Soal-soal dan penyelesaian METODE Distribusi Momen {
Metode Cross
}
No. 01. Analisislah Portal berikut dengan Metode Cross q = 300 kg/m’
2EI
B
C 2.00 m
P = 600 kg
P = 600 kg
EI
EI 3.00 m
A
D 5.00 m O
a. Perhitungan MOMEN PRIMER (M o
2
M AB
=
- Pab /L
MoBA
=
Pa 2b/L 2
=
2
o
M BC o
2
- qL /12 2
M CB
=
MoCD
=
- Pa 2b/L 2
MoDC
=
Pab 2/L 2
) 2
= - 600.3.2
qL /12
= + 600.3
2
= - 300.6
2
= + 300.6
2
= - 600.3
2
/5 2
=
-288 kg.m
2
=
432 kg.m
=
-625 kg.m
.2/5
/12 /12
=
625 kg.m
2
=
-432 kg.m
/5 2
=
288 kg.m
.2/5 2
= + 600.3.2
q = 300 kg/m’
B
625
432
625
C 432
P = 600 kg
P = 600 kg
288
A b. Perhitungan Koefisien Distribusi Titik Simpul A = µAB Titik Simpul D
0
µDC
0
=
288
D
5m Titik Simpul B B
C 2.EI
5m
EI A
µBA
=
µBC
=
kBA kBA + kBC kBC kBA + kBC
kBA
=
kBC
=
4.EIBA LBA 4.EIBC LBC
= =
4.EI 5 4.2EI 5
=
0.80
=
1.60
=
1.60
=
0.80
maka
µBA
=
µBC
=
0.80 2.40 1.60 2.40
=
0.33333
=
0.66667 1.00000
Titik Simpul C 5m B
C 2.EI EI
5m D
µCB
=
µCD
=
kCB kCB + kCD kCD kCB + kCD
kCB
=
kCD
=
maka
µCB
=
µCD
=
1.60 2.40 0.80 2.40
=
0.66667
=
0.33333 1.00000
c. Proses Distribusi Momen Lihat halaman selanjutnya….
4.EICB LCB 4.EICD LCD
= =
4.2EI 5 4.EI 5
Tabel Distribusi Mom en Joint Batang K No. DF 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
FEM Bal CO Bal CO Bal CO Bal CO Bal CO Bal CO Bal CO Bal CO Bal CO Bal CO Bal CO Bal CO Bal CO Bal CO Bal CO Bal CO Bal CO Bal
Total Check Statika
A AB 0.80 0
B
C
BA BC CB CD 0.80 1.60 1.60 0.80 0.3333333 0.66666667 0.6666667 0.33333333
-288.00000432.00000 -625.00000 625.00000 -432.00000 0.00000 64.33333 128.66667 -128.66667 -64.33333 32.16667 0.00000 -64.33333 64.33333 0.00000 0.00000 21.44444 42.88889 -42.88889 -21.44444 10.72222 0.00000 -21.44444 21.44444 0.00000 0.00000 7.14815 14.29630 -14.29630 -7.14815 3.57407 0.00000 -7.14815 7.14815 0.00000 0.00000 2.38272 4.76543 -4.76543 -2.38272 1.19136 0.00000 -2.38272 2.38272 0.00000 0.00000 0.79424 1.58848 -1.58848 -0.79424 0.39712 0.00000 -0.79424 0.79424 0.00000 0.00000 0.26475 0.52949 -0.52949 -0.26475 0.13237 0.00000 -0.26475 0.26475 0.00000 0.00000 0.08825 0.17650 -0.17650 -0.08825 0.04412 0.00000 -0.08825 0.08825 0.00000 0.00000 0.02942 0.05883 -0.05883 -0.02942 0.01471 0.00000 -0.02942 0.02942 0.00000 0.00000 0.00981 0.01961 -0.01961 -0.00981 0.00490 0.00000 -0.00981 0.00981 0.00000 0.00000 0.00327 0.00654 -0.00654 -0.00327 0.00163 0.00000 -0.00327 0.00327 0.00000 0.00000 0.00109 0.00218 -0.00218 -0.00109 0.00054 0.00000 -0.00109 0.00109 0.00000 0.00000 0.00036 0.00073 -0.00073 -0.00036 0.00018 0.00000 -0.00036 0.00036 0.00000 0.00000 0.00012 0.00024 -0.00024 -0.00012 0.00006 0.00000 -0.00012 0.00012 0.00000 0.00000 0.00004 0.00008 -0.00008 -0.00004 0.00002 0.00000 -0.00004 0.00004 0.00000 0.00000 0.00001 0.00003 -0.00003 -0.00001 0.00001 0.00000 -0.00001 0.00001 0.00000 0.00000 0.00000 0.00001 -0.00001 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -239.75000528.50000 -528.50000 528.50000 -528.50000 0.00000 0.00000
D DC 0.80 0 288.00000 0.00000 -32.16667 0.00000 -10.72222 0.00000 -3.57407 0.00000 -1.19136 0.00000 -0.39712 0.00000 -0.13237 0.00000 -0.04412 0.00000 -0.01471 0.00000 -0.00490 0.00000 -0.00163 0.00000 -0.00054 0.00000 -0.00018 0.00000 -0.00006 0.00000 -0.00002 0.00000 -0.00001 0.00000 0.00000 0.00000 0.00000 0.00000 239.75000
P ro ses D istrib usi M o m e n Join t A B a ta n g AB K kA B N o. D F (µ ) 0 1 2 3 4 5
M AB
Bal
0
Bal CO Bal
o
o
o
CO
CB kC B µC B
o
o
o
CD kC D µC D
o
M BC
M CB o
o
D DC kDC 0
o
M DC
o
0
M CD o
o
(M B A +MB C ).(-µB A ) (M B A +MB C ).(-µB C )(M C B +MC D).(-µC B ) (M C B +MC D).(-µC D) µB A ) (B + C ).(-
G = B al.2 B A / 2 H = B al.2 A B / 2 0
BC kB C µB C
M BA
A = B al.1 B A / 2 B = B al.1 A B / 2 0
C
BA kA B µB A
o
F EM CO
B
µB A ) (H + I).(-
C = B al. 1 C B / 2 D = B al. 1 B C / 2 E = B al. 1 DC / 2F = B al. 1 C D / 2 µB C ) (B + C ).(I = B al. 2 C B / 2 µB C ) (H + I).(-
µC B ) (D + E ).(-
µC D ) (D + E ).(-
J = B al. 2 B C / 2 K = B al. K D C / 2L = B al. 2 C D / 2 µC B ) (J + K ).(-
µC D ) (J + K ).(-
0
P roses tersebut diatas diulang hingga hasilbagi ( C O ) sudah mendekati nilai 0 , ( 0,00000 )
Bal CO
0.00000
Bal 0.00000 T ota l M AB C he ck Statika
0.00000
0.00000
0.00000 0.00000 MBA MBC jumlah satu titik simpul harus = 0
0.00000
0.00000
0.00000 0.00000 MCB MCD jumlah satu titik simpul harus = 0
0.00000 0.00000 MDC
M A B D ip e roleh d a ri h a sil p en ju m lah a n ke b a w a h (m en u ru t ko lo m ) d im ulai d a riOAMB om e n P rim e r M sa m p a i p a d a k o nd isi b ala nce (b a l) su d a h b e rn ila i 0 ,0 0 00 0 . U ntu k M om en T o ta l p a da T itik sim p ul ya n g la in d ilak u ka n d en ga n ca ra ya n g sa m a .
