no 2 sendi sendi jepit
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7/26/2019 No 2 Sendi Sendi Jepit
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PENOMORAN GLOBAL
PENOMORAN LOKAL
TABEL DATA BATANG
BATANGNODE
EI Li j
1.0000 1.0000 2.0000 1.0000 3.0000
2.0000 2.0000 3.0000 1.0000 2.50003.0000 3.0000 4.0000 1.0000 3.0000
2 . STRUKTUR GELAGAR
1 2 3 4
V1 V2 V3
1 2 3 4
1 2 3
1 2
V1 V2
1 2
1
2 3
V2 V3
2 3
2
3 4
V3
3 4
3
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MATRIKS KEKAKUAN LOKAL
Elemen 1
V1
1 = EI 0.4444
0.6667
-0.4444
0.6667
Elemen 2
V2
2 = EI 0.7680
0.9600
-0.7680
0.9600
Elemen 3
V3
3 = EI 0.4444
0.6667
-0.4444
0.6667
MATRIKS KEKAKUAN GLOBAL
V1 Ө1
0.4444 0.6667
0.6667 1.3333
-0.4444 -0.6667
EI 0.6667 0.6667
0 0
0 0
0 0
0 0
REARRANGEMENT
Ө1 Ө2
1.3333 0.6667
k l
k l
k l
k g =
[ ]
+−++
−+−−
+−++
+−++
=
L
EI
L
EI
L
EI
L
EI
L
EI
L
EI
L
EI
L
EI
L
EI
L
EI
L
EI
L
EI
L
EI
L
EI
L
EI
L
EI
kl i
4626
612612
2646
612612
22
2323
22
2323
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0.6667 2.9333
EI 0.0000 0.8000
0 0
0.6667 0.6667
-0.6667 0.2933
0.0000 -0.9600
0 0
Ө1 Ө2
1.3333 0.6667
0.6667 2.9333
EI 0.0000 0.8000
0.0000 0.0000
0.6667 0.6667
-0.6667 0.2933
0.0000 -0.96000.0000 0.0000
MOMEN PRIMER
Elemen 1
Elemen 2
Elemen 3
k g =
k g =
2000 kg/m
EI
4 m
1 2
M 12 M 21
21
1500 kg/m
2 EI
3,5 m
2 3
M 23 M 32
23$2"%1
2000 kg/m
2000 kg
EI
3 m 2,5 m
3 4
M 34 M 43
342"%12
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ANALISIS BEBAN JOIN EKUIVALEN
Beban jon e!"#alen
El)*)+ 1
262.9630
1 = 177.7778
287.0370
-188.8889
262.9630 V1
177.7778 Ө1
412.0370 V2
= -136.8056 Ө2 =
167.1875 V3
-16.9271 Ө3
182.8125 V4
-77.3438 Ө4
Anal$a beban jon
A,
A,
2000 kg/m
EI
4 m
1 2
1500 kg/m
2 EI
3,5 m
2 3
2666,6667 kgm 2666,6667 kgm 1531,25 kgm 1531,25 kgm 6
4000 kg 4000 kg 2625 kg 2625 kg
666,6667 kg
4000 kg
437,5 kg
4000 kg 2625 kg 2625 kg
6625 kg 8
666,6667 kg
666,6667 kg 666,6667 kg 437,5 kg
437,5 kg
437,5 kg
2000 kg/m2000 kg/m
1500 kg/m
2000 kg
EI 2 EI EI
4 m 3,5 m 3 m 2,5 m A B C D
2666,6667 kgm 2666,6667 kgm 1531,25 kgm 1531,25 kgm6281,3361 kgm
2625 k
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-177.7778
136.8056
16.9271
= - A, = 77.3438
-262.9630
-412.0370
-167.1875
-182.8125
= '
0 -177.7778
0 136.8056
0 16.9271
= 0 ' 77.3438
-200 -263
0 -412
0 -167.188
0 -182.813
Ө1 Ө2
-177.7778 1.3333 0.6667
136.8056 0.6667 2.9333
16.9271 = EI 0.0000 0.8000
77.3438 0.0000 0.0000-462.9630 0.6667 0.6667
-412.0370 -0.6667 0.2933
AE
A A AE
2000 kg/m2000 kg/m
1500 kg/m
2000 kg
EI 2 EI EI
4 m 3,5 m 3 m 2,5 m A B C D
2666,6667 kgm 2666,6667 kgm 1531,25 kgm 1531,25 kgm6281,3361 kgm
4000 kg 4000 kg 2625 kg 2625 kg 6364,012 kg 663
EI 2 EI EI
