apakah struktur gelagar dibawah ini sst tau...

Apakah Struktur Gelagar dibawah ini SST tau SSTT??



Struktur Gelagar GERBER

Penemu Struktur Gerber : JGH.Gerber

Merupakan Struktur gelagar yang terdiri dari Gelagar anak dan Gelagar Induk.

Dimana, Salah satu/kedua tumpuan Gelagar anak menumpu pada Gelagar Induk.

Reaksi tumpuan pada salah satu tumpuan Gelagar anak akan diteruskan

Ke Gelagar induk sebagai beban Terpusat luar.

* SATU sendi dengan TIGA tumpuan.

* DUA sendi dengan EMPAT tumpuan.

Contoh Pengujian Gelagar Gerber

STRUKTUR BALOK GERBER

** Balok : S - C.

MC = 0 RS. 5 - P2. 2,5 = 0 RS = 0,5 P2

MS = 0 RC. 5 - P2. 2,5 = 0 RC = 0,5 P2

V = 0 RS + RC = P2 0,5 P2 + 0,5 P2 = P2

P2 = P2 ok

ME = 2,5 RS

MB = 0

RA. 5 + RS. 1,5 - P1. 2,5 = 0

5 RA + 0,5 P2. 1,5 - 2,5 P1 = 0

5 RA + 0,75 P2 - 2,5 P1 = 0

RA = 0,5 P1 - 0,15 P2

MA = 0

RB. 5 - RS. 6,5 - P1. 2,5 = 0

5 RB - 0,5 P2. 6,5 - 2,5 P1 = 0

5 RB - 3,25 P2 - 2,5 P1 = 0

RB = 0,5 P1 + 0,65 P2

RBA = RB - RS

= 0,5 P1 + 0,65 P2 - 0,5 P2

= 0,5 P1 + 0,15 P2

RBS = RS = 0,5 P2

MD = RA. 2,5 = (0,5 P1 - 0,15 P2) 2,5 = 1,25 P1 - 0,375 P2

MB = RS. 1,5

= 0,5 P2. 1,5

= 0,75 P2

46) Gambar bidang momen dan gaya lintang. P1 = 400 kg, P2 = 500 kg

RS = RC = 0,5 P2

= 0,5. 500

= 250 kg

Balok : S – C

ME = RC. 2

= 250. 2

= 500 kgm

Balok : A – B – S.

MB = 0

RA. 4 + RS. 2 - P1. 2 = 0

4 RA + 250. 2 - 400. 2 = 0

4 RA + 500 - 800 = 0

4 RA = 300

RA = 75 kg

MA = 0

RB. 4 - RS. 6 - P1. 2 = 0

4 RB - 250. 6 - 400. 2 = 0

4 RB - 1500 - 800 = 0

4 RB - 2300 = 0

RB = 575 kg

RBS = RS

= 250 kg

V = 0

RA + RB = P1 + RS

75 + 575 = 400 + 250

650 = 650 ok

RBA = RB - RBS = 575 - 250 = 325 kg

MB = RS. 2 = 250. 2 = 500 kgm

MD = RA. 2 = 75. 2 = 150 kgm

BIDANG GESER

BIDANG MOMEN

47) Gambar bidang momen dan gaya lintang. P = 500 kg, W = 2000 kg/m

Balok : S – C

RS = RC = 0,5 P

= 0,5. 500

= 250 kg

MD = RC. 2 = 250. 2 = 500 kgm

Balok : A – B – S.

