.0

+-1660973003 . 500.0

500000.0 41666666666.7 41666666666.7 41666666666.7

= - 12.1 - -16.7 + -15.6 + -19.9

= -30.9 ≤ -0.45 x Fc

= -30.9 ≤ -16.2 (Tidak Aman)

e = 200 e = -320

Ya = 725.0 Ya = 725.0

As = 1051250.0 As = 1051250.0

Ic = 184187760417 Ic = 184187760417

Mo = 1561192976.2 Mo = -2756290773.8

Mt = 2114397719 Mt = -3725756281.1

Pso = 9951534.2 Pso = 9951534.2


LAPANGAN BENTANGAN CD (LANTAI)

AWAL

ATAS


As Ic Ic

- 9951534.2 + 9951534.2 200.0 725.0-

1561192976.2 . 725.0

1051250.0 184187760416.7 184187760416.7

- 9.5 + 7.8 - 6.1

= -7.8 ≤ - 0.60 X Fci

= -7.8 ≤ -18.36 (Aman)

AWAL

BAWAH

= - Pso-

Pso . e . Yb+

Mbs . Yb

As Ic Ic

= - 9951534.2-

9951534.2 200.0 725.0+

1561192976.2 . 725.0

1051250.0 184187760416.7 184187760416.7

9.5 + 7.8 - 6.1

= -11.2 ≤ - 0.6 X Fci

= -11.2 ≤ -18.36 (Aman)

AKHIR

ATAS


Ps = Pso x 0.85

Ps = 9951534.2 x 0.85

Ps = 8458804.1

= -ps

+Ps . e . Ya

-Mo Ya

-Mt Ya

As Ic Ic Ic

= -8458804.1

+8458804.1 200.0 725.0

-1561192976.2 . 725.0

-2114397719 . 725.0

1051250.0 184187760416.7 184187760416.7 184187760416.7

= - 8.0 + 6.7 - 6.1 - 8.3

= -15.9 ≤ - 0.45 x Fc

= -15.9 ≤ -16.2 (Aman)

AKHIR

BAWAH

= -Ps - Ps e Yb + Mo Yb + Mt. Yb

As Ic Ic Ic

= -8458804.1

-8458804.1 200.0 725.0

+1561192976.2 . 725.0

+2114397718.9 . 725.0

1051250.0 184187760416.7 184187760416.7 184187760416.7

= - 8.0 - 6.7 + 6.1 + 8.3

= -0.2 ≤ - 0.45 X Fc

= -0.2 ≤ -16.2 (Aman)

TUMPUAN

AWAL

ATAS


As Ic Ic

- 9951534.2 + 9951534.2 -320.0 725.0-

-2756290773.8 . 725.0

1051250.0 184187760416.7 184187760416.7

= - 9.5 + -12.5 - -10.8

= -11.15 ≤ - 0.60 X Fci

= -11.15 ≤ -18.36 (Aman)

AWAL

BAWAH

- Pso-

Pso . e . Yb+

Mbs . Yb

As Ic Ic

- 9951534.2-

9951534.2 -320.0 725.0+

-2756290773.8 . 725.0

1051250.0 184187760416.7 184187760416.7

= - 9.5 + 12.5 + -10.8

= -7.8 ≤ - 0.6 X Fci

= -7.8 ≤ -18.4 (Aman)

AKHIR

ATAS


Ps = Pso x 0.85

Ps = 9951534.2 x 0.85

Ps = 8458804.1

= -ps

+Ps . e . Ya

-Mo Ya

-Mt Ya

As Ic Ic Ic

= -8458804.1

+8458804.1 -320.0 725.0

--2756290773.8 . 725.0

--3725756281 . 725.0

1051250.0 184187760416.7 184187760416.7 184187760416.7

= - 8.0 + -10.7 + 10.8 + 14.7

= 6.8 ≤ 0.5 x √Fc

= 6.8 ≤ 3.0 (Tidak Aman)

AKHIR

BAWAH

= -Ps - Ps e Yb + Mt. Yb

As Ic Ic

= -8458804.1

-8458804.1 -320.0 725.0

+-2756290773.8 . 725.0

+-3725756281 . 725.0

1051250.0 184187760416.7 184187760416.7 184187760416.7

= - 8.0 - -10.7 + -10.8 + -14.7

= -22.9 ≤ - 0.45 x Fc

= -22.9 ≤ - 16.2 (Tidak Aman)

MENENTUKAN LETAK KABEL PRATEKAN

1.LAPANGAN ATAPA Tahap Awal

1 Tegangan Pada Serat Atas (TARIK)

St =Mo .b

=755080687.658 500

= 9.06096825190112IC 41666666666.667

=- Pso

+Pso .e .b

- St ≤ 0.25√FciAC IC

=- Pso

+Pso .e. 500

- 9.06096825190112 ≤ 0.25√Fci500000 41666666666.667

= -0.0000020000000 Pso + 0.000000012000 Pso.e - 9.06096825190112 ≤ 1.3829317

► e ≤1.38293166859 + 0.0000020000000 Pso + 9.06096825190112

0.000000012000 Pso

► e ≤10.44389992050 + 0.000002 Pso

0.000000012000 Pso

► e ≤10.44389992050

+ 166.670.0000000120000 Pso

► Pso ≤10.44389992050

-0.0000020000000 + 0.000000012000 e

≈ 1= 0 → e = 166.6667 mm

Pso

≈ e = 0 → Pso = -5221949.96

1= -0.0000001914993456 N

Pso

-1.91499345572549 N

2 Tegangan Pada Serat Bawah (TEKAN)

St =Mo .b

=755080687.658 500

= 9.06096825190112IC 41666666666.667

=- Pso

-Pso .e .b

+ St ≥ 0.6xFciAC IC

=- Pso

-Pso .e. 500

+ 9.0609682519 ≥ 0.6xFci500000 41666666666.667

= -0.0000020000000 Pso - 0.000000012000 Pso.e + 9.06096825190112 ≥ -17.2800=

► e ≥-17.28000000000 + 0.0000020000000 Pso + -9.06096825190112

-0.000000012000 Pso

► e ≥-26.34096825190 + 0.0000020000000 Pso

-0.000000012000 Pso

► e ≥-26.34096825190

+ -166.67-0.000000012000 Pso

► Pso ≥-26.34096825190

-0.0000020000000 + 0.000000012000 e

≈ 1= 0 → e = -166.6667 mm

Pso

≈ e = 0 → Pso = 13170484.13

1= 0.0000000759273532 N

Pso= 0.759273532 N

x107

x107

B Tahap Akhir1 Tegangan Pada Serat Atas (TARIK)