d. Perhitungan Mom en Desain Karena kondisi beban dan rangka sim etris, m aka dianalisis Portal tanpa Pergoyangan. untuk itulah proses distribusi m om en (cross) hanya satu kali yaitu akibat beban luar (tanpa pergoyangan). H arga m om en desain sam a dengan harga cross dari beban luar (lihat jum lah m om en dari proses cross). M AB = -239.8 kg.m M BA = 528.5 kg.m M BC = -528.5 kg.m M CB = 528.5 kg.m q = 300 kg/m ’ MCD = -528.5 kg.m MDC = 239.8 kg.m
B
528,50
C
528,50
528,50
528,50
P = 600 kg
P = 600 kg
239,75
239,75
A
D
l. Free Body untuk Perhitungan Reaksi Perletakan Batang AB ΣMB = 0 RAH ={(600.2)+(239,75)-(528,5)}/(5) = ΣH = 0 RAH + RBH = P RBH = P - RAH = Batang BC ΣMC = 0 RBV = {(300.5.5/2)+(528,5)-(528,5)}/(5) = ΣH = 0 RBV + RCV = Q RCV = Q - RBV =
182.25kg
g
417.75kg
g
750.00kg
g
750.00kg
g
Batang CD RCH = - RBH= RDH = - RAH=
q = 300 kg/m ’ 528,50 528,50
528,50 528,50
B
C
750
750
B 417,75
417,75
C
P = 600 kg
P = 600 kg
A 182,25 239,75
182,25 D 239,75
g -417.7 kg g -182.3 kg
m . Perhitungan M om en, G aya Lintang dan Gaya N orm al Potongan AB interval Potongan BC
interval 2
M x1 =RAH.X - M AB 0
- M BC M x = RBV.x - 1/2.q.x Dx = RBV - q.x Nx = - RBH
Pot. AB Interval 0
Pot. BC Interval 0
0
x 0 1 2 3 0 1 2
Mx
Dx
-239.8 182.3 -57.5 182.3 124.7 182.3 307.0 182.3 307.0 -417.7 -110.7 -417.7 -528.5 -417.7
Nx -750 -750 -750 -750 -750 -750 -750
528,5 528,5
-
528,5
-
-
B
C
+
-
x 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Mx
-528.5 750
+
-
A 239,8
307
G br. Bidang M om en
600
71.5
450
259
300
409.0
0
371.5 -150 259
-300
71.5 -450 -191 -600 -528.5 -750
Nx -418 -418 -418 -418 -418 -418 -418 -418 -418 -418 -418
750 417,75 C
528,5 B
417 ,75
750
+
G br. Bidang Lintang
D 239,8 417,75 B
A 182 ,25
417,75
C
Gbr. Bidang N orm al
750 A
-191
371.5 150
409,0 307
Dx
0
D 750
D 182,25
No. 02. Analisislah Portal berikut dengan Metode Cross P2 = 400 kg
P3 = 1000 kg
P1 = 600 kg
P4 = 400 kg
2 EI
B
C 3.00 m
EI α
EI
D 1.00 m
A 1m
2.00 m
2.00 m
4.00 m
sudut ( α )= 36.87 o
O a. Perhitungan MOMEN PRIMER (M )
MoBE
=
PL
= + 400.1
=
400 kg.m
o
=
- PL/8
= - 1000.4/8
=
-500 kg.m
o
=
+ PL/8
= + 1000.4/8
=
500 kg.m
M BC M CB
Momen primer akibat pergoyangan MXAB = MXBA = MAB=MBA (6.EIAB.∆h)/LAB2 = -0.375 EI.∆H misal EI.∆H = X, maka MXAB = MXBA = -37.5 X MBC=MCB
MCD=MDC
MXBC = MXCB =
∆v = ∆h / Tan α
=
(6.EIBC.∆v)/LBC2 1.000 X
∆r = ∆h / Sin α
=
(6.EICD.∆r)/LCD2 -0.400 X
MXCD = MXDC =
MAB=MBA = -37.5 .X MBC=MCB = 100 .X MCD=MDC = -40 .X
b. Perhitungan Koefisien Distribusi Titik Simpul A
µAB
= Titik Simpul D
0
µDC
0
=
4m Titik Sim pul B B
C 2.EI
4m
EI A
µ BA
=
µ BC
=
kBA kBA + kBC kBC kBA + kBC
kBA
=
kBC
=
4.EIBA LBA 4.EIBC LBC
= =
4.EI 4 4.2EI 4
=
1.00
=
2.00
=
2.00
=
0.80
m aka
µ BA
=
µ BC
=
1.00 3.00 2.00 3.00
=
0.33333
=
0.66667 1.00000
Titik Sim pul C 4m B
C 2.EI EI
5m D
µ CB
=
µ CD
=
kCB kCB + kCD kCD kCB + kCD
kCB
=
kCD
=
m aka
µ CB
=
µ CD
=
2.00 2.80 0.80 2.80
=
0.71429
=
0.28571 1.00000
c. Proses Distribusi Mom en Lihat halam an selanjutnya….