MB = 0

RA. 4 + RS. 2 + W. 2. 1 - W. 4. 2 = 0

4 RA + 250. 2 + 2000. 2 - 2000. 8 = 0

4 RA + 500 + 4000 - 16000 = 0

4 RA - 11500 = 0

RA = 2875 kg

MA = 0

RB. 4 - RS. 6 - W. 4. 2 - W. 2. 5 = 0

4 RB - 250. 6 - 2000. 8 - 2000. 10 = 0

4 RB - 1500 - 16000 - 20000 = 0

4 RB - 37500 = 0

RB = 9375 kg

V = 0

RA + RB = Q + RS

2875 + 9375 = 2000. 6 + 250

2250 = 12250 ok

RBS = RS + Q = 250 + 2000. 2 = 4250 kg

RBA = RB - RBS = 9375 - 4250 = 5125 kg

MX = RA. X - 0,5 W. X2

= 2875 X - 0,5. 2000 X2

X20002875dX

dMX

0dX

dMX

2000 X = 2875 X = 1,44 m

M maks = 2875. 1,44 - 1000. 1,442

= 4140 - 2074

= 2066 kgm

MB = RS. 2 + W. 2. 1 = 250. 2 + 2000. 2 = 500 + 4000 = 4500 kgm

BIDANG GESER

BIDANG MOMEN


Balok : S – C.