St =Mo .b

=755080687.658 500

= 9.06096825190112IC 41666666666.667

Sp =MT .b

=957239497.181 500

= 11.4868739661682IC 41666666666.667

=- Ps

+Ps .e .b

- St - Sp ≥ 0.45 FcAC IC

=- Pso.0.85

+0.85Pso .e. 500

+ -20.547842218069300 ≥ -17.1500000 41666666666.667

= -0.000001700000 Pso + 0.00000001020000 Pso.e + -20.547842218069300 ≥ -17.10

► e ≤-17.10000000000 + 0.0000017000000 Pso + 20.5478422181

0.00000001020000 Pso

► e ≤3.44784221807 + 0.0000017000000 Pso

0.00000001020000 Pso

► e ≤3.44784221807

+ 166.670.00000001020000 Pso

► Pso ≤3.44784221807

-0.0000017000000 + 0.00000001020000 e

≈ 1= 0 → e = 166.6667 mm

Pso

≈ e = 0 → Pso = -2028142.48

1= -0.0000004930620059 N

Pso

= -4.93062006 N


St =Mo .b

=755080687.658 500

= 9.06096825190112IC 41666666666.667

Sp =MT .b

=957239497.181 500

= 11.4868739661682IC 41666666666.667

=- Ps

-Ps .e .b

+ St + Sp ≤ 0.5 √FcAC IC

=- Pso.0.85

-0.85Pso .e. 500

+ 20.547842218069300 ≤ 3.08221500000 41666666666.667

= -0.00000170000 Pso - 0.00000001020000 Pso.e + 20.547842218069300 ≤ 3.08221

► e ≥3.08220700148 + 0.0000017000000 Pso + -20.5478422181

-0.0000000102000 Pso

► e ≥-17.46563521658 + 0.0000017000000 Pso

-0.0000000102000 Pso

► e ≥-17.46563521658

+ -166.67-0.0000000102000 Pso

► Pso ≥-17.46563521658

-0.0000017000000 + 0.00000001020000 e

≈ 1= 0 → e = -166.6667 mm

Pso

≈ e = 0 → Pso = 10273903.07

1= 0.0000000973339921 N

Pso0.9733399209 N

x107

x107

a). Tahap Awal b). Tahap akhir1 e ≤ 166.6667 mm 1 e ≤ 166.6667 mm

1/pso ≤ -1.91499346 N 1/pso ≤ -4.930620 N2 e ≥ 166.6667 mm 2 e ≥ -166.6667 mm

1/pso ≥ 0.729369 N 1/pso ≥ 0.973340 N3 e ≥ -166.6667 mm 3 e ≤ 166.6667 mm

1/pso ≥ 0.7592735 N 1/pso ≤ 0.4301325 N

b1 a1

7

6b2

5a3

4

3

2

1

0-500 -400 -300 -200 -100 100 200 300 400 500 600

-1

-2

-3

-4

-5

-6

-7

-8

x 107 x 107

x 107 x 107

x 107 x 107

2.TUMPUAN ATAPA Tahap Awal


St =Mo .b

=-1298419312.342 500

= -15.5810317480989IC 41666666666.667

=- Pso

+Pso .e .b


=- Pso

+Pso .e. 500

- -15.5810317480989 ≤ 0.25√Fci500000 41666666666.667

= -0.0000020000000 Pso + 0.000000012000 Pso.e - -15.5810317480989 ≤ 1.3829317

► e ≤1.38293166859 + 0.0000020000000 Pso + -15.5810317480989

0.000000012000 Pso

► e ≤-14.19810007950 + 0.000002 Pso

0.000000012000 Pso

► e ≤-14.19810007950

+ 166.670.0000000120000 Pso

► Pso ≤-14.19810007950

-0.0000020000000 + 0.000000012000 e

≈ 1= 0 → e = 166.6667 mm

Pso

≈ e = 0 → Pso = 7099050.04

1= 0.0000001408639176 N

Pso

= 1.40863917622824 N


St =Mo .b

=-1298419312.342 500

= -15.5810317480989IC 41666666666.667

=- Pso

-Pso .e .b


=- Pso

-Pso .e. 500

+ -15.5810317481 ≥ 0.6xFci500000 41666666666.667

= -0.0000020000000 Pso - 0.000000012000 Pso.e + -15.5810317480989 ≥ -17.7600=

► e ≥-17.76000000000 + 0.0000020000000 Pso + 15.5810317480989

-0.000000012000 Pso

► e ≥-2.17896825190 + 0.0000020000000 Pso

-0.000000012000 Pso

► e ≥-2.17896825190

+ -166.67-0.000000012000 Pso

► Pso ≥-2.17896825190

-0.0000020000000 + 0.000000012000 e

≈ 1= 0 → e = -166.6667 mm

Pso

≈ e = 0 → Pso = 1089484.13

1= 0.0000009178655991 N

Pso= 9.1786560 N

x107

x107


St =Mo .b

=-1298419312.342 500

= -15.5810317480989IC 41666666666.667

Sp =MT .b

=-1660973002.819 500

= -19.9316760338319IC 41666666666.667

=- Ps

+Ps .e .b

- St - Sp ≤ 0.45 FcAC IC

=- Pso.0.85

+0.85Pso .e. 500

+ 35.512707781930700 ≤ -16.65500000 41666666666.667

= -0.000001700000 Pso + 0.00000001020000 Pso.e + 35.512707781930700 ≤ -16.65

► e ≤-16.65000000000 + 0.0000017000000 Pso + -35.5127077819

0.00000001020000 Pso

► e ≤-52.16270778193 + 0.0000017000000 Pso

0.00000001020000 Pso

► e ≤-52.16270778193

+ 166.670.00000001020000 Pso

► Pso ≤-52.16270778193

-0.0000017000000 + 0.00000001020000 e

≈ 1= 0 → e = 166.6667 mm

Pso

≈ e = 0 → Pso = 30683945.75

1= 0.0000000325903327 N

Pso

= 0.325903327 N


St =Mo .b

=-1298419312.342 500

= -15.5810317480989IC 41666666666.667

Sp =MT .b

=-1660973002.819 500

= -19.9316760338319IC 41666666666.667

=- Ps

-Ps .e .b


=- Pso.0.85

-0.85Pso .e. 500

+ -35.512707781930700 ≤ 3.04138500000 41666666666.667

= -0.00000170000 Pso - 0.00000001020000 Pso.e + -35.512707781930700 ≤ 3.04138

► e ≤3.04138126515 + 0.0000017000000 Pso - 35.5127077819

-0.0000000102000 Pso

► e ≥-32.47132651678 + 0.0000017000000 Pso

-0.0000000102000 Pso

► e ≥-32.47132651678

+ -166.67-0.0000000102000 Pso

► Pso ≥-32.47132651678

0.0000017000000 + 0.00000001020000 e

≈ 1= 0 → e = -166.6667 mm

Pso

≈ e = 0 → Pso = -19100780.30

1= -0.0000000523538821 N

Pso

= -0.5235388 N

x107

x107

Tahap Awal Tahap akhir1 e ≤ 166.7 mm 1 e ≤ 166.7 mm

1/pso ≤ 1.408639176 N 1/pso ≤ 0.325903 N2 e ≥ -166.7 mm 2 e ≥ -166.7 mm

