tugas 3 manto
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a
3
1. Menentukan Properties Sifat Penamp
E = 200000000
A = 0.1
I = 0.0013333333
Batang EIa 1
b 2
c 1.5
2. Menentukan Kondisi Batas (Boundar
Kondisi Batas
V1= 0
H1= 0
M1= 0
V2= 0
V3= 0
V4= 0
3. Menentukan Matriks Kekakuan E#em
Matriks $ransformasi
% = 0
1
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1
0
0
T1 = T2 = T3 = 0
0
0
3333333.33333
0
Ka = 0
3333333.33333
0
0
3333333.33333
0
0
Tt*K = 3333333.33333
0
0
3333333.33333
0
0
Tt*K*T = 3333333.33333
0
0
0
3333333.33333
0
0
3333333.33333
0
0
0
00
0
& Matriks da#am kekakuan 'atang (da#a
Batang a
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0
0
. )ektor Be'an *uar dan +aa ,epit -u
EI
3
2EI
4
1.5 EI
2
+aa ,epit pada 'atang 1
So1
So2
{So}1= So3
So4
So5
So6
Beban titi ei!a"en batang 1
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{#o}1=$Tt{So}1
1 0
0 1
0 0
{#o}1 = 0 0
0 0
0 0
%aa &
0
10.3125
{#e'}1 = 0
0
0
0
Be'an titik ekui/a#en menadi
{#e'}={#e'}1({#e'}2({#e'}3
0
10.3125
{#e'} = 0
0
0
0
0
3.645)33333
{#e'} = 0
$).333333333
0
15
#=#'(#e'
0
0
{#} = 0
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0
0
0
itungan Perpindaan
K+{,}={#}
13333333.3333 0 $10000000
0 -11111.1111 0
10000000 0 1-500000
0 266666.666- 0
0 0 -500000
0 0 0
5.-6230)E$00) 0 2.30-623E$00)
0 0.0000015) 0
$2.30-62E$00) 0 3.0-6231E$00)
0 $5.1136E$00- 0
2.30-623E$00) 0 $3.0-623E$00)
0 2.556)2E$00- 0
%aa &
,1,2
,3
,4 =
,5
,6
4eformasi gaa 'atang
/1 1/2 0
/3 0
/4 = 0
/5 0
/6 0
1 3333333.33333
2 0
3 0
4 = 3333333.333335 0
6 0
'atang a
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/1 1
/2 0
/3 0
/4 0 0
/5 0
/6 0
1 10000000
2 0
3 0
4 0 10000000
5 0
6 0
/1 1
/2 0
/3 0
/4 0 0
/5 0
/6 0
1 -500000
2 0
3 0
4 0 -500000
5 0
6 0
'atang b
'atang c
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b c
3 4 2 2
ang
5 = 6 k78m
p = 30 k7
E 4 EI 2 EI 12 EI33333333.33333333 1-----.---) ))))).))))) 44444.4444 14)14.)14)
10000000 533333.3333 266666.6666- 200000 100000
-500000 400000 200000 150000 -5000
!ondition"
n
k78m2
m2
m2
6 EI2
2 3
P
5
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0 0 0 0 0
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
0 0 $3333333.33333 0 0
14)14.)14)14)14) 44444.444444 0 $14)14.)14)1 44444.44444
44444.4444444445 1-----.----) 0 $44444.44444 ))))).))))
0 0 3333333.33333 0 0
$14)14.)14)14)14) $44444.44444 0 14)14.)14)1 $44444.44444
44444.4444444445 ))))).))))) 0 $44444.44444 1-----.---)
0 0 $3333333.33333 0 0
14)14.)14)14)14) 44444.444444 0 $14)14.)14)1 44444.44444
44444.4444444445 1-----.----) 0 $44444.44444 ))))).))))
0 0 3333333.33333 0 0
$14)14.)14)14)14) $44444.44444 0 14)14.)14)1 $44444.44444
44444.4444444445 ))))).))))) 0 $44444.44444 1-----.---)
0 0 $3333333.33333 0 0
14)14.)14)14)14) 44444.444444 0 $14)14.)14)1 44444.44444
44444.4444444445 1-----.----) 0 $44444.44444 ))))).))))