RS = RC = 0,5 P + 0,5 W. 4

= 0,5. 2000 + 0,5. 2500. 4

= 1000 + 5000

= 6000 kg

ME = RC. 2 - W. 2. 1 = 6000. 2 - 2500. 2 = 12000 - 5000 = 7000 kgm

Balok : A – B – S

MB = 0

RA. 6 + RS. 2 + W. 2. 1 - W. 6. 3 - P. 3 = 0

6 RA + 6000. 2 + 2500. 2 - 2500. 18 - 2000. 3 = 0

6 RA + 12000 + 5000 - 45000 - 6000 = 0

6 RA - 34000 = 0

RA = 5667 kg

MA = 0

RB. 6 - RS. 8 - W. 6. 3 - W. 2. 7 - P. 3 = 0

6 RB - 6000. 8 - 2500. 18 - 2500. 14 - 2000. 3 = 0

6 RB - 48000 - 45000 - 35000 - 6000 = 0

6 RB - 134000 = 0

RB = 22333 kg

V = 0

RA + RB = Q + RS + P

5667 + 22333 = 2500. 8 + 6000 + 2000

28000 = 28000 ok

RBS = RS + Q

= 6000 + 2500. 2

= 11000 kg

RBA = RB - RBS

= 22333 - 11000

= 11333 kg

MX = RA. X - 0,5 W. X2 = 5667 X - 0,5. 2500 X2

X25005667dX

dMX

0dX

dMX

2500 X = 5667 X = 2,27 m

M maks = 5667. 2,27 - 1250. 2,272 = 12864 - 6441 = 6423 kgm

MB = RS. 2 + W. 2. 1 = 6000. 2 + 2500. 2 = 12000 + 5000 = 17000 kgm

MD = RA. 3 - W. 3. 4,5 = 5667.3 - 2500. 4,5 = 17001 - 11250 = 5751 kgm

BIDANG GESER

BIDANG MOMEN

49) Gambar bidang momen dan gaya lintang. P1 = 600 kg, P2 = 1000 kg, P3 = 800 kg

S1

Balok : A – S1

RA = RS1 = 0,5 P1 = 0,5. 600 = 300 kg

ME = RA. 1,5 = 300. 1,5 = 450 kgm

Balok : S2 – D

MD = 0

RS2. 3 - P3. 2 = 0

3 RS2 - 800. 2 = 0

RS2 = 533 kg

MS2 = 0

RD. 3 - P3. 1 = 0

3 RD - 800. 1 = 0

3 RD - 800 = 0

RD = 267 kg

V = 0 RS2 + RD = P3 533 + 267 = 800 800 = 800 ok

MG = RD. 2 = 267. 2 = 534 kgm

Balok : S1 – B – C – S2

MC = 0

RB. 5 + RS2. 1 - RS1. 6 - P2. 3 = 0

5 RB + 533. 1 - 300. 6 - 1000. 3 = 0

5 RB + 533 - 1800 - 3000 = 0

5 RB - 4267 = 0

RB = 853 kg

MB = 0

RC. 5 + RS1. 1 - P2. 2 - RS2. 6 = 0

5 RC + 300. 1 - 1000. 2 - 533. 6 = 0

5 RC + 300 - 2000 - 3198 = 0

5 RC - 4898 = 0

RC = 980 kg

V = 0 RB + RC = RS1 + P2 + RS2 853 + 980 = 300 + 1000 + 533 1833 = 1833 ok

RBS1 = RS1

= 300 kg

RBC = RB - RBS1

= 853 - 300

= 553 kg

RCS2 = RS2

= 533 kg

RCB = RC - RCS2

= 980 - 533

= 447 kg

MB = RS1. 1

= 300. 1

= 300 kgm

MC = RS2. 1

= 533. 1

= 533 kgm

MF = RB. 2 - RS1. 3 = 853. 2 - 300. 3 = 1706 - 900 = 806 kgm

BIDANG GESER

BIDANG MOMEN

50) Gambar bidang momen dan gaya lintang. W1 = 1500 kg/m, W2 = 1800 kg/m, W3 = 2200 kg/m

Balok : A – S1

RA = RS1 = 0,5 W1. 3

= 0,5. 1500. 3

= 2250 kg

M maks = 1/8 W1. 32 = 1/8. 1500. 9 = 1688 kgm

Balok : S2 – D

RS2 = RD = 0,5 W2. 4

= 0,5. 1800. 4

= 3600 kg

M maks = 1/8 W2. 42

= 1/8. 1800. 16

= 3600 kgm

Balok : S1 – B – C – S2

MC = 0

RB. 5 + RS2. 1 + W2. 1. 0,5 - RS1. 6 - W1. 1. 5,5 - W3. 5. 2,5 = 0

5 RB + 3600. 1 + 1800. 0,5 - 2250. 6 - 1500. 5,5 - 2200. 12,5 = 0

5 RB + 3600 + 900 - 13500 - 8250 - 27500 = 0

5 RB – 44750 = 0

RB = 8950 kg

MB = 0

RC. 5 + RS1. 1 + W1. 1. 0,5 - RS2. 6 - W2. 1. 5,5 - W3. 5. 2,5 = 0

5 RC + 2250. 1 + 1500. 0,5 - 3600. 6 - 1800. 5,5 - 2200. 12,5 = 0

5 RC + 2250 + 750 - 21600 - 9900 - 27500 = 0

5 RC - 56000 = 0

RC = 11200 kg

RBS1 = RS1 + Q = 2250 + 1500. 1 = 3750 kg

RBC = RB - RBS1

= 8950 - 3750

= 5200 kg

RCS2 = RS2 + Q = 3600 + 1800. 1 = 5400 kg

RCB = RC - RCS2

= 11200 - 5400

= 5800 kg

V = 0

RB + RC = RS1 + RS2 + W1. 1 + W2. 1 + W3. 5

8950 + 11200 = 2250 + 3600 + 1500. 1 + 1800. 1 + 2200. 5

20150 = 20150 ok

MX = RB. X - RS1 (1 + X) - W1. 1 (0,5 + X) - 0,5 W3. X2

= 8950 X - 2250 (1 + X) - 1500 (0,5 + X) - 0,5. 2200 X2

= 8950 X - 2250 - 2250 X - 750 - 1500 X - 1100 X2

= 5200 X - 3000 - 1100 X2

x20005200dX

dMX

0dX

dMX

2200 X = 5200 X = 2,36 m

M maks = 5200. 2,36 - 3000 - 1100. 2,362 = 12272 - 3000 - 6127 = 3145 kgm

MB = RS1. 1 + W1. 1. 0,5 = 2250. 1 + 1500. 0,5 = 2250 + 750 = 3000 kgm

MC = RS2. 1 + W2. 1. 0,5 = 3600. 1 + 1800. 0,5 = 3600 + 900 = 4500 kgm

BIDANG GESER

BIDANG MOMEN

51) Gambar bidang momen dan gaya lintang. P1 = 500 kg, P2 = 800 kg, W1 = 1500 kg/m, W2 = 1800 kg/m, W3 = 2200 kg/m