1/pso ≥ 7.196916 N 1/pso ≥ -0.523539 N3 e ≤ -166.7 mm 3 e ≤ 166.7 mm

1/pso ≤ 9.1786560 N 1/pso ≤ 0.8482345 N

a2

7

6

5

4

a13

2b1

1

0-500 -400 -300 -200 -100 100 200 300 400 500 600

-1

-2

-3b2

-4

-5

-6

-7

-8

x 107 x 107

x 107 x 107

x 107 x 107

3.LAPANGAN LANTAIA Tahap Awal


St =Mo .b

=1561192976.199 725

= 6.14516895793793IC 184187760416.667

=- Pso

+Pso .e .b


=- Pso

+Pso .e. 725

- 6.14516895793793 ≤ 0.25√Fci1051250 184187760416.667

= -0.0000009512485 Pso + 0.000000003936 Pso.e - 6.14516895793793 ≤ 1.3829317

► e ≤1.38293166859 + 0.0000009512485 Pso + 6.14516895793793

0.000000003936 Pso

► e ≤7.52810062653 + 0.000001 Pso

0.000000003936 Pso

► e ≤7.52810062653

+ 241.670.0000000039362 Pso

► Pso ≤7.52810062653

-0.0000009512485 + 0.000000003936 e

≈ 1= 0 → e = 241.6667 mm

Pso

≈ e = 0 → Pso = -7913915.78

1= -0.0000001263596969 N

Pso

= -1.26359696936255 N


St =Mo .b

=1561192976.199 725

= 6.14516895793793IC 184187760416.667

=- Pso

-Pso .e .b


=- Pso

-Pso .e. 725

+ 6.1451689579 ≥ 0.6xFci1051250 184187760416.667

= -0.0000009512485 Pso - 0.000000003936 Pso.e + 6.14516895793793 ≥ -18.3600=

► e ≥-18.36000000000 + 0.0000009512485 Pso + -6.14516895793793

-0.000000003936 Pso

► e ≥-24.50516895794 + 0.0000009512485 Pso

-0.000000003936 Pso

► e ≥-24.50516895794

+ -241.67-0.000000003936 Pso

► Pso ≥-24.50516895794

-0.0000009512485 + 0.000000003936 e

≈ 1= 0 → e = -241.6667 mm

Pso

≈ e = 0 → Pso = 25761058.87

1= 0.0000000388182801 N

Pso= 0.388182801 N

x107

x107


St =Mo .b

=1561192976.199 725

= 6.14516895793793IC 184187760416.667

Sp =MT .b

=2114397718.856 725

= 8.32269387880566IC 184187760416.667

=- Ps

+Ps .e .b

- St - Sp ≥ 0.45 FcAC IC

=- Pso.0.85

+0.85Pso .e. 725

+ -14.467862836743600 ≥ -16.651051250 184187760416.667

= -0.000000808561 Pso + 0.00000000334577 Pso.e + -14.467862836743600 ≥ -16.65

► e ≤-16.65000000000 + 0.0000008085612 Pso + -14.4678628367

0.00000000334577 Pso

► e ≤-31.11786283674 + 0.0000008085612 Pso

0.00000000334577 Pso

► e ≤-31.11786283674

+ 241.670.00000000334577 Pso

► Pso ≤-31.11786283674

0.0000008085612 + 0.00000000334577 e

≈ 1= 0 → e = 241.6667 mm

Pso

≈ e = 0 → Pso = -38485474.48

1= -0.0000000259838293 N

Pso

= -0.259838293 N


St =Mo .b

=1561192976.199 725

= 6.14516895793793IC 184187760416.667

Sp =MT .b

=2114397718.856 725

= 8.32269387880566IC 184187760416.667

=- Ps

-Ps .e .b


=- Pso.0.85

-0.85Pso .e. 725

+ 14.467862836743600 ≤ 3.041381051250 184187760416.667

= -0.00000080856 Pso - 0.00000000334577 Pso.e + 14.467862836743600 ≤ 3.04138

► e ≥3.04138126515 + 0.0000008085612 Pso + -14.4678628367

-0.0000000033458 Pso

► e ≥-11.42648157159 + 0.0000008085612 Pso

-0.0000000033458 Pso

► e ≥-11.42648157159

+ -241.67-0.0000000033458 Pso

► Pso ≥-11.42648157159

-0.0000008085612 + 0.00000000334577 e

≈ 1= 0 → e = -241.6667 mm

Pso

≈ e = 0 → Pso = 14131869.12

1= 0.0000000707620479 N

Pso

= 0.70762048 N

x107

x107

a). Tahap Awal b). Tahap akhir1 e ≤ 241.6667 mm 1 e ≤ 241.6667 mm

1/pso ≤ -1.26359697 N 1/pso ≤ -0.259838 N2 e ≥ 241.6667 mm 2 e ≥ -241.6667 mm

1/pso ≥ 1.547962 N 1/pso ≥ 0.707620 N3 e ≥ -241.6667 mm 3 e ≤ 241.6667 mm

1/pso ≥ 0.3881828 N 1/pso ≤ 0.2445537 N

a1

7

6

5a2

4

3b2

2b1

1

0-500 -400 -300 -200 -100 100 200 300 400 500 600

-1

-2

-3

-4

-5

-6

-7

-8

x 107 x 107

x 107 x 107

x 107 x 107

4.TUMPUAN LANTAIA Tahap Awal


St =Mo .b

=-2756290773.801 725

= -10.8493138006828IC 184187760416.667

=- Pso

+Pso .e .b


=- Pso

+Pso .e. 725

- -10.8493138006828 ≤ 0.25√Fci1051250 184187760416.667

= -0.0000009512485 Pso + 0.000000003936 Pso.e - -10.8493138006828 ≤ 1.3829317

► e ≤1.38293166859 + 0.0000009512485 Pso + -10.8493138006828

0.000000003936 Pso

► e ≤-9.46638213209 + 0.000001 Pso

0.000000003936 Pso

► e ≤-9.46638213209

+ 241.670.0000000039362 Pso

► Pso ≤-9.46638213209

-0.0000009512485 + 0.000000003936 e

≈ 1= 0 → e = 241.6667 mm

Pso

≈ e = 0 → Pso = 9951534.22

1= 0.0000001004870182 N

Pso

= 1.00487018208328 N


St =Mo .b

=-2756290773.801 725

= -10.8493138006828IC 184187760416.667

=- Pso

-Pso .e .b


=- Pso

-Pso .e. 725

+ -10.8493138007 ≥ 0.6xFci1051250 184187760416.667

= -0.0000009512485 Pso - 0.000000003936 Pso.e + -10.8493138006828 ≥ -17.7600=

► e ≥-17.76000000000 + 0.0000009512485 Pso + 10.8493138006828

-0.000000003936 Pso

► e ≥-6.91068619932 + 0.0000009512485 Pso

-0.000000003936 Pso

► e ≥-6.91068619932

+ -241.67-0.000000003936 Pso

► Pso ≥-6.91068619932

-0.0000009512485 + 0.000000003936 e

≈ 1= 0 → e = -241.6667 mm

Pso

≈ e = 0 → Pso = 7264858.87

1= 0.0000001376489232 N

Pso= 1.37648923166 N

x107

x107


St =Mo .b

=-2756290773.801 725

= -10.8493138006828IC 184187760416.667

