Apakah Struktur Gelagar dibawah ini SST tau SSTT??
Apakah Struktur Gelagar dibawah ini SST tau SSTT??
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.
* 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
48) Gambar bidang momen dan gaya lintang. P = 2000 kg, W = 2500 kg/m
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
Balok : S2 – C – D
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
BIDANG MOMEN
54) Gambar bidang momen dan gaya lintang. P = 1500 kg, W = 1800 kg/m
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
Balok : S2 – C – D
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
Balok : S2 – C – D
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
Balok : S2 – C – D
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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