Balok : A – S1

MS1 = 0 RA 3 - P1. 1 - W2. 3. 1,5 = 0 3 RA - 500. 1 - 2000. 4,5 = 0 3 RA - 1500 - 9000 = 0 3 RA - 10500 = 0 RA = 3167 kg

MA = 0 RS1 - P1. 2 - W2. 3. 1,5 = 0 3 RS1 - 500. 1 - 2000. 4,5 = 0 3 RS1 - 500 - 9000 = 0 3 RS1 - 9400 = 0 RS1 = 3333 kg

V = 0

RA + RS1 = P1 + Q

3167 + 3333 = 500 + 2000. 3

6500 = 6500 ok MX = RA. X - W2. X. 0,5 X

= 3167 X - 0,5. 2000 X2

x20003167dX

dMX

0dX

dMX

2000 X = 3167 X = 1,58 m

M maks = 3167. 1,58 - 1000. 1,582

= 5004 - 2496

= 2508 kgm

ME = RS1. 1 - W2. 1. 0,5

= 3333. 1 - 2000. 0,5

= 3333 - 1000

= 2333 kgm

Balok : S2 – D

MD = 0

RS2 3 - P1. 2 - W1. 3. 1,5 = 0

3 RS2 - 500. 2 - 1800. 4,5 = 0

3 RS2 - 1000 - 8100 = 0

3 RS2 - 9100 = 0

RS2 = 3033 kg

MS2 = 0

RD. 3 - P1. 1 - W1. 3. 1,5 = 0

3 RD - 500. 1 - 1800. 4,5 = 0

3 RD - 500 - 8100 = 0

3 RD - 8600 = 0

RD = 2867 kg

V = 0 RS2 + RD = P1 + Q 3033 + 2867 = 500 + 1800. 3 5900 = 5900 ok

MX = RD. X - W1. X. 0,5 X = 2867 X - 0,5. 1800 X2

x18002867dX

dMX

0dX

dMX

1800 X = 2867 X = 1,59 m

M maks = 2867. 1,59 - 900. 1,582

= 5004 - 2496

= 2283 kgm

MG = RS2. 1 - W1. 1. 0,5

= 3033. 1 - 1800. 0,5

= 3033 - 900

= 2133 kgm

Balok : S1 – B – C – S2

MC = 0

RB. 4 + RS2. 1 + W3. 1. 0,5 - S1. 5 - W3. 1. 4,5 - W3. 4. 2 - P2. 2 = 0

4 RB + 3033. 1 + 2200. 0,5 - 3333. 5 - 2200. 4,5 - 2200. 8 - 800. 2 = 0

4 RB + 3033 + 1100 - 16665 - 9900 - 17600 - 1600 = 0

4 RB - 41632 = 0

RB = 10408 kg

MB= 0

RC. 4 + RS1. 1 + W3. 1. 0,5 - RS2. 5 - W3. 1. 4,5 - W3. 4. 2 - P2. 2 = 0

4 RC + 3333. 1 + 2200. 0,5 - 3033. 5 - 2200. 4,5 - 2200. 8 - 800. 2 = 0

4 RC + 3333 + 1100 - 15165 - 9900 - 17600 - 1600 = 0

4 RC - 39832 = 0

RC = 9958 kg

V = 0

RB + RC = RS1 + RS2 + P2 + Q

10408 + 9958 = 3333 + 3033 + 800 + 2200. 6

20366 = 20366 ok

RBS1 = RS1 + Q = 3333 + 2200 .1 = 5533 kg

RCS2 = RS2 + Q = 3033 + 2200. 1 = 5233 kg

RBC = RB - RBS1 = 10408 - 5533 = 4875 kg

RCB = RC - RCS2 = 9958 - 5233 = 4725 kg

MX = RC. X - RS2 (1 + X) - W3. 1 (0,5 + X) - W3. X. 0,5 X