Sp =MT .b

=-3725756281.144 725

= -14.6653246541395IC 184187760416.667

=- Ps

+Ps .e .b

- St - Sp ≤ 0.45 FcAC IC

=- Pso.0.8

+0.8Pso .e. 725

+ 25.514638454822300 ≤ -16.651051250 184187760416.667

= -0.000000760999 Pso + 0.00000000314896 Pso.e + 25.514638454822300 ≤ -16.65

► e ≤-16.65000000000 + 0.0000007609988 Pso + -25.5146384548

0.00000000314896 Pso

► e ≤-42.16463845482 + 0.0000007609988 Pso

0.00000000314896 Pso

► e ≤-42.16463845482

+ 241.670.00000000314896 Pso

► Pso ≤-42.16463845482

-0.0000007609988 + 0.00000000314896 e

≈ 1= 0 → e = 241.6667 mm

Pso

≈ e = 0 → Pso = 55406970.22

1= 0.0000000180482708 N

Pso

= 0.180482708 N


St =Mo .b

=-2756290773.801 725

= -10.8493138006828IC 184187760416.667

Sp =MT .b

=-3725756281.144 725

= -14.6653246541395IC 184187760416.667

=- Ps

-Ps .e .b


=- Pso.0.8

-0.8Pso .e. 725

+ -25.514638454822300 ≤ 3.041381051250 184187760416.667

= -0.00000076100 Pso - 0.00000000314896 Pso.e + -25.514638454822300 ≤ 3.04138

► e ≤3.04138126515 + 0.0000007609988 Pso - 25.5146384548

-0.0000000031490 Pso

► e ≥-22.47325718967 + 0.0000007609988 Pso

-0.0000000031490 Pso

► e ≥-22.47325718967

+ -241.67-0.0000000031490 Pso

► Pso ≥-22.47325718967

0.0000007609988 + 0.00000000314896 e

≈ 1= 0 → e = -241.6667 mm

Pso

≈ e = 0 → Pso = -29531264.53

1= -0.0000000338624172 N

Pso

= -0.338624172 N

x107

x107

Tahap Awal Tahap akhir1 e ≤ 241.7 mm 1 e ≤ 241.7 mm

1/pso ≤ 1.004870182 N 1/pso ≤ 0.180483 N2 e ≥ -241.7 mm 2 e ≥ -241.7 mm

1/pso ≥ -0.876782 N 1/pso ≥ -0.338624 N3 e ≤ -241.7 mm 3 e ≤ 241.7 mm

1/pso ≤ 1.3764892 N 1/pso ≤ 0.8584657 N

a2

7

6

a15

4

3

2b2

1

0-500 -400 -300 -200 -100 100 200 300 400 500 600

-1b1

-2

-3

-4

-5

-6

-7

-8

x 107 x 107

x 107 x 107

x 107 x 107

TABEL RESUME NILAI Pso

NO BAGIAN DAERAH PERSMN NILAI Pso Pso DIPAKAI UNIT e UNIT1

ATAP

LAPANGAN

a1 -5221949.96

7099050.04

N 150

mm2 a2 13170484.13 mm3 b1 -2028142.48 mm4 b2 10273903.07 mm5

TUMPUAN

a1 7099050.04

N -230

mm6 a2 1089484.13 mm7 b1 30683945.75 mm8 b2 -19100780.3039892 mm9

LANTAI

LAPANGAN

a1 -7913915.78

9951534.22

N 200

mm10 a2 25761058.87 mm11 b1 -38485474.48 mm12 b2 14131869.12 mm13

TUMPUAN

a1 9951534.22

N -320

mm14 a2 7264858.87 mm15 b1 55406970.22 mm16 b2 -29531264.53 mm


1.LAPANGAN ATAPA Tahap Awal


St =Mo .b

=755080687.658 500

=IC 41666666666.667

=- Pso

+Pso .e .b

- StAC IC

=- Pso

+Pso .e. 500

- 9.06096825190112500000 41666666666.667

= -0.0000020000000 Pso + 0.000000012000 Pso.e - 9.06096825190112

► e ≤1.38293166859 + 0.0000020000000 Pso

0.000000012000 Pso

► e ≤10.44389992050 + 0.000002 Pso

0.000000012000 Pso

► e ≤10.44389992050

+ 166.670.0000000120000 Pso

► Pso ≤10.44389992050

-0.0000020000000 + 0.000000012000 e

≈ 1= 0 → e = 166.6667

Pso

≈ e = 0 → Pso = -5221949.96

1= -0.0000001914993456

Pso

-1.91499345572549


St =Mo .b

=755080687.658 500

=IC 41666666666.667

=- Pso

-Pso .e .b

+ StAC IC

=- Pso

-Pso .e. 500

+ 9.0609682519500000 41666666666.667

= -0.0000020000000 Pso - 0.000000012000 Pso.e + 9.06096825190112=

► e ≥18.36000000000 + 0.0000020000000 Pso

0.000000012000 Pso

► e ≥27.42096825190 + 0.0000020000000 Pso

0.000000012000 Pso

► e ≥27.42096825190

+ 166.670.000000012000 Pso

x107

► Pso ≥27.42096825190

0.0000020000000 + 0.000000012000 e

≈ 1= 0 → e = 166.6667

Pso

≈ e = 0 → Pso = 13710484.13

1= 0.0000000729368847

Pso0.7293688470907070


St =Mo .b

=755080687.658 500

=IC 41666666666.667

=- Pso

-Pso .e .b

+ StAC IC

=- Pso

-Pso .e. 500

+ 9.0609682519500000 41666666666.667

= -0.0000020000000 Pso - 0.000000012000 Pso.e + 9.06096825190112=

► e ≥-17.28000000000 + 0.0000020000000 Pso

-0.000000012000 Pso

► e ≥-26.34096825190 + 0.0000020000000 Pso

-0.000000012000 Pso

► e ≥-26.34096825190

+ -166.67-0.000000012000 Pso

► Pso ≥-26.34096825190

-0.0000020000000 + 0.000000012000 e

≈ 1= 0 → e = -166.6667

Pso

≈ e = 0 → Pso = 13170484.13

1= 0.0000000759273532

Pso= 0.759273532


St =Mo .b

=755080687.658 500

= 9.06096825190112IC 41666666666.667

Sp =MT .b

=957239497.181 500

= 11.4868739661682IC 41666666666.667

=- Ps

+Ps .e .b

- St - SpAC IC

=- Pso.0.85

+0.85Pso .e. 500

+ -20.547842218069300500000 41666666666.667

= -0.000001700000 Pso + 0.00000001020000 Pso.e + -20.547842218069300

x107

► e ≤-17.10000000000 + 0.0000017000000 Pso +

0.00000001020000 Pso

► e ≤3.44784221807 + 0.0000017000000 Pso

0.00000001020000 Pso

► e ≤3.44784221807

+ 166.670.00000001020000 Pso

► Pso ≤3.44784221807

-0.0000017000000 + 0.00000001020000 e

≈ 1= 0 → e = 166.6667 mm

Pso

≈ e = 0 → Pso = -2028142.48

1= -0.0000004930620059 N

Pso

= -4.93062006 N


St =Mo .b

=755080687.658 500

= 9.06096825190112IC 41666666666.667