4.EICB LCB 4.EICD LCD
= =
4.2EI 4 4.EI 5
T a b e l D is t r ib u s i M o m e n , a k ib a t B e b a n L u a r A B C D J o in t B atang AB BA BE BC CB CD DC K 1.00 1.00 0.00 2.00 2.00 0.80 0.80 No. DF 0 0.33333333 0 0.66666667 0 .71428571 0.28571429 0 F E M 0.00000 0.00000 400.00000 -500.00000500.00000 0.00000 0.00000 1 B a l 0.00000 33.33333 0.00000 66.66667 -357.14286-1 42.857140 .00000 C O 16.66667 0.00000 0.00000-178.5714333.33333 0.00000 -71.42857 2 B a l 0.00000 59.52381 0.00000 119.04762-23.80952 -9.52381 0.00000 C O 29.76190 0.00000 0.00000 -11.90476 59.52381 0.00000 -4.76190 3 B a l 0.00000 3.96825 0.00000 7.93651 -42.51701 -17.00 6800.00000 CO 1.98413 0.00000 0.00000 -21.25850 3.96825 0.00000 -8.50340 4 B a l 0.00000 7.08617 0.00000 14.17234 -2.83447 -1.13379 0.00000 CO 3.54308 0.00000 0.00000 -1.41723 7.08617 0.00000 -0.56689 5 B a l 0.00000 0.47241 0.00000 0.94482 -5.06155 -2.02462 0.00000 CO 0.23621 0.00000 0.00000 -2.53077 0.47241 0.00000 -1.01231 6 B a l 0.00000 0.84359 0.00000 1.68718 -0.33744 -0.13497 0.00000 CO 0.42180 0.00000 0.00000 -0.16872 0.84359 0.00000 -0.06749 7 B a l 0.00000 0.05624 0.00000 0.11248 -0.60257 -0.24103 0.00000 CO 0.02812 0.00000 0.00000 -0.30128 0.05624 0.00000 -0.12051 8 B a l 0.00000 0.10043 0.00000 0.20086 -0.04017 -0.01607 0.00000 CO 0.05021 0.00000 0.00000 -0.02009 0.10043 0.00000 -0.00803 9 B a l 0.00000 0.00670 0.00000 0.01339 -0.07173 -0.02869 0.00000 CO 0.00335 0.00000 0.00000 -0.03587 0.00670 0.00000 -0.01435 10 B a l 0.00000 0.01196 0.00000 0.02391 -0.00478 -0.00191 0.00000 CO 0.00598 0.00000 0.00000 -0.00239 0.01196 0.00000 -0.00096 11 B a l 0.00000 0.00080 0.00000 0.00159 -0.00854 -0.00342 0.00000 CO 0.00040 0.00000 0.00000 -0.00427 0.00080 0.00000 -0.00171 12 B a l 0.00000 0.00142 0.00000 0.00285 -0.00057 -0.00023 0.00000 CO 0.00071 0.00000 0.00000 -0.00028 0.00142 0.00000 -0.00011 13 B a l 0.00000 0.00009 0.00000 0.00019 -0.00102 -0.00041 0.00000 CO 0.00005 0.00000 0.00000 -0.00051 0.00009 0.00000 -0.00020 14 B a l 0.00000 0.00017 0.00000 0.00034 -0.00007 -0.00003 0.00000 CO 0.00008 0.00000 0.00000 -0.00003 0.00017 0.00000 -0.00001 15 B a l 0.00000 0.00001 0.00000 0.00002 -0.00012 -0.00005 0.00000 CO 0.00001 0.00000 0.00000 -0.00006 0.00001 0.00000 -0.00002 16 B a l 0.00000 0.00002 0.00000 0.00004 -0.00001 0.00000 0.00000 CO 0.00001 0.00000 0.00000 0.00000 0.00002 0.00000 0.00000 17 B a l 0.00000 0.00000 0.00000 0.00000 -0.00001 -0.00001 0.00000 CO 0.00000 0.00000 0.00000 -0.00001 0.00000 0.00000 0.00000 18 B a l 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 T o ta l 52.70270105.405404 00.00000 -505.40540172.97297-1 72.97297 -86.48649 C h e c k S t a t ik a 0.00000 0.00000
T a b e l D istrib u si M o m e n , a k ib a t P e le p a sa n P e n d e l 1 J o in t B a ta n g K No. DF FEM B al CO 2 B al CO 3 B al CO 4 B al CO 5 B al CO 6 B al CO 7 B al CO 8 B al CO 9 B al CO 10 B al CO 11 B al CO 12 B al CO 13 B al CO 14 B al CO 15 B al CO 16 B al CO 17 B al CO 18 B al T o ta l C h e c k Sta tik a 1
A AB 1.00 0
B BA BE 1.00 0.00 0.333333 0
D BC CB CD DC 2.00 2.00 0.80 0.80 0.666666670.714285710.285714 0
-37.50000 -37.500000.00000 100.00000 0.00000-20.833330.00000 -41.66667 -10.416670.00000 0.00000 -21.42857 0.00000 7.14286 0.00000 14.28571 3.57143 0.00000 0.00000 7.44048 0.00000 -2.480160.00000 -4.96032 -1.240080.00000 0.00000 -2.55102 0.00000 0.85034 0.00000 1.70068 0.42517 0.00000 0.00000 0.88577 0.00000 -0.295260.00000 -0.59051 -0.147630.00000 0.00000 -0.30369 0.00000 0.10123 0.00000 0.20246 0.05062 0.00000 0.00000 0.10545 0.00000 -0.035150.00000 -0.07030 -0.017570.00000 0.00000 -0.03615 0.00000 0.01205 0.00000 0.02410 0.00603 0.00000 0.00000 0.01255 0.00000 -0.004180.00000 -0.00837 -0.002090.00000 0.00000 -0.00430 0.00000 0.00143 0.00000 0.00287 0.00072 0.00000 0.00000 0.00149 0.00000 -0.000500.00000 -0.00100 -0.000250.00000 0.00000 -0.00051 0.00000 0.00017 0.00000 0.00034 0.00009 0.00000 0.00000 0.00018 0.00000 -0.000060.00000 -0.00012 -0.000030.00000 0.00000 -0.00006 0.00000 0.00002 0.00000 0.00004 0.00001 0.00000 0.00000 0.00002 0.00000 -0.000010.00000 -0.00001 0.00000 0.00000 0.00000 -0.00001 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -45.27027 -53.040540.00000 53.04054 0.00000
C
100.00000-40.00000 -40.00000 -42.85714-17.142860.00000 -20.83333 0.00000 -8.57143 14.88095 5.95238 0.00000 7.14286 0.00000 2.97619 -5.10204 -2.040820.00000 -2.48016 0.00000 -1.02041 1.77154 0.70862 0.00000 0.85034 0.00000 0.35431 -0.60739 -0.242950.00000 -0.29526 0.00000 -0.12148 0.21090 0.08436 0.00000 0.10123 0.00000 0.04218 -0.07231 -0.028920.00000 -0.03515 0.00000 -0.01446 0.02511 0.01004 0.00000 0.01205 0.00000 0.00502 -0.00861 -0.003440.00000 -0.00418 0.00000 -0.00172 0.00299 0.00120 0.00000 0.00143 0.00000 0.00060 -0.00102 -0.000410.00000 -0.00050 0.00000 -0.00020 0.00036 0.00014 0.00000 0.00017 0.00000 0.00007 -0.00012 -0.000050.00000 -0.00006 0.00000 -0.00002 0.00004 0.00002 0.00000 0.00002 0.00000 0.00001 -0.00001 -0.000010.00000 -0.00001 0.00000 0.00000 0.00001 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 52.70270 -52.70270 -46.35135 0.00000
P e r h it u n g a n R e a k s i A k i b a t B e b a n L u a r T a b e l D is t r ib u s i M o m e n A B C D J o in t Batang AB BA BE BC CB CD DC M . B e b a n L u5a 2.7 r 0 2 7100 5 .4 05 4400 0 .0 0 0 0 0-5 0 5 .4 0 5 4107 2 .9 7 2 9 -71 7 2 .9 7 3-8 6 .4 8 6 4 9 M . P e n d e l 1-4 5 .2 7 0 2-573 .0 4 0 5 40 .0 0 0 0 0 5 3 .0 4 0 5 45 2 .7 0 2 7 0-5 2 .7 0 2 7-4 6 .3 5 1 3 5
1 0 5 .4 0 5 4 0 1 5 8 .1 0 8 1 1 B ΣM B = 0 R A H .h + M A B + M B A = 0 R A H =3 9 .5 2 7 0 2T 7o n h = 4 ΣH = 0 RAH + RBH = 0 R B H =-3 9 .5 2 7 0T 3o n A 5 2 .7 0 2 7 0
4 1 6 .8 9 1 8 9 -1 7 2 .9 7C3
g r = 5
g
ΣM D = 0 R C H .h + M C D + M D C - R C V .4 = 0 R C H =6 4 2 .3 T4 o n g ΣH = 0 RCH + RDH = 0 R D H =- 6 4 2 . T3 o n g
D - 8 6 .4 8 6
1 0 0 0K g -5 0 5 .4 0 5 4 0 B
1 7 2 .9 7 3 0 2
2
C
4 ΣM C = 0 R B V .L + M B C + M C B - P .2 = 0 R B V =5 8 3 .1 0 8 1K 1g ΣV = 0 RBV + RCV = P R C V =4 1 6 .8 9 1 8K 9g
5 8 3 .1 0 8 1 -3 9 .5 2 7 0 3 B
HOB C =
4 1 6 .8 9 1 8 9 1 8
6 0 2 .8 1T5o n
g
6 4 2 .3 4 2 3 4 C
HOA B =-6 0 2 .8T2o n g D 3 9 .5 2 7 0A3
-6 4 2 .3 4 2 3
P e rh itu n g a n R e a k s i A k ib a t P e n d e l 1 T a b e l D ist rib u s i M o m e n A B C D J o in t B a ta n g AB BA BE BC CB CD DC M . B e b a n L u5a2r.7 0 2 7 01 0 5 .4 0 5 4 04 0 0 .0 0 0 0 0-5 0 5 .4 0 5 4 10 7 2 .9 7 2 9 7-1 7 2 .9 7 2 9-87 6 .4 8 6 4 9 M . P e n d e l -4 1 5 .2 7 0 2 -75 3 .0 4 0 5 4 0 .0 0 0 0 0 5 3 .0 4 0 5 4 5 2 .7 0 2 7 0 -5 2 .7 0 2 7 0-4 6 .3 5 1 3 5
-5 3.04 0 5 4 B ΣM B = 0 R A H .h + M A B + M B A = 0 R A H =- 2 4 . 5 7 7 7 0 T2 o7 1n h 3 =4 ΣH = 0 RAH + RBH = 0 R B H =2 4 . 5 7 7 7 0 2T 7o 1n A -4 5.27 0 2 7
5 3 .0 4 0 5 4 B
2 6 .4 3 5 8 1 ΣM D = 0 R C H .h + M C D + M D C - R C V .4 = 0 R C H =6 8 . 2 6 5T8o ng ΣH = 0 RCH + RDH = 0 R D H =- 6 8 . 2 6T6o ng