0 0 3333333.33333 0 0
$14)14.)14)14)14) $44444.44444 0 14)14.)14)1 $44444.44444
44444.4444444445 ))))).))))) 0 $44444.44444 1-----.---)
0 0 1 0 2
0 0 $3333333.33333 0 0
14)14.)14)14)14) 44444.444444 0 $14)14.)14)1 44444.44444
44444.4444444445 1-----.----) 0 $44444.44444 ))))).))))
0 0 13333333.3333 0 0
$14)14.)14)14)14) $44444.44444 0 114)14.)14) 155555.5556
44444.4444444445 ))))).))))) 0 155555.5556 -11111.1111
0 0 10000000 0 0
0 0 0 $100000 $2000000 0 0 200000 266666.666-
0 0 0 0 0
m koordiat #oka#"
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0 0 0 0 0
0 0 0 0 0
13333333.3333 0 $10000000
0 -11111.1111 0
K= 10000000 0 1-500000
0 266666.666- 0
0 0 -500000
0 0 0
ng
= 6 %
$4.6)-5 %
10.3125 %
$2.)125
3 $12.1)-5
$6.66666666- %
6.66666666- %
$10 $10
# = 30
$15 %
15 %
$15
$15
2
0
$2.)125
= $12.1)-5 %
0
$4.6)-5
10.3125 %
7%1 =
7%2 =
781 =
782=
7%2 =
7%3 =
782 =78
3 =
7%3 =
7%4 =
783 =
784 =
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0 0 0 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 0
$6.666666666- 0
0 0
6.666666666- $15
0 0
0 15
0 0
3.645)333333 3.645)333333
0 = 0
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$).3333333333 $).3333333333
0 0
15 15
0 0 0 ,1
266666.66666666- 0 0 ,2
0 $-500000 0 ,3 =
33333.333333333 0 200000 ,4
0 -500000 0 ,5
200000 0 400000 ,6
0 2.30-6E$00) 0
$5.1136363636E$00- 0 2.556)1)2E$00-
0 3.0-62E$00) 0
1.36363636364E$006 0 $6.)1)1)2E$00-
0 1.02564E$00- 0
$6.)1)1)1)1)2E$00- 0 2.)4001E$006
0 %1.3226-4005-E$005 9a:
0 %
$2.34552556)2E$005 9a:
0 %
4.22-62-)40E$005 9a:
0 0 0 0 01 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
0 0 $3333333.33333 0 0
14)14.)14)14)14) 44444.444444 0 $14)14.)14)1 44444.44444
44444.4444444445 1-----.----) 0 $44444.44444 ))))).))))
0 0 3333333.33333 0 0$14)14.)14)14)14) $44444.44444 0 14)14.)14)1 $44444.44444
44444.4444444445 ))))).))))) 0 $44444.44444 1-----.---)
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0 0 0 0 0
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
0 0 $10000000 0 0
100000 200000 0 $100000 200000
200000 533333.33333 0 $200000 266666.666-
0 0 10000000 0 0
$100000 $200000 0 100000 $200000
200000 266666.6666- 0 $200000 533333.3333
0 0 0 0 0
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
0 0 $-500000 0 0
-5000 150000 0 $-5000 150000
150000 400000 0 $150000 200000
0 0 -500000 0 0
$-5000 $150000 0 -5000 $150000
150000 200000 0 $150000 400000
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1
0
0
Tt= 0
0
0
10000000
0
Kb = 0
10000000
0
0
10000000
0
0
Tt*K = 10000000
0
0
10000000
0
0
Tt*K*T = 10000000
0
0
1
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
$10000000 0 0 0 0
0 $100000 200000 0 0
0 $200000 266666.66666666- 0 0
1-500000 0 0 $-500000 0
0 1-5000 $50000 0 $-50000 $50000 33333.333333333 0 $150000
-500000 0 0 -500000 0
Batang b
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0 $-5000 $150000 0 -5000
0 150000 200000 0 $150000
0 0 0
266666.66666- 0 0
0 $-500000 0
33333.333333 0 200000
0 -500000 0
200000 0 400000
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0 0 0
$2.)125 $2.)125 0
$12.1)-5 = $12.1)-5 0
0 0 1
$4.6)-5 $4.6)-5 0
10.3125 10.3125 2
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0
3.645)333333
0
$).3333333333
0
15
0 00 0
0 = 0
0 0
0 0
1.3226-4E$005 1.3226-4005-E$005
0 0 0
0 2.)125 3.4312)5511
0 ( 12.1)-5 = 13.4250-102
0 0 00 4.6)-5 4.06)-144)