Sp =MT .b

=957239497.181 500

= 11.4868739661682IC 41666666666.667

=- Ps

-Ps .e .b

+ St + SpAC IC

=- Pso.0.85

-0.85Pso .e. 500

+ 20.547842218069300500000 41666666666.667

= -0.00000170000 Pso - 0.00000001020000 Pso.e + 20.547842218069300

► e ≥3.08220700148 + 0.0000017000000 Pso +

-0.0000000102000 Pso

► e ≥-17.46563521658 + 0.0000017000000 Pso

-0.0000000102000 Pso

► e ≥-17.46563521658

+ -166.67-0.0000000102000 Pso

► Pso ≥-17.46563521658

-0.0000017000000 + 0.00000001020000 e

≈ 1= 0 → e = -166.6667 mm

Pso

≈ e = 0 → Pso = 10273903.07

1= 0.0000000973339921 N

Pso0.9733399209 N


St =Mo .b

=755080687.658 500

= 9.06096825190112

x107

x107

St =IC

=41666666666.667

= 9.06096825190112

Sp =MT .b

=957239497.181 500

= 11.4868739661682IC 41666666666.667

=- Ps

+Ps .e .b

- St - SpAC IC

=- Pso.0.8

+0.8Pso .e. 500

+ -20.547842218069300500000 41666666666.667

= -0.00000160000 Pso + 0.00000000960000 Pso.e + -20.547842218069300

► e ≤16.65000000000 + 0.0000016000000 Pso +

0.0000000096000 Pso

► e ≤37.19784221807 + 0.0000016000000 Pso

0.0000000096000 Pso

► e ≤37.19784221807

+ 166.670.0000000096000 Pso

► Pso ≤37.19784221807

0.0000016000000 + 0.00000000960000 e

≈ 1= 0 → e = 166.6667 mm

Pso

≈ e = 0 → Pso = 23248651.39

1= 0.0000000430132477 N

Pso0.4301324766689780

a). Tahap Awal b). Tahap akhir1 e ≤ 166.6667 mm 1 e ≤

1/pso ≤ -1.91499346 N 1/pso ≤2 e ≥ 166.6667 mm 2 e ≥

1/pso ≥ 0.729369 N 1/pso ≥3 e ≥ -166.6667 mm 3 e ≤

1/pso ≥ 0.7592735 N 1/pso ≤

7

6

5

4

3

2

1

x 107

x 107

x 107

1

0-500 -400 -300 -200 -100 100 200 300 400

-1

-2

-3

-4

-5

-6

-7

-8


2.TUMPUAN ATAPA Tahap Awal


9.06096825190112 St =Mo .b

=-1298419312.342

IC 41666666666.667

St ≤ 0.25√Fci =- Pso

+Pso .e .b

AC IC

9.06096825190112 ≤ 0.25√Fci =- Pso

+Pso .e. 500

500000 41666666666.667

9.06096825190112 ≤ 1.3829317 = -0.0000020000000 Pso + 0.000000012000

+ 9.06096825190112► e ≤

1.38293166859 + 0.00000200000000.000000012000

► e ≤-14.19810007950 + 0.000002

0.000000012000

► e ≤-14.19810007950

+ 166.670.0000000120000 Pso

► Pso ≤-14.19810007950

-0.0000020000000 + 0.000000012000

mm ≈ 1= 0 → e =

Pso

≈ e = 0 → Pso =

N1

=Pso

N =


9.06096825190112 St =Mo .b

=-1298419312.342

IC 41666666666.667

St ≤ 0.6xFci =- Pso

-Pso .e .b

AC IC

9.0609682519 ≤ 0.6xFci =- Pso

-Pso .e. 500

500000 41666666666.667

9.06096825190112≤

18.3600 = -0.0000020000000 Pso - 0.000000012000=

+ 9.06096825190112► e ≥

18.36000000000 + 0.0000020000000-0.000000012000

► e ≥2.77896825190 + 0.0000020000000

-0.000000012000

► e ≥2.77896825190

+ -166.67-0.000000012000 Pso

► Pso ≥2.77896825190

0.0000020000000 + 0.000000012000

mm ≈ 1= 0 → e =

Pso

≈ e = 0 → Pso =

N1

=Pso


9.06096825190112 St =Mo .b

=-1298419312.342

IC 41666666666.667

St ≥ 0.6xFci =- Pso

-Pso .e .b

AC IC

9.0609682519 ≥ 0.6xFci =- Pso

-Pso .e. 500

500000 41666666666.667

9.06096825190112 ≥ -17.2800 = -0.0000020000000 Pso - 0.000000012000=

+ -9.06096825190112► e ≥

-17.76000000000 + 0.0000020000000-0.000000012000

► e ≥-2.17896825190 + 0.0000020000000

-0.000000012000

► e ≥-2.17896825190

+ -166.67-0.000000012000 Pso

► Pso ≥-2.17896825190

-0.0000020000000 + 0.000000012000

mm ≈ 1= 0 → e =

Pso

≈ e = 0 → Pso =

N1

=Pso

N =B Tahap Akhir


9.06096825190112 St =Mo .b

=-1298419312.342

IC 41666666666.667

11.4868739661682 Sp =MT .b

=-1660973002.819

IC 41666666666.667

St - Sp ≥ 0.45 Fc =- Ps

+Ps .e .b

AC IC

-20.547842218069300 ≥ -17.1 =- Pso.0.85

+0.85Pso .e. 500

500000 41666666666.667

-20.547842218069300 ≥ -17.10 = -0.000001700000 Pso + 0.00000001020000 Pso.e

20.5478422181► e ≤

-16.65000000000 + 0.00000170000000.00000001020000 Pso

► e ≤-52.16270778193 + 0.0000017000000

0.00000001020000 Pso

► e ≤-52.16270778193

+ 166.670.00000001020000 Pso

► Pso ≤-52.16270778193

-0.0000017000000 + 0.00000001020000

≈ 1= 0 → e = 166.6667

Pso

≈ e = 0 → Pso = 30683945.75

1= 0.0000000325903327

Pso

= 0.325903327


9.06096825190112 St =Mo .b

=-1298419312.342

IC 41666666666.667

11.4868739661682 Sp =MT .b

=-1660973002.819

IC 41666666666.667

St + Sp ≤ 0.5 √Fc =- Ps

-Ps .e .b

AC IC

20.547842218069300 ≤ 3.08221 =- Pso.0.85

-0.85Pso .e. 500

500000 41666666666.667

20.547842218069300 ≤ 3.08221 = -0.00000170000 Pso - 0.00000001020000 Pso.e

-20.5478422181► e ≤

3.04138126515 + 0.0000017000000-0.0000000102000 Pso

► e ≥-32.47132651678 + 0.0000017000000

-0.0000000102000 Pso

► e ≥-32.47132651678

+ -166.67-0.0000000102000 Pso

► Pso ≥-32.47132651678

0.0000017000000 + 0.00000001020000

≈ 1= 0 → e = -166.6667

Pso

≈ e = 0 → Pso = -19100780.30

1= -0.0000000523538821

Pso

= -0.52353883 Tegangan Pada Serat Bawah (TEKAN)