- 5 2 . 7 0 2C 7
g r = 5
g D
-4 6 .3 5 1 3 5
5 2 .7 0 2 7 0 2
2
C
4 ΣM C = 0 R B V .L + M B C + M C B = 0 R B V =- 2 6 . 4 3 5 8 1 K0 g7 8 ΣV = 0 RBV + RCV = 0 R C V =2 6 . 4 3 5 8 1 0K 7g 8
-2 6 .4 3 5 8 2 4 .57 7 7 0 B
HxB C = 9 2 . 8 4 3 4T 7o n
2 6 .4 3 5 8 1 0 7 8 C
D - 2 4 . 5 7 7 A7 0
g
6 8.26 5 7 6 5 7 3
HXA D = - 9 2 . 8 4T3o ng -6 8 .2 6 5 7 6 5 7 3
P e r h it u n g a n M o m e n D e s a in K a r e n a k o n d is i b e b a n d a n r a n g k a s im e t r is , m a k a d ia n a lis is P o r t a l t a n p a P e r g o y a n g a n . u n t u k it u la h p r o s e s d is t r ib u s i m o m e n ( c r o s s ) h a n y a s a t u k a li y a it u a k ib a t b e b a n lu a r ( t a n H a r g a m o m e n d e s a in s a m a d e n g a n h a r g a c r o s s d a r i b e b a n lu a r ( lih a t ju m la h m o m e n d a r M A B = 5 2 .7 k g .m M B A = 1 0 5 . 4k g .m M B C = - 5 0 5 . 4k g .m M C B = 1 7 3 k g .m M C D = - 1 7 3 k g .m M D C = - 8 6 .4 9k g .m
P e r h itu n g a n H a r g a X T a b e l D is tr ib u s i M o m e n A B C D J o in t B a ta n g AB BA BE BC CB CD DC M . B e b a n L u 5a 2r .7 0 2 7100 5 .4 0 544000 .0 0 0 -0500 5 .4 0 5 14 70 2 .9 7 2 9- 177 2 .9 7 2- 98 76 .4 8 6 4 9 M . P e n d e l 1- 4 5 .2 7 0 -2573 .0 4 0 504.0 0 0 0 05 3 .0 4 0 5 45 2 .7 0 2 7 0-5 2 .7 0 2 7- 406 .3 5 1 3 5 M . P 1 . X - 1 9 3 .6 6-6242 6 .9 0 706.0 2 0 0 0 02 2 6 .9 0 7 62 22 5 .4 6 2 3- 25 2 5 .4 6 2- 139 8 .2 9 1 2 M o m e n A k h i r /- 1D4e0s.9a i6n-3172 1 .5 0 24 20 10 .0 0 0 -0207 8 .4 9 7 37 99 8 .4 3 5 3- 32 9 8 .4 3 5- 238 4 .7 7 7 7 C h e c k S t a t ik a 0 .0 0 0 0 0 0 .0 0 0 0 0 - 1 4 0 .9 6- 31 72 1 . 5 0 2 2 41 0 0 - 2 7 8 . 4 9 7 7389684. 4 3 5-33 29 8 . 4 3 5 3- 22 80 45 . 7 7 7 7 H a r g a X4 =. 2 7 8 0 0 3 5
HOB C = - 3 9 7 . 1 8k g4 7 HXB C = 9 2 . 8 4 3 X4 6 8
g g
S y a r a t S t a t ik a : HOB C +XBHC= 0 - 3 9 7 . 1 8+4 7 9 2 , 8 4 3 4 7 . X = 0 M aka H a rg a X X = 4 .2 7 8 0 0 3 5
P e r h it u n g a n R e a k s i A k h ir T a b e l M o m e n A k h ir J o in t A B C D B a ta n g AB BA BE BC CB CD DC M . B e b a n L u a52 r .7 027 0 10 5.405 40400 .000 00-50 5.4 05 401 72 .9 72 97-17 2.972 97-86 .48 64 9 M . P e n d e l 1 -45.27 02 7 -53.040 54 0.00 00 0 53.04 05 4 52.70 27 0-52.70270 -46 .35 13 5 M . A k h ir -14 0.96 367-1 21 .5 022 14 00 .000 00-27 8.4 97 79398 .4 35 3-39 8.435 32-2 84 .77 77 3