A B C D2666,6667 kgm 2666,6667 kgm 1531,25 kgm 1531,25 kgm 6281,3361 kgm 6529,
4000 kg 4000 kg 2625 kg 2625 kg 6364,012 kg 663
EI 2 EI EI
A B C D2666,6667 kgm 2666,6667 kgm 1531,25 kgm 1531,25 kgm 6281,3361 kgm 6529,
4000 kg 6625 kg 8989,012 kg 663
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-167.1875 0.0000 -0.9600
-182.8125 0.0000 0.0000
BESARN%A PERPINDA&AN
-177.7778 1.3333 0.6667136.8056 = EI 0.6667 2.9333
16.9271 0.0000 0.8000
Ө1 1.3333 0.6667
Ө2 = 1 0.6667 2.9333
Ө3 EI 0.0000 0.8000
Ө1 0.85496 -0.20992
Ө2 = 1 -0.20992 0.41985
Ө3 EI 0.05725 -0.11450
Ө1 -179.7428
Ө2 = 1 92.8190
Ө3 EI -19.5437
De'o(ma$ S)("!)"( Global
0 V1
-179.7428 Ө1
0 V2
Ө = 1 92.8190 Ө2
EI 0 V3
-19.5437 Ө3
0 V4
0.0000 Ө4
REAKSI TUMPUAN
,4 -77
G1 = 463 ' EI
G2 412
G3 167
G4 183
,4 -77 -13.029116306
/= /Ө/{ {
/= /Ө/{+ { /= /' /Ө/{ { {
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G1 = 463 ' -57.949224272
G2 412 128.29353089
G3 167 -83.373422922
G4 183 13.029116306
,4 -90.3729 g*
G1 = 405.0137 g
G2 540.3306 gG3 83.8141 g
G4 195.8416 g
Kon)(ol
= 0
G1'G2'G3'G4-10025-15015-250-300-200
0.0000
, = 0
.-G10-G24-G375-G413'200042'30004'150035(4'3505"'300
PER&ITUNGAN GA%A UJUNG BATANG LOKAL
Elemen 1
G1 263
,1 = 177.7778 ' EIG2 287
,2 -188.8889
263 -57.9492
= 178 ' -177.7778
287 57.9492
-189 3.9301
205.0137
= 0344.9863
-184.9588
/=8({
@@
"/ /= ' { [ _ [ _
Ө_
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Elemen 2
G2 125
,2 = 52.08 ' EI
G3 125
,3 -52.08
125.0000 70.344306616
= 52.0833 ' 132.87545059
125.0000 -70.344306616
-52.0833 42.985315946
195.3443
= 184.9588
54.6557
-9.0980
Elemen 3
G3 42.1875
,3 = 35.1563 ' EI
G4 182.8125
,4 -77.3438
42.1875 -13.029116306
35.1563 ' -26.058232612
182.8125 13.029116306
-77.3438 -13.029116306
29.1584
9.0980
195.8416
-90
Kon)(ol *(eebo+,
2000 kg/m
EI
4 m
1 2
1500 kg/m
2 EI
3,5 m
2 3
2000 kg
EI
3 m 2,
3
2338,2244 kgm 2338,2244 kgm 7513,9898 kgm 7513,9898 kgm
4000 kg 4000 kg 2625 kg 2625 kg 5500 kg
3415,4439 kg
668,0641 kg 909,0909 kg
1366,18 kg
4584,5561 kg 1146,2099 kg 4103,7901 kg 7775,2709 kg
584,5561 kg
2146,8542 kg
584,5561 kg 668,0641 kg
2146,8542 kg
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Kon)(ol
= 0
34154439'5730766'11879061'52247291 =
1025.0000 =
PER&ITUNGAN MOMEN DAN LINTANG (,)+gg:++
I
, =
, =
, =
I
, =
,*C
I
3415,4439 kg
668,0641 kg 909,0909 kg
1366,18 kg
4584,5561 kg 1146,2099 kg 4103,7901 kg 7775,2709 kg
5730,766 kg 11879,061 kg
584,5561 kg
2146,8542 kg
584,5561 kg 668,0641 kg
2146,8542 kg
2000 kg/m
EI
4 m
1 2
2338,2244 kgm
3415,4439 kg 4584,5561 kg
1500 kg/m
2 EI
3,5 m
2 3
2338,2244 kgm 7513,9898 kgm
1146,2099 kg 4103,7901 kg
2000 kg/m
3 4
7513,9898 kgm
2000 kg
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, =
I
, =
PER&ITUNGAN MOMEN DAN LINTANG (,)+g