9.06096825190112 St =Mo .b

=-1298419312.342

9.060968251901129.06096825190112 St =IC

=41666666666.667

11.4868739661682 Sp =MT .b

=-1660973002.819

IC 41666666666.667

St - Sp ≤ 0.45 Fc =- Ps

+Ps .e .b

AC IC

-20.547842218069300 ≤ 16.65 =- Pso.0.8

+0.8Pso .e. 500

500000 41666666666.667

-20.547842218069300 ≤ 16.65 = -0.00000160000 Pso + 0.00000000960000 Pso.e

20.5478422181► e ≤

16.65000000000 + 0.00000160000000.0000000096000 Pso

► e ≤-18.86270778193 + 0.0000016000000

0.0000000096000 Pso

► e ≤

-18.86270778193+ 166.67

0.0000000096000 Pso

► Pso ≤-18.86270778193

-0.0000016000000 + 0.00000000960000

≈ 1= 0 → e = 166.6667

Pso

≈ e = 0 → Pso = 11789192.36

1= 0.0000000848234526

Pso0.8482345262925070

Tahap akhir Tahap Awal166.6667 mm 1 e ≤ 166.7 mm

-4.930620 N 1/pso ≤ 1.408639176 N-166.6667 mm 2 e ≥ -166.7 mm

0.973340 N 1/pso ≥ 7.196916 N166.6667 mm 3 e ≤ -166.7 mm

0.4301325 N 1/pso ≤ 9.1786560 N

b1 a1

7

6b2

a35

4

a13

2b1

1

x 107 x 107

x 107 x 107

x 107 x 107

1

0500 600 -500 -400 -300 -200 -100

-1

-2

-3

-4

-5

-6

-7

-8

3.LAPANGAN LANTAIA Tahap Awal

1 Tegangan Pada Serat Atas (TARIK)-1298419312.342 500

= -15.5810317480989 St =Mo .b

41666666666.667 ICPso .e .b

- St ≤ 0.25√Fci =- Pso

IC AC

500- -15.5810317480989 ≤ 0.25√Fci =

- Pso41666666666.667 1051250

Pso.e - -15.5810317480989 ≤ 1.3829317 = -0.0000009512485

0.0000020000000 Pso + -15.5810317480989► e ≤

1.38293166859Pso

0.000002 Pso► e ≤

7.52810062653Pso

166.67 ► e ≤7.52810062653

0.0000000039362

-14.19810007950► Pso ≤

7.528100626530.000000012000 e -0.0000009512485

166.6667 mm ≈ 1=

Pso

7099050.04 ≈ e =

0.0000001408639176 N

1.40863917622824 N

2 Tegangan Pada Serat Bawah (TEKAN)-1298419312.342 500

= -15.5810317480989 St =Mo .b

41666666666.667 ICPso .e .b

+ St ≤ 0.6xFci =- Pso

IC AC

500+ -15.5810317481 ≤ 0.6xFci =

- Pso41666666666.667 1051250

Pso.e + -15.5810317480989 ≤ 18.3600 = -0.0000009512485=

0.0000020000000 Pso + -15.5810317480989► e ≥

0.00000000000Pso

0.0000020000000 Pso► e ≥

6.14516895794Pso

-166.67 ► e ≥6.14516895794

0.000000003936

x107

2.77896825190► Pso ≥

6.145168957940.000000012000 e 0.0000009512485

-166.6667 mm ≈ 1=

Pso

1389484.13 ≈ e =

0.0000007196915613 N

7.1969156129501800


= -15.5810317480989 St =Mo .b

41666666666.667 ICPso .e .b

+ St ≥ 0.6xFci =- Pso

IC AC

500+ -15.5810317481 ≥ 0.6xFci =

- Pso41666666666.667 1051250

Pso.e + -15.5810317480989 ≥ -17.7600 = -0.0000009512485=

0.0000020000000 Pso + 15.5810317480989► e ≥

-18.36000000000Pso

0.0000020000000 Pso► e ≥

-24.50516895794Pso

-166.67 ► e ≥-24.50516895794

-0.000000003936

-2.17896825190► Pso ≥

-24.505168957940.000000012000 e -0.0000009512485

-166.6667 mm ≈ 1=

Pso

1089484.13 ≈ e =

0.0000009178655991 N

9.1786560 NB Tahap Akhir

1 Tegangan Pada Serat Atas (TARIK)-1298419312.342 500

= -15.5810317480989 St =Mo .b

41666666666.667 IC-1660973002.819 500

= -19.9316760338319 Sp =MT .b

41666666666.667 IC

- St - Sp ≤ 0.45 Fc =- PsAC

+ 35.512707781930700 ≤ -16.65 =- Pso.0.851051250

+ 35.512707781930700 ≤ -16.65 = -0.000000808561 Pso

x107

0.0000017000000 Pso + -35.5127077819► e ≤

-16.65000000000Pso

0.0000017000000 Pso► e ≤

-31.11786283674Pso

166.67 ► e ≤-31.11786283674

0.00000000334577

-52.16270778193► Pso ≤

-31.11786283674e 0.0000008085612

166.6667 mm ≈ 1= 0

Pso

30683945.75 ≈ e = 0

0.0000000325903327 N

0.325903327 N


= -15.5810317480989 St =Mo .b

41666666666.667 IC-1660973002.819 500

= -19.9316760338319 Sp =MT .b

41666666666.667 IC

+ St + Sp ≤ 0.5 √Fc =- PsAC

+ -35.512707781930700 ≤ 3.04138 =- Pso.0.851051250

+ -35.512707781930700 ≤ 3.04138 = -0.00000080856 Pso

0.0000017000000 Pso - 35.5127077819► e ≥

3.04138126515Pso

0.0000017000000 Pso► e ≥

-11.42648157159Pso

-166.67 ► e ≥-11.42648157159

-0.0000000033458

-32.47132651678► Pso ≥

-11.42648157159e -0.0000008085612

-166.6667 mm ≈ 1= 0

Pso

-19100780.30 ≈ e = 0

-0.0000000523538821 N

-0.5235388 N3 Tegangan Pada Serat Bawah (TEKAN)