1.3226-4E$005 $10.3125 $-.)3-35-5
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0 0
0 0
1.3226-4E$005 = 1.3226-4005-E$005
0 0
0 0
$2.345526E$005 $2.34552556)2E$005
0 0 0
0 10 ).034)3665
1.3226-4E$005 ( 6.666666666- = -.)3-35-55
0 0 0
0 10 11.0651634
$2.345526E$005 $6.666666666- $15.4634233
0 0
0 0
$2.345526E$005 = $2.34552556)2E$005
0 0
0 0
4.22-62)E$005 4.22-62-)40E$005
0 0 0
0 15 1).)65)55)2
$2.345526E$005 ( 15 = 15.4634233
0 0 0
0 15 11.1341441)
4.22-62)E$005 $15 0
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0 0 0 0 0
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
0 0 $10000000 0 0
100000 200000 0 $100000 200000
200000 533333.3333333 0 $200000 266666.6666666-
0 0 10000000 0 0
$100000 $200000 0 100000 $200000
200000 266666.666666- 0 $200000 533333.33333333
0 0 $10000000 0 0
100000 200000 0 $100000 200000
200000 533333.3333333 0 $200000 266666.6666666-
0 0 10000000 0 0
$100000 $200000 0 100000 $200000
200000 266666.666666- 0 $200000 533333.33333333
0 0 $10000000 0 0
100000 200000 0 $100000 200000
200000 533333.3333333 0 $200000 266666.6666666-
0 0 10000000 0 0
$100000 $200000 0 100000 $200000
200000 266666.666666- 0 $200000 533333.33333333
0 2 3 0 4
0
0
0
0
0
0
0
150000200000
0
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$150000
400000
+aa ,epit pada 'atang 2
0
$10
{So}2= $6.666666666- %
0
$10
6.666666666- %
Beban titi ei!a"en batang 2
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{#o}2=$Tt{So}2
1 0 0 0
0 1 0 0
0 0 1 0
{#o}2 = 0 0 0 1
0 0 0 0
0 0 0 0
%aa &
0
$6.666666666-
{#e'}2 = 0
6.666666666-
0
0
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%
% $
13.4
3
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%
%
%
%
(
3 % 3%
3.43 3.43).0
(
$
3 % 3%
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-500000 0 0
0 -5000 150000
Kc = 0 150000 400000
-500000 0 0
0 $-5000 $150000
0 150000 200000
-500000 0 0
0 -5000 150000
0 150000 400000
Tt*K = -500000 0 0
0 $-5000 $150000
0 150000 200000
-500000 0 0
0 -5000 150000
0 150000 400000
Tt*K*T = -500000 0 0
0 $-5000 $150000
0 150000 200000
3 0 4
Batang c
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0 0 0 0 1
0 0 $10 $10 0
0 0 $6.66666- = $6.666666- 2
0 0 0 0 3
1 0 $10 $10 0
0 1 6.666666- 6.666666- 4
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$$
15.46
-.)4
0
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(
4 % 2 % 2 %
4.0- 11.
1).)- 1).)-
11.13
((
(
$$
4 % 2 % 2 %
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$-500000 0 0
0 $-5000 150000
0 $150000 200000
-500000 0 0
0 -5000 $150000
0 $150000 400000
$-500000 0 0
0 $-5000 150000
0 $150000 200000
-500000 0 0
0 -5000 $150000
0 $150000 400000
$-500000 0 0
0 $-5000 150000
0 $150000 200000
-500000 0 0
0 -5000 $150000
0 $150000 400000
5 0 6
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+aa ,epit pada 'atang 3
0
$15
{So}3= $15 %%
0
$15
15 %%
Be'an titik eki/a#en 'atang 3
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{#o}3=$Tt{So}3
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
{#o}3 = 0 0 0 1 0
0 0 0 0 1
0 0 0 0 0
%aa &
0
0
{#e'}3 = 0
$15
0
15
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M
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4
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0 0 0 3
0 $15 $15 0
0 $15 = $15 4
0 0 0 5
0 $15 $15 0
1 15 15 6
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