0-4
,= -90.3729 - 2000.0000
0.0000 = 0.00000.5000 = -295.1864
1.0000 = -1090.3729
1.5000 = -2385.5593
2.0000 = -4180.7457
2.5000 = -6475.9322
3.0000 = -9271.1186
3.5000 = -12566.3050
4.0000 = -16361.4915
4-75
,= -90.3729 - 8000.00004.0000 = -16361.4915
4.5000 = -21891.6710
2000 kg/m
EI
3 m 2,5 m
3 4
7513,9898 kgm
7775,2709 kg 5224,7291 kg
2000 kg
2000 kg/m 20001500 kg/m
3000 kg 3000 kg 2000 kg
EI 2 EI EI
4 m 3,5 m 3 m 2,5 m A B C D
3415,4439 kg 8730,766 kg 14879,061 kg 52
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5.0000 = -27796.8506
5.5000 = -34077.0302
6.0000 = -40732.2097
6.5000 = -47762.3893
7.0000 = -55167.5688
7.5000 = -62947.7484
75-105,= -90.3729 - 8000.0000
7.5000 = -62947.7484
8.0000 = -72395.2627
8.5000 = -82342.7770
9.0000 = -92790.2913
9.5000 = -103737.8055
10.0000 = -115185.3198
10.5000 = -127132.8341
105-13
,= -90.3729 - 8000.0000
10.5000 = -127132.8341
11.0000 = -140580.3484
11.5000 = -154527.8627
12.0000 = -168975.3769
12.5000 = -183922.8912
13.0000 = -199370.4055
GAMBAR DIAGRAM GA%A MOMEN DAN LINTANG
2000 kg/m 1500 kg/m
3000 kg 3000 kg 2000 kg
EI 2 EI EI
4 m 3,5 m 3 m 2,5 m A B C
7513,9898 kgm
2338,2244 kgm
7513,9898 kgm
4000 kgm
2296,875 kgm
10227,2727 kgm
+
+
Bi!a"g M%me"
&'(e)(%sisi
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2916,3143 kgm
2338,2244 kgm
1900,2920 kgm
7513,9898 kgm
6811,8228 kgm
6811,8228 kgm6811,8228 kgm
3415,4439 kg
4584,5561 kg
1146,2099 kg
4103,7901 kg
1.7077
4.7641
7775,2709 kg
1775,2709 kg
7513,9898 kgm
224,7291 kg
10227,2727 kgm
+
+
+
+ +
+
Bi!a"g #i"$a"g
Bi!a"g M%me"
0 2 4
1 3 5m
0 2000 4000
1000 3000 5000 kgm
0 2000 4000
1000 3000 5000 kg
&ka*a a)ak
&ka*a a-a M%me"
&ka*a a-a #i"$a"g
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1.7077
4.7641
0 2 4
1 3 5m
0 2000 4000
1000 3000 5000 kgm
0 2000 4000
1000 3000 5000 kg
&ka*a a-a M%me"
&ka*a a-a #i"$a"g
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12EI 6EI 4EI 2EI
L L
0.4444 0.6667 1.3333 0.6667
0.7680 0.9600 1.6000 0.80000.4444 0.6667 1.3333 0.6667
L3 L2
4
V4
4
4
V4
4
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Ө1 V2 Ө2
0.6667 -0.4444 0.6667 V1
1.3333 -0.6667 0.6667
-0.6667 0.4444 -0.6667 V2
0.6667 -0.6667 1.3333
Ө2 V3 Ө3
0.9600 -0.7680 0.9600 V2
1.6000 -0.9600 0.8000 Ө2
-0.9600 0.7680 -0.9600 V3
0.8000 -0.9600 1.6000 Ө3
Ө3 V4 Ө4
0.6667 -0.4444 0.6667 V3
1.3333 -0.6667 0.6667 Ө3
-0.6667 0.4444 -0.6667 V4
0.6667 -0.6667 1.3333 Ө4
V2 Ө2 V3 Ө3 V4
-0.4444 0.6667 0 0 0
-0.6667 0.6667 0 0 0
1.2124 0.2933 -0.7680 0.9600 0
0.2933 2.9333 -0.9600 0.8000 0
-0.7680 -0.9600 1.2124 -0.2933 -0.4444
0.9600 0.8000 -0.2933 2.9333 -0.6667
0 0 -0.4444 -0.6667 0.4444
0 0 0.6667 0.6667 -0.6667
Ө3 Ө4 V1 V2 V3
0 0 0.6667 -0.6667 0
Ө1
Ө2