-1298419312.342 500= -15.5810317480989 St =

Mo .b

x107

x107

41666666666.667= -15.5810317480989 St =

IC-1660973002.819 500

= -19.9316760338319 Sp =MT .b

41666666666.667 IC

- St - Sp ≤ 0.45 Fc =- PsAC

+ 35.512707781930700 ≤ 16.65 =- Pso.0.81051250

+ 35.512707781930700 ≤ 16.65 = -0.00000076100 Pso

0.0000016000000 Pso + -35.5127077819► e ≤

16.65000000000Pso

0.0000016000000 Pso► e ≤

31.11786283674Pso

166.67

► e ≤31.11786283674

0.0000000031490

-18.86270778193► Pso ≤

31.11786283674e 0.0000007609988

166.6667 mm ≈ 1= 0

Pso

11789192.36 ≈ e = 0

0.0000000848234526 N

0.8482345262925070

Tahap akhir a). Tahap Awal1 e ≤ 166.7 mm 1 e ≤ 241.6667

1/pso ≤ 0.325903 N 1/pso ≤ -1.263596972 e ≥ -166.7 mm 2 e ≥ 241.6667

1/pso ≥ -0.523539 N 1/pso ≥ 1.5479623 e ≤ 166.7 mm 3 e ≥ -241.6667

1/pso ≤ 0.8482345 N 1/pso ≥ 0.3881828

a2

x 107

x 107

x 107

100 200 300 400 500 600 -500

b2

4.TUMPUAN LANTAIA

Tegangan Pada Serat Atas (TARIK)Mo .b

=1561192976.199 725

= 6.14516895793793IC 184187760416.667

- Pso+

Pso .e .b- St ≤ 0.25√Fci

AC IC

- Pso+

Pso .e. 725- 6.14516895793793 ≤ 0.25√Fci

1051250 184187760416.667

Pso + 0.000000003936 Pso.e - 6.14516895793793 ≤ 1.3829317

1.38293166859 + 0.0000009512485 Pso + 6.145168957937930.000000003936 Pso

7.52810062653 + 0.000001 Pso0.000000003936 Pso

7.52810062653+ 241.67

0.0000000039362 Pso

7.52810062653-0.0000009512485 + 0.000000003936 e

0 → e = 241.6667 mm

0 → Pso = -7913915.78

1= -0.0000001263596969 N

Pso

= -1.26359696936255 N

Tegangan Pada Serat Bawah (TEKAN)Mo .b

=1561192976.199 725

= 6.14516895793793IC 184187760416.667

- Pso-

Pso .e .b+ St ≤ 0.6xFci

AC IC

- Pso-

Pso .e. 725+ 6.1451689579 ≤ 0.6xFci

1051250 184187760416.667

Pso - 0.000000003936 Pso.e + 6.14516895793793≤

0.0000

0.00000000000 + 0.0000009512485 Pso + 6.145168957937930.000000003936 Pso

6.14516895794 + 0.0000009512485 Pso0.000000003936 Pso

6.14516895794+ 241.67

0.000000003936 Pso

x107

6.145168957940.0000009512485 + 0.000000003936 e

0 → e = 241.6667 mm

0 → Pso = 6460108.87

1= 0.0000001547961529 N

Pso1.5479615291056200


=1561192976.199 725

= 6.14516895793793IC 184187760416.667

- Pso-

Pso .e .b+ St ≥ 0.6xFci

AC IC

- Pso-

Pso .e. 725+ 6.1451689579 ≥ 0.6xFci

1051250 184187760416.667

Pso - 0.000000003936 Pso.e + 6.14516895793793 ≥ -18.3600

-18.36000000000 + 0.0000009512485 Pso + -6.14516895793793-0.000000003936 Pso

-24.50516895794 + 0.0000009512485 Pso-0.000000003936 Pso

-24.50516895794+ -241.67

-0.000000003936 Pso

-24.50516895794-0.0000009512485 + 0.000000003936 e

0 → e = -241.6667 mm

0 → Pso = 25761058.87

1= 0.0000000388182801 N

Pso= 0.388182801 N

BTegangan Pada Serat Atas (TARIK)

Mo .b=

1561192976.199 725= 6.14516895793793

IC 184187760416.667MT .b

=2114397718.856 725

= 8.32269387880566IC 184187760416.667

+Ps .e .b

- St - Sp ≥ 0.45 FcIC

+0.85Pso .e. 725

+ -14.467862836743600 ≥ -16.65184187760416.667

+ 0.00000000334577 Pso.e + -14.467862836743600 ≥ -16.65

x107

-16.65000000000 + 0.0000008085612 Pso + -14.46786283670.00000000334577 Pso

-31.11786283674 + 0.0000008085612 Pso0.00000000334577 Pso

-31.11786283674+ 241.67

0.00000000334577 Pso

-31.117862836740.0000008085612 + 0.00000000334577 e

→ e = 241.6667 mm

→ Pso = -38485474.48

1= -0.0000000259838293 N

Pso

= -0.259838293 N


=1561192976.199 725

= 6.14516895793793IC 184187760416.667

MT .b=

2114397718.856 725= 8.32269387880566

IC 184187760416.667

-Ps .e .b

+ St + Sp ≤ 0.5 √FcIC

-0.85Pso .e. 725

+ 14.467862836743600 ≤ 3.04138184187760416.667

- 0.00000000334577 Pso.e + 14.467862836743600 ≤ 3.04138

3.04138126515 + 0.0000008085612 Pso + -14.4678628367-0.0000000033458 Pso

-11.42648157159 + 0.0000008085612 Pso-0.0000000033458 Pso

-11.42648157159+ -241.67

-0.0000000033458 Pso

-11.42648157159-0.0000008085612 + 0.00000000334577 e

→ e = -241.6667 mm

→ Pso = 14131869.12

1= 0.0000000707620479 N

Pso

= 0.70762048 NTegangan Pada Serat Bawah (TEKAN)