= 9958 X - 3033 (1 + X) - 2200 (0,5 + X) - 0,5. 2200 X2

= 9958 X - 3033 - 3033 X - 1100 - 2200 X - 1100 X2

= 4725 X - 4133 - 1100 X2

x22004725dX

dMX

0dX

dMX

2200 X = 4725 X = 2,15 m > 2 m tidak mungkin

MX = RB. X - RS1 (1 + X) - W3. 1 (0,5 + X) - W3. X. 0,5 X

= 10408 X - 3333 (1 + X) - 2200 (0,5 + X) - 0,5. 2200 X2

= 10408 X - 3333 - 3333 X - 1100 - 2200 X - 1100 X2

= 4875 X - 4433 - 1100 X2

x22004875dX

dMX

0dX

dMX

2200 X = 4875

X = 2,22 m > 2 m

M maks = MF = RB. 2 - RS1. 3 - W3. 1. 2,5 - W3. 2. 1

= 10408. 2 - 3333. 3 - 2200. 2,5 - 2200. 2

= 20816 - 9999 - 5500 - 4400

= 917 kgm

MB = RS1. 1 + W3. 1. 0,5 = 3333. 1 + 2200. 0,5 = 3333 + 1100 = 4433 kgm

MC = RS2. 1 + W3. 1. 0,5

= 3033. 1 + 2200. 0,5

= 3033 + 1100

= 4133 kgm

tidak mungkin

BIDANG GESER

BIDANG MOMEN

52) Gambar bidang momen dan gaya lintang. P1 = 1000 kg, P2 = 1250 kg, P3 = 1500 kg

RS1 = RS2 = 0,5. P2

= 0,5. 1250

= 625 kg

MF = RS1. 2

= 625. 2

= 1250 kgm

Balok : S1 – S2.

Balok : A – B - S1 MB = 0

RA. 4 + RS1. 1 - P1. 3 = 0

4 RA + 625. 1 - 1000. 3 = 0

4 RA + 625 - 3000 = 0

4 RA - 2375 = 0

RA = 594 kg

MA = 0

RB. 4 - RS1. 5 - P1. 1 = 0

4 RB - 625. 5 - 1000. 1 = 0

4 RB - 3125 - 1000 = 0

4 RB - 4125 = 0

RB = 1031 kg

V = 0

RA + RB = P1 + RS1

594 + 1031 = 1000 + 625

1625 = 1625 ok

RBS1 = RS1

= 625 kg

RBA = RB - RBS1

= 1031 - 625

= 406 kg

MB = RS1. 1

= 625. 1

= 625 kgm

ME = RA. 1

= 594. 1

= 594 kgm

Balok : S2 – C - D

MD = 0

RC. 4 - RS2. 5 - P3. 3 = 0

4 RC - 625. 5 - 1500. 3 = 0

4 RC - 3125 - 4500 = 0

4 RC - 7625 = 0

RC = 1906 kg

MC = 0

RD. 4 + RS2. 1 - P3. 1 = 0

4 RD + 625. 1 - 1500. 1 = 0

4 RD + 625 - 1500 = 0

4 RD - 875 = 0

RD = 219 kg

V = 0 RC + RD = RS2 + P3 1906 + 219 = 625 + 1500 2125 = 2125 ok

RCS2 = RS2 = 625 kg

RCD = RC – RCS2 = 1906 – 625 = 1281 kg

MC = RS2. 1

= 625. 1

= 625 kgm

MG = RD. 3

= 219. 3

= 657 kgm

BIDANG GESER

BIDANG MOMEN

53) Gambar bidang momen dan gaya lintang. W1 = 1500 kg/m, W2 = 1800 kg/m, W3 = 2100 kg/m