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0.8000 0 0.6667 0.2933 -0.9600
2.9333 0.6666666667 0.0000 0.9600 -0.2933
0.6667 1.3333 0 0 0.6667
0 0 0.4444 -0.4444 0
0.96 0 -0.4444 1.2124 -0.768
-0.2933 0.6666666667 0.0000 -0.7680 1.2124
-0.6667 -0.6667 0 0 -0.4444
Ө3 Ө4 V1 V2 V3
0.0000 0.0000 0.6667 -0.6667 0.0000
0.8000 0.0000 0.6667 0.2933 -0.9600
2.9333 0.6667 0.0000 0.9600 -0.2933
0.6667 1.3333 0.0000 0.0000 0.6667
0.0000 0.0000 0.4444 -0.4444 0.0000
0.9600 0.0000 -0.4444 1.2124 -0.7680
-0.2933 0.6667 0.0000 -0.7680 1.2124-0.6667 -0.6667 0.0000 0.0000 -0.4444
= 177.7777778 g*
= -188.8889 g*
= 52.0833 g*
= -52.0833 g*
= 35.1563
= -77.3438
12= (1 /"
(1 / !"!
#2( 〖 #2〗2
32= #2( 〖 #2〗
$2"%12
( #32(6&2'4&'2 "
43= #3( 2"%122
!
(4&'2
"!
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El)*)+ 2 El)*)+ 3
125.0000
2 = 52.0833
125.0000
-52.0833
177.7778 Ө1
-136.8056 Ө2
-16.9271 Ө3
-77.3438 Ө4
262.9630 V1
412.0370 V2
167.1875 V3
182.8125 V4
A, A,
kg/m
3
2000 kg/m
2000 kg
EI
3 m 2,5 m
3 4
1531,25 kgm 6281,3361 kgm 6529,27 kgm
2625 kg 5500 kg 5500 kg
909,0909 kg 1090,9091 kg
1142,0611 kg
1187,14 kg
2625 kg 6364,012 kg 6635,988 kg
8989,012
437,5 kg
437,5 kg 1142,0611 kg
1187,14 kg
2000 kg/m
00 kg
I
2,5 mD
6529,27 kgm
Reaksi
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Ө1
Ө2
Ө3
Ө4
V1
V2
V3
V4
= &)&+ ji+
= &)&+ ji
-177.7778 Ө1
136.8056 Ө2
16.9271 Ө3
= 77.3438 Ө4
-463 V1
-412 V2
-167.188 V3
-182.813 V4
Ө3 Ө4 V1 V2 V3
0.0000 0.0000 0.6667 -0.6667 0.0000
0.8000 0.0000 0.6667 0.2933 -0.9600
2.9333 0.6667 0.0000 0.9600 -0.2933
0.6667 1.3333 0.0000 0.0000 0.66670.0000 0.0000 0.4444 -0.4444 0.0000
0.9600 0.0000 -0.4444 1.2124 -0.7680
A
AE
2000 kg/m
00 kg
I
2,5 mD
6529,27 kgm
kg 6635,988 kg
I
D6529,27 kgm
kg 6635,988 kg
I
D6529,27 kgm
6635,988 kg
Reaksi
Aksi
Aksi
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-0.2933 0.6667 0.0000 -0.7680 1.2124
-0.6667 -0.6667 0.0000 0.0000 -0.4444
0.0000 Ө10.8000 Ө2
2.9333 Ө3
0.0000 -1 -177.7778
0.8000 136.8056
2.9333 16.9271
0.05725 -177.7778
-0.11450 136.8056
0.37214 16.9271
*
0.0000 0.0000 0.6667
0.6667 0.6667 0.0000 1
-0.6667 0.2933 0.9600 EI
0.0000 -0.9600 -0.2933
0.0000 0.0000 -0.6667
Ө/= /{ $(1" /{
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1225.0000
1225
= 0
= 0 O
75'2000105'200055(75'5505"
3.268E-013
0.4444 0.6667 -0.4444 0.6667
0.6667 1.3333 -0.6667 0.6667 1-0.4444 -0.6667 0.4444 -0.6667 EI
0.6667 0.6667 -0.6667 1.3333
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0.7680 0.9600 -0.7680 0.9600
0.9600 1.6000 -0.9600 0.8000 1
-0.7680 -0.9600 0.7680 -0.9600 EI
0.9600 0.8000 -0.9600 1.6000
0.4444 0.6667 -0.4444 0.6667
0.6667 1.3333 -0.6667 0.6667 1
-0.4444 -0.6667 0.4444 -0.6667 EI
0.6667 0.6667 -0.6667 1.3333
2000 kg/m