Mo .b=

1561192976.199 725= 6.14516895793793

x107

x107

IC=

184187760416.667= 6.14516895793793

MT .b=

2114397718.856 725= 8.32269387880566

IC 184187760416.667

+Ps .e .b

- St - Sp ≤ 0.45 FcIC

+0.8Pso .e. 725

+ -14.467862836743600 ≤ 16.65184187760416.667

+ 0.00000000314896 Pso.e + -14.467862836743600 ≤ 16.65

16.65000000000 + 0.0000007609988 Pso + 14.46786283670.0000000031490 Pso

31.11786283674 + 0.0000007609988 Pso0.0000000031490 Pso

31.11786283674+ 241.67

0.0000000031490 Pso

31.117862836740.0000007609988 + 0.00000000314896 e

→ e = 241.6667 mm

→ Pso = 40890816.63

1= 0.0000000244553688 N

Pso0.2445536876783130

Tahap Awal b). Tahap akhir241.6667 mm 1 e ≤ 241.6667 mm

-1.26359697 N 1/pso ≤ -0.259838 N241.6667 mm 2 e ≥ -241.6667 mm

1.547962 N 1/pso ≥ 0.707620 N-241.6667 mm 3 e ≤ 241.6667 mm

0.3881828 N 1/pso ≤ 0.2445537 N

a1

7

6

5a2

4

3b2

2b1

1

x 107 x 107

x 107 x 107

x 107 x 107

1

0-400 -300 -200 -100 100 200 300 400 500 600

-1

-2

-3

-4

-5

-6

-7

-8

4.TUMPUAN LANTAITahap Awal


St =Mo .b

=-2756290773.801 725

= -10.8493138006828IC 184187760416.667

=- Pso

+Pso .e .b

- StAC IC

=- Pso

+Pso .e. 725

- -10.84931380068281051250 184187760416.667

= -0.0000009512485 Pso + 0.000000003936 Pso.e - -10.8493138006828

► e ≤1.38293166859 + 0.0000009512485 Pso +

0.000000003936 Pso

► e ≤-9.46638213209 + 0.000001 Pso

0.000000003936 Pso

► e ≤-9.46638213209

+ 241.670.0000000039362 Pso

► Pso ≤-9.46638213209

-0.0000009512485 + 0.000000003936 e

≈ 1= 0 → e = 241.6667 mm

Pso

≈ e = 0 → Pso = 9951534.22

1= 0.0000001004870182 N

Pso

= 1.00487018208328 N


St =Mo .b

=-2756290773.801 725

= -10.8493138006828IC 184187760416.667

=- Pso

-Pso .e .b

+ StAC IC

=- Pso

-Pso .e. 725

+ -10.84931380071051250 184187760416.667

= -0.0000009512485 Pso - 0.000000003936 Pso.e + -10.8493138006828=

► e ≥0.00000000000 + 0.0000009512485 Pso +

-0.000000003936 Pso

► e ≥-10.84931380068 + 0.0000009512485 Pso

-0.000000003936 Pso

► e ≥-10.84931380068

+ -241.67-0.000000003936 Pso

x107

► Pso ≥-10.84931380068

0.0000009512485 + 0.000000003936 e

≈ 1= 0 → e = -241.6667 mm

Pso

≈ e = 0 → Pso = -11405341.13

1= -0.0000000876782192 N

Pso-0.8767821920814330


St =Mo .b

=-2756290773.801 725

= -10.8493138006828IC 184187760416.667

=- Pso

-Pso .e .b

+ StAC IC

=- Pso

-Pso .e. 725

+ -10.84931380071051250 184187760416.667

= -0.0000009512485 Pso - 0.000000003936 Pso.e + -10.8493138006828=

► e ≥-17.76000000000 + 0.0000009512485 Pso +

-0.000000003936 Pso

► e ≥-6.91068619932 + 0.0000009512485 Pso

-0.000000003936 Pso

► e ≥-6.91068619932

+ -241.67-0.000000003936 Pso

► Pso ≥-6.91068619932

-0.0000009512485 + 0.000000003936 e

≈ 1= 0 → e = -241.6667 mm

Pso

≈ e = 0 → Pso = 7264858.87

1= 0.0000001376489232 N

Pso= 1.37648923166 N

Tahap Akhir1 Tegangan Pada Serat Atas (TARIK)

St =Mo .b

=-2756290773.801 725

= -10.8493138006828IC 184187760416.667

Sp =MT .b

=-3725756281.144 725

= -14.6653246541395IC 184187760416.667

=- Ps

+Ps .e .b

- St - SpAC IC

=- Pso.0.8

+0.8Pso .e. 725

+ 25.5146384548223001051250 184187760416.667

= -0.000000760999 Pso + 0.00000000314896 Pso.e + 25.514638454822300

x107

► e ≤-16.65000000000 + 0.0000007609988 Pso + -25.5146384548

0.00000000314896 Pso

► e ≤-42.16463845482 + 0.0000007609988 Pso

0.00000000314896 Pso

► e ≤-42.16463845482

+ 241.670.00000000314896 Pso

► Pso ≤-42.16463845482

-0.0000007609988 + 0.00000000314896 e

≈ 1= 0 → e = 241.6667 mm

Pso

≈ e = 0 → Pso = 55406970.22

1= 0.0000000180482708 N

Pso

= 0.180482708 N


St =Mo .b

=-2756290773.801 725

= -10.8493138006828IC 184187760416.667

Sp =MT .b

=-3725756281.144 725

= -14.6653246541395IC 184187760416.667

=- Ps

-Ps .e .b

+ St + SpAC IC

=- Pso.0.8

-0.8Pso .e. 725

+ -25.5146384548223001051250 184187760416.667

= -0.00000076100 Pso - 0.00000000314896 Pso.e + -25.514638454822300

► e ≤3.04138126515 + 0.0000007609988 Pso - 25.5146384548

-0.0000000031490 Pso

► e ≥-22.47325718967 + 0.0000007609988 Pso

-0.0000000031490 Pso

► e ≥-22.47325718967

+ -241.67-0.0000000031490 Pso

► Pso ≥-22.47325718967

0.0000007609988 + 0.00000000314896 e

≈ 1= 0 → e = -241.6667 mm

Pso

≈ e = 0 → Pso = -29531264.53

1= -0.0000000338624172 N

Pso

= -0.338624172 N3 Tegangan Pada Serat Bawah (TEKAN)

St =Mo .b

=-2756290773.801 725

= -10.8493138006828

x107

x107

St =IC

=184187760416.667

= -10.8493138006828

Sp =MT .b

=-3725756281.144 725

= -14.6653246541395IC 184187760416.667

=- Ps

+Ps .e .b

- St - SpAC IC

=- Pso.0.8

+0.8Pso .e. 725

+ 25.5146384548223001051250 184187760416.667

= -0.00000076100 Pso + 0.00000000314896 Pso.e + 25.514638454822300

► e ≤16.65000000000 + 0.0000007609988 Pso + -25.5146384548

0.0000000031490 Pso

► e ≤-8.86463845482 + 0.0000007609988 Pso

0.0000000031490 Pso

► e ≤-8.86463845482

+ 241.670.0000000031490 Pso

► Pso ≤-8.86463845482

-0.0000007609988 + 0.00000000314896 e

≈ 1= 0 → e = 241.6667 mm

Pso

≈ e = 0 → Pso = 11648688.97

1= 0.0000000858465706 N

Pso0.8584657059819310

Tahap Awal Tahap akhir1 e ≤ 241.7 mm 1 e ≤ 241.7

1/pso ≤ 1.004870182 N 1/pso ≤ 0.1804832 e ≥ -241.7 mm 2 e ≥ -241.7

1/pso ≥ -0.876782 N 1/pso ≥ -0.3386243 e ≤ -241.7 mm 3 e ≤ 241.7

1/pso ≤ 1.3764892 N 1/pso ≤ 0.8584657

a2

7

6

a15

4

3

2b2

1

x 107

x 107

x 107

1

0-500 -400 -300 -200 -100 100 200 300 400 500

-1

-2

-3

-4

-5

-6

-7

-8


NO BAGIAN DAERAH PERSMN NILAI Pso1

ATAP

LAPANGAN

a1 -5221949.962 a2 13170484.13

-10.84931380068283 b1 -2028142.484 b2 10273903.07

St ≤ 0.25√Fci5

TUMPUAN

a1 7099050.046 a2 1089484.137 b1 30683945.75

-10.8493138006828 ≤ 0.25√Fci8 b2 -19100780.30398929

LANTAI

LAPANGAN

a1 -7913915.7810 a2 25761058.87

-10.8493138006828 ≤ 1.3829317 11 b1 -38485474.4812 b2 14131869.12

-10.8493138006828 13

TUMPUAN

a1 9951534.2214 a2 7264858.8715 b1 55406970.2216 b2 -29531264.53

-10.8493138006828

St ≤ 0.6xFci

-10.8493138007 ≤ 0.6xFci

-10.8493138006828 ≤ 0.0000

-10.8493138006828

-10.8493138006828

St ≥ 0.6xFci

-10.8493138007 ≥ 0.6xFci

-10.8493138006828 ≥ -17.7600

10.8493138006828

-10.8493138006828

-14.6653246541395

≤ 0.45 Fc

≤ -16.65

≤ -16.65

-25.5146384548

-10.8493138006828

-14.6653246541395

≤ 0.5 √Fc

≤ 3.04138

≤ 3.04138

25.5146384548

-10.8493138006828

-10.8493138006828

-14.6653246541395

≤ 0.45 Fc

≤ 16.65

≤ 16.65

-25.5146384548

Tahap akhir241.7 mm

0.180483 N-241.7 mm

-0.338624 N241.7 mm

0.8584657 N

x 107

x 107

x 107

600b1


NILAI Pso Pso DIPAKAI UNIT e UNIT-5221949.96

7099050.04

N 250

mm13170484.13 mm-2028142.48 mm10273903.07 mm7099050.04

N -275

mm1089484.13 mm

30683945.75 mm-19100780.3039892 mm

-7913915.78

9951534.22

N 225

mm25761058.87 mm-38485474.48 mm14131869.12 mm9951534.22

N -325

mm7264858.87 mm

55406970.22 mm-29531264.53 mm

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