Balok : S1 – S2

1800

RS1 = RS2 = 0,5. W2. 4

= 0,5. 1800. 4

= 3600 kg

M maks = 1/8. W. 42

= 1/8. 1800. 16

= 3600 kgm

Balok : A – B -S1 MB = 0

RA. 4 + RS1. 1 + W1. 1. 0,5 - W1. 4. 2 = 0

4 RA + 3600. 1 + 1500. 0,5 - 1500. 8 = 0

4 RA + 3600 + 750 - 12000 = 0

4 RA - 7650 = 0

RA = 1913 kg

MA = 0

RB. 4 - RS1. 5 - W1. 4. 2 - W1. 1. 4,5 = 0

4 RB - 3600. 5 - 1500. 8 - 1500. 4,5 = 0

4 RB - 18000 - 12000 - 6750 = 0

4 RB - 36750 = 0

RB = 9187 kg

V = 0 RA + RB = RS1 + W1. 5 1913 + 9187 = 3600 + 1500. 5 11100 = 11100 ok

RBS1 = RS1 + Q = 3600 + 1500. 1 = 5100 kg

RBA = RB - RBS1

= 9187 - 5100

= 4087 kg

Balok : A – B -S1 V = 0 RA + RB = RS1 + W1. 5 1913 + 9187 = 3600 + 1500. 5 11100 = 11100 ok