2000 kg
EI
3 m 2,5 m
4
gm
500 kg 5500 kg
909,0909 kg 1090,9091 kg
366,18 kg
775,2709 kg 5224,7291 kg
1366,18 kg
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20004'150035'20004'2000
1025
;-g; < :j:+g &>+g"
NTE?VAL 0@@3
205.0137
= 0.0000 = 0 g*
= 1.0000 = 205.0137 g*
205.0137 - 250 ( - 1"
= 1.0000 = 205.0137 g*
= 2.0000 = 410.0275 g*
205.0137 - 250 ( - 1" -
= 2.0000 = 410.0275 g*
= 3.0000 = 615.0412 g*
TE?VAL 0@@25
195.3443 - 100
= 0.0000 = -184.9588 g*
= 0.5000 = -99.7866 g* = 1.0000 = -39.6145 g*
= 1.5000 = -4.4423
= 2.0000 = 5.7298
= 2.5000 = -9.0980
= D = 0 F
= 0.1302 , = -160.3672 g*
TE?VAL 0@@15
.2 /2
909,0909 kg 1090,9091 kg
366,18 kg
775,2709 kg 5224,7291 kg
kg
1366,18 kg
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29.1584
= 0.0000 = 0.0000 g*
= 0.5000 = 14.5792 g*
= 1.0000 = 29.1584 g*
= 1.5000 = 43.7376 g*
TE?VAL 15@@3
29.1584 - 150.0000 .
= 1.5000 = -125.0124 g*
= 2.0000 = -241.6832 g*
= 2.5000 = -395.8540 g*
= 3.0000 = -587.5248 g*
:++ ?)Ci T>l"
(-2" ' 405.0137 (-4" -
.2 /2
2000 kg/m
kg
2,5 mD
5224,7291 kg
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(-2" ' 405.0137 (-4" -
(-2" ' 405.0137 (-4" -
2000 kg/m
2000 kg
EI
m 2,5 mD
10227,2727 kgm
+
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6811,8228 kgm
1775,2709 kg
24,7291 kg
5224,7291 kg
10227,2727 kgm
+
+
+
4
3 5m
4000
000 5000 kgm
4000
000 5000 kg
me"
$a"g
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4
3 5m
4000
000 5000 kgm
4000
000 5000 kg
me"
$a"g
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Ra-m A"la
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Ө4
0 V1
0 Ө1
0 V2
0 Ө2
0.6667 V3
0.6667 Ө3
-0.6667 V4
1.3333 Ө4
V4
0 Ө1
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0 Ө2
-0.666666667 Ө3
-0.6667 Ө4
0 V1
0 V2
-0.444444444 V3
0.4444 V4
V4
0.0000 Ө1
0.0000 Ө2
-0.6667 Ө3
-0.6667 Ө4
0.0000 V1
0.0000 V2
-0.4444 V30.4444 V4
-136.8056
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A B
266.6667 283.3333
59.2593 -59.2593
-62.9630 62.9630
262.9630 287.0370
412.0370
42.1875
3 = 35.1563
182.8125
-77.3438
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):il)+
V4
0.0000 Ө1
0.0000 Ө2
-0.6667 Ө3
-0.6667 Ө40.0000 V1
0.0000 V2
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-0.4444 V3
0.4444 V4
-179.7428
92.8190
-19.5437
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= 0
= 0 O
0
-179.74283030
92.81899385
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0
92.8190
0
-19.5437
0
-19.54367446
0
0
A B B
266.6667 283.3333 125.0000 125.0000 56.2500
-61.6529 61.6529 73.9835 -73.9835 3.0327
-3.6392 3.6392 -30.1243
205.0137 344.9863 195.3443 54.6557 29.1584
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540.3306 83.8141
300 ( - 2"
- 184.9588