-1 2 1 .5 0 2 2 B ΣM B = 0 R A H .h 3 + M A B + M B A = 0 R A H =-6 5 .6 1 6 4 7 2T1o7n h 3 =4 ΣH = 0 RAH + RBH = 0 R B H = 6 5 . 6 1 6 4 7 2T1o7n A - 1 4 0 .9 6 4
529.984 -3 9 8 . 4 3 5 C ΣM D = 0 R C H . h + M C D + M D C - R C V .4 = 0 g R C H = 9 3 4 .3 8 3 5 2T7o8n g L = 5 ΣH = 0 RCH + RDH = 0 g R D H =-9 3 4 .3 8 3 5 2T7o8n g D -2 8 4 .7 7 7 7
1 0 0 0K g -2 7 8 .4 9 7 8 B
3 9 8 .4 3 5 2
2
C
4 ΣM B = 0 R B V . L + M B C + M C B - P .2 = 0 R B V = 4 7 0 . 0 1 5 6 1K6g6 ΣV = 0 RBV + RCV = P R C V = 5 2 9 . 9 8 4 3 8K3g4
1 0 0 0 . T0 o n g
HB C = 470.0156166
5 2 9 .9 8 4 3 8 3 4 9 3 4 .3 8 3 5 2 8
6 5 .6 1 6 B
C
-1 0 0 0 . 0T0o n g
HA D = D
-9 3 4 .3 8 3 5 2 7 8
-6 5 . 6 1 6 A 8 7 0 .0 1 5 6 1 7
5 2 9 .9 8 4 3 8 3
F re e B o d y u n t u k P e r h it u n g a n R e a k s i P e rle t a k a n B atan g A B B atan g C D ΣM B = 0 R C H = - R=B H - 2 2 9 .k5g g R A H {=( 6 0 0 . 2 ) + ( 2 3 9 , 7 5 ) - ( 5 2 8 =, 5 ) } /2( 25 9) . 4k6g g R D H = - R=A H - 3 7 0 .k5g g ΣH = 0 RAH + RBH = P R B H P= - R A H = 3 7 0 . 5k4g g B atan g BC ΣM C = 0 R B V {=( 3 0 0 . 5 . 5 / 2 ) + ( 5 2 8 , 5 ) - ( 5= 2 8 , 58 )1} 6/ .( 45k9)g ΣH = 0 RBV + RCV = Q R C V Q= - R B V = 6 8 3 . 5k1g
g
g
P e r h itu n g a n M o m e n , G a y a L in ta n g d a n G a y a N o r m a l P o to n g a n A B in te rv a l P o to n g a n B C 2 M x 1 =R A H .X - M A B 0 < X < 2 M x = R B V .x - 1 / 2 .q- .xM B C D x 1 =R A H D x = R B V - q .x N x 1 =- R A V = R B V Nx = - RBH M x 2 =R A H .(3 + X ) - P .X - M A B0 < X < 3 D x 2 =R A H - P N x 2 =- R A V P o t. A B In te rv a l 0 < X < 2
0 < X < 3
x 0 1 2 3 0 1 2
Mx
Dx
Nx -5 2 .7 2 2 9 .5 -8 1 6 .5 1 7 6 .8 2 2 9 .5 -8 1 6 .5 4 0 6 .2 2 2 9 .5 -8 1 6 .5 6 3 5 .7 2 2 9 .5 -8 1 6 .5 6 3 5 .7-3 7 0 .5-8 1 6 .5 2 6 5 .1-3 7 0 .5-8 1 6 .5 -1 0 5 .4-3 7 0 .5-8 1 6 .5
P o t. B C In te r v a l x 0 < X < 5 0 0 .5 1 1 .5 2 2 .5 3 3 .5 4 4 .5 5
Mx
in te r v a l 0 < X < 5
Dx
Nx -5 0 5 .48 1 6 .5 -3 7 1 -1 3 4 .76 6 6 .5 -3 7 1 1 6 1 .1 5 1 6 .5 -3 7 1 3 8 1 .8 3 6 6 .5 -3 7 1 5 2 7 .6 2 1 6 .5 -3 7 1 5 9 8 .3 6 6 .4 9 -3 7 1 5 9 4 .1 -8 3 .5 1 -3 7 1 5 1 4 .8 -2 3 3 .5 -3 7 1 3 6 0 .5 -3 8 3 .5 -3 7 1 1 3 1 .3 -5 3 3 .5 -3 7 1 -1 7 3 -6 8 3 .5 -3 7 1
Coba anda selesaikan Gambar Bidang Momen, Lintang dan Normalnya.