RBS1 = RS1 + Q = 3600 + 1500. 1 = 5100 kg

RBA = RB - RBS1

= 9187 - 5100

= 4087 kg

MX = RA. X - 0,5 W1. X2 = 1913 X - 0,5. 1500 X2

X15001913dX

dMX

0dX

dMX

1500 X = 1913

X = 1,28 m

M maks = 1913. 1,28 - 750. 1,282

= 2449 - 1229

= 1220 kgm

MB = RS1. 1

= 3600. 1

= 3600 kgm

Balok : S2 – C – D

MD = 0

RC. 4 - RS2. 5 - W3. 1. 4,5 - W3. 4. 2 = 0

4 RC - 3600. 5 - 2100. 4,5 - 2100. 8 = 0

4 RC - 18000 - 9450 - 16800 = 0

4 RC - 44250 = 0

RC = 11063 kg

MC = 0

RD. 4 + RS2. 1 + W3. 1. 0,5 - W3. 4. 2 = 0

4 RD + 3600. 1 + 2100. 0,5 - 2100. 8 = 0

4 RD + 3600 + 1050 - 16800 = 0

4 RD - 12150 = 0

RD = 3037 kg

V = 0

RC + RD = RS2 + W3. 5

11063 + 3037 = 3600 + 2100, 5

14100 = 14100 ok

RCS2 = RS2 + Q = 3600 + 2100. 1 = 5700 kg

RCD = RC - RCS2 = 11063 - 5700 = 5363 kg


RCS2 = RS2 + Q = 3600 + 2100. 1 = 5700 kg

RCD = RC - RCS2 = 11063 - 5700 = 5363 kg

X21003037dX

dMX

0dX

dMX

MX = RD. X - 0,5 W3. X2

= 3037 X - 0,5. 2100 X2

2100 X = 3037

X = 1,45 m

M maks = 3037. 1,45 - 1050. 1,452

= 4404 - 2208

= 2196 kgm

MC = RS2. 1 + W3. 1. 0,5

= 3600. 1 + 0,5. 2100

= 3600 + 1050

= 4650 kgm

BIDANG MOMEN

Balok : S1 – S2 MS2 = 0

RS1. 4 - W. 1,5. 3,25 - P. 1 = 0

4 RS1 - 1800. 4,875 - 1500. 1 = 0

4 RS1 - 8775 - 1500 = 0

4 RS1 - 10275 = 0

RS1 = 2569 kg

MS1 = 0

RS2. 4 - W. 1,5. 0,75 - P. 3 = 0

4 RS2 - 1800. 1,125 - 1500. 3 = 0

4 RS2 - 2025 - 4500 = 0

4 RS1 - 6525 = 0

RS2 = 1631 kg

V = 0

RS1 + RS2 = Q + P

2569 + 1631 = 1800. 1,5 + 1500

4200 = 4200 ok

MX = RS1. X - 0,5 W. X2

= 2569 X - 0,5. 1800 X2

X18002569dX

dMX

0dX

dMX

1800 X = 2569

X = 1,43 m

M maks = 2569. 1,43 - 900. 1,432

= 3674 - 1840

= 1833 kgm

MF = RS1. 1,5 - 0,5 W. 1,52

= 2569. 1,5 - 0,5. 1800. 2,25

= 3854 - 2025

= 1829 kgm

MG = RS2. 1

= 1631. 1

= 1631 kgm

Balok : A – B – S1

MB = 0

RA. 4 + RS1. 1 + W. 1. 0,5 - W. 2. 3 = 0

4 RA + 2569. 1 + 1800. 0,5 - 1800. 6 = 0

4 RA + 2569 + 900 - 10800 = 0

4 RA - 7331 = 0

RA = 1833 kg

MA = 0

RB. 4 - RS1. 5 - W. 1. 4,5 - W. 2. 1 = 0

4 RB - 2569. 5 - 1800. 4,5 - 1800. 2 = 0

4 RB - 12845 - 8100 - 3600 = 0

4 RB - 24545 = 0

RB = 6136 kg

V = 0

RA + RB = RS1 + Q1 + Q2

1833 + 6136 = 2569 + 1800. 1 + 1800. 2

7969 = 7969 ok

RBS1 = RS1 + Q

= 2569 + 1800. 1

= 4369 kg

RBA = RB - RBS1

= 6136 - 4369

= 1767 kg

ME = RA. 2 - Q. 1

= 1833. 2 - 1800. 2

= 3666 - 3600

= 66 kgm

MB = RS1. 1 + Q. 0,5

= 2569. 1 + 1800. 0,5

= 2569 + 900

= 3469 kgm

MX = RA. X - 0,5 W. X2

= 1833 X - 0,5. 1800 X2

X18001833dX

dMX

0dX

dMX

1800 X = 1833 X = 1,02 m

Balok : A – B – S1

M maks = 1833. 1,02 - 900. 1,022

= 1870 - 936

= 934 kgm

Balok : S2 – C – D MD = 0

RC. 4 - RS2. 5 - W. 3. 3,5 - P. 1 = 0

4 RC - 1631. 5 - 1800. 10,5 - 1500. 1 = 0

4 RC - 8155 - 18900 - 1500 = 0

4 RC - 28555 = 0

RC = 7139 kg

MC = 0

RD. 4 + RS2. 1 + W. 1. 0,5 - W. 2. 1 - P. 3 = 0

4 RD + 1631. 1 + 1800. 0,5 - 1800. 2 - 1500. 3 = 0

4 RD + 1631 + 900 - 3600 - 4500 = 0

4 RD - 5569 = 0

RD = 1392 kg

V = 0

RC + RD = Q + P + RS2

7139 + 1392 = 1800. 3 + 1500 + 1631

8531 = 8531 ok

RCS2 = RS2 + Q = 1631 + 1800. 1 = 3431 kg

RCD = RC - RCS2 = 7139 - 3431 = 3708 kg

MX = RC. X - RS2 (1 + X) - W. 1 (0,5 + X) - 0,5 W. X2

= 7139 X - 1631 (1 + X) - 1800 (0,5 + X) - 0,5. 1800 X2

= 7139 X - 1631 - 1631 X - 900 - 1800 X - 900 X2

= 3708 X - 2531 - 900 X2


X18003708dX

dMX

0dX

dMX

1800 X = 3708 X = 2,06 m > 2 m tidak mungkin

MC = RS2. 1 + W. 1. 0,5

= 1631. 1 + 1800. 0,5

= 1631 + 900

= 2531 kgm

MH = RD. 2 - P. 1

= 1392. 2 - 1500. 1

= 2784 - 1500

= 1284 kgm

MI = RD. 1

= 1392. 1

= 1392 kgm

BIDANG GESER

BIDANG MOMEN

55) Gambar bidang momen dan gaya lintang. P = 1200 kg, W1 = 1600 kg/m, W2 = 1200 kg/m, W3 = 2200 kg/m