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-
3000.0000 (-4" - 1500.0000
05( - 15"2
.402 /2
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3000.0000 (-4" - 5250.0000 (-575" '
3000.0000 (-4" - 5250.0000 (-575" '
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B D
125.0000 125.0000 56.2500 168.7500
20.8333 -20.8333 11.7188 -11.7188
-20.8333 20.8333 -25.7813 25.781342.1875 182.8125
125.0000 125.0000
167.1875
0.0000
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D
168.7500
-3.0327
30.1243
195.8416
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- 1500
D = ,% = 195.3443 = 195.3443
= 0.0000 = -554.6557 g
= 0.5000 = -1304.6557 g = 1.0000 = -2054.6557 g
= 1.5000 = -2804.6557 g
= 2.0000 = -3554.6557 g
= 2.5000 = 195.3443 g
= 0.0000 = 195.3443 g
= 0.0000 g
- 2000.0000
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D = ,% = 29.1584 = 29.1584
= 0.0000 = -970.8416 g
= 0.5000 = -1970.8416 g
= 1.0000 = -2970.8416 g
= 1.5000 = 29.1584 g
= 0.0000 = 29.1584 g
= 0.0000 = 29.1584 g = 0.0000 g
- 2000.0000
D = ,% = 29.1584 = -4970.8416
= 1.5000 = -5970.8416 g
= 2.0000 = -6970.8416 g
= 2.5000 = -7970.8416 g
= 3.0000 = -1970.8416 g
= 0.0000 = -1970.8416 g
= 0.0000 g
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3000.0000 (-75"540.3306 (-75" - -
3000.0000 (-75"
540.3306 (-75" - -
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- 2000.0000
0-4
D=
4-75
D=
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75-1052000.0000 D=
105-13
2000.0000 - 2000.0000 (-105" D=
.7,502 /2
.7,502 /2
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-90.3729 - 2000.0000 ,A
0.0000 = -90.37290.5000 = -1090.3729
1.0000 = -2090.3729
1.5000 = -3090.3729
2.0000 = -4090.3729
2.5000 = -5090.3729
3.0000 = -6090.3729
3.5000 = -7090.3729
4.0000 = -8090.3729
-90.3729 - 8000.0000 ' 405.0137 - 3000.00004.0000 = HHH
4.5000 = HHH
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5.0000 = HHH
5.5000 = HHH
6.0000 = HHH
6.5000 = HHH
7.0000 = HHH
7.5000 = HHH
-90.3729 - 8000.0000 ' 405.0137 - 3000.0000
7.5000 = HHH
8.0000 = HHH
8.5000 = HHH
9.0000 = HHH
9.5000 = HHH
10.0000 = HHH
10.5000 = HHH
-90.3729 - 8000.0000 ' 405.0137 - 3000.0000
10.5000 = HHH
11.0000 = HHH
11.5000 = HHH
12.0000 = HHH
12.5000 = HHH
13.0000 = HHH
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= -0.0452 = 2.0418
- 1500.0000 (-4" ,A 140=
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- 5250.0000 ' 540.3306 - 3000.0000 -
- 5250.0000 ' 540.3306 - 3000.0000 -
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-7.1236-3.1236 ,= 21697.4751
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2000.0000 (-75"
2000.0000 (-75" - 2000.0000
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