Balok : S1 – S2

RS1 = RS2 = 0,5. 1200. 3,5 = 2100 kg

M maks = 1200. 3,52

= 1838 kgm

8

1

Balok : A – B – S1 MB = 0

RA. 4 + RS1. 1 + W1. 1. 0,5 - W1. 4. 2 - P. 2 = 0

4 RA + 2100. 1 + 1600. 0,5 - 1600. 8 - 1200. 2 = 0

4 RA + 2100 + 800 - 12800 - 2400 = 0

4 RA - 12300 = 0

RA = 3075 kg

MA = 0

RB. 4 - RS1. 5 - W1. 5. 2,5 - P. 2 = 0

4 RB - 2100. 5 - 1600. 12,5 - 1200. 2 = 0

4 RB - 10500 - 20000 - 2400 = 0

4 RB - 32900 = 0

RB = 8225 kg

V = 0 RA + RB = RS1 + Q + P 3075 + 8225 = 2100 + 1600. 5 + 1200 11300 = 11300 ok

RBS1 = RS1 + Q

= 2100 + 1600. 1

= 3700 kg

RBA = RB - RBS1 = 8225 - 3700 = 4525 kg

Balok : A – B – S1 MX = RA. X - 0,5 W1. X

2

= 3075 X - 0,5. 1600 X2

X16003075dX

dMX

0dX

dMX

1600 X = 3075

X = 1,92 m

M maks = 3075. 1,92 - 800. 1,922

= 5904 - 2949

= 2955 kgm

ME = RA. 2 - W1. 2. 1

= 3075. 2 - 1600. 2

= 6150 - 3200

= 2950 kgm

MB = RS1. 1 + W1. 1. 0,5

= 2100. 1 + 1600. 0,5

= 2100 + 800

= 2900 kgm


MD = 0

RC. 4 - RS2. 5,5 - W3. 5,5. 2,75 - P. 2 = 0

4 RC - 2100. 5,5 - 2200. 15,125 - 1200. 2 = 0

4 RC - 11550 - 33275 - 2400 = 0

4 RC - 47225 = 0

RC = 11806 kg

MC = 0

RD. 4 + RS2. 1,5 + W3. 1,5. 0,75 - W3. 4. 2 - P. 2 = 0

4 RD + 2100. 1,5 + 2200. 1,125 - 2200. 8 - 1200. 2 = 0

4 RD + 3150 + 2475 - 17600 - 2400 = 0

4 RD - 14375 = 0

RD = 3594 kg

V = 0

RC + RD = RS2 + P + W3. 5,5

11806 + 3594 = 2100 + 1200 + 2200. 5,5

15400 = 15400 ok

RCS2 = RS2 + W3. 1,5

= 2100 + 2200. 1,5

= 5400 kg

RCD = RC - RCS2

= 11806 - 5400

= 6406 kg


MX = RD. X - 0,5 W3. X2

= 3594 X – 0,5. 2200 X2

X22003594dX

dMX

0dX

dMX

2200 X = 3594

X = 1,63 m

M maks = 3594. 1,63 - 1100. 1,632

= 5858 - 2923

= 2935 kgm

MC = RS2. 1,5 + W3. 1,5. 0,75

= 2100. 1,5 + 2200. 1,125

= 3150 + 2475

= 5625 kgm

MF = RD. 2 - W3. 2. 1

= 3594. 2 - 2200. 2

= 7188 - 4400

= 2788 kgm

BIDANG GESER

BIDANG MOMEN

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