L = y+z = 8 +4= 12 m
30
A B C P = 5 t L = y+z = 8+4= 12 m A = 100 cm 2 E = 300 t/cm 2 α =60 o P= x = 5 t cos 60 = 1 2 AB AC AC = 6 cos60
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Transcript of L = y+z = 8 +4= 12 m
A B
CP = 5 t L = y+z = 8+4= 12 m
A = 100 cm2
E = 300 t/cm2
α =60o
P= x = 5 t
cos 60 = 12AB
AC
AC = 6cos60
AC= 12 m
MATRIK KEKAKUAN ELEMEN
ELEMEN 1 (di pilih nodal i=A, dan j=C )
L = 1200 cm
[Kl1] = AEL [10−100000
−10100000 ]
[Kl1] = 100X3001200 [10−100000
−10100000 ]
[Kl1]=
[T1]=
[T1]=
[T1]t =
[Kg1] = [T1]t [Kl1] [T1]
[Kg1]=
25 0 -25 0 0 0 0 0
-25 0 25 0 0 0 0 0
cos60
sin 60 0 0
-sin60
cos 60 0 0
0 0cos60
sin60
0 0-sin60
cos60
0,5 0,866 0 0 -
0,866 0,5 0 0
0 0 0,50,866
0 0-
0,866 0,5 0,500
-0,866 0 0
0,866 0,500 0 0
0 0 0,500-
0,866 0 0 0,866 0,500
UA VA UB VB
6,25010,82
5-
6,250
-10,82
5 UA
10,825
18,750
-10,82
5
-18,75
0 VA
-6,250
-10,82
5 6,25010,82
5 UB-
10,825
-18,75
010,82
518,75
0 VB
Y
Xi = BY
Xj=C
ELEMEN 2 ( dipilih nodal i=B, dan j=C )
L = 1200 cm
[Kl2] = AEL [10−100000
−10100000 ]
[Kl2] = 100X3001200 [10−100000
−10100000 ]
[Kl2] =25 0 -25 0 0 0 0 0 -25 0 25 0 0 0 0 0
cos120
sin120 0 0
-sin120
cos120 0 0
0 0cos120
sin120
0 0-sin120
cos120
[T2]=
[T2]=
[T2]t =
[Kg2] = [T2]t [Kl2] [T2]
[Kg2] =
ELEMEN 3 (pilih nodal i=A, dan j=B )
L = 12 m
[Kl3] = AEL [10−100000
−10100000 ]
-0,500 0,866 0 0
-0,866
-0,500 0 0
0 0-
0,5000,866
0 0-
0,866
-0,500
-0,500
-0,866 0 0
0,866-
0,500 0 0
0 0-
0,500-
0,866
0 0 0,866-
0,500
UB VB UC VC
6,250
-10,82
5-
6,25010,82
5 UB-
10,825
18,750
10,825
-18,75
0 VB
-6,250
10,825 6,250
-10,82
5 UC
10,825
-18,75
0
-10,82
518,75
0 VC
[Kl3] = 100X3001200 [10−100000
−10100000 ]
[Kl3] =
[T3]=
[T3]=
[T3]t =
[Kg3] = [T3]t [Kl3] [T3]
[Kg3] =
Overal stiffness matrix
25 0 -25 0 0 0 0 0
-25 0 25 0 0 0 0 0
cos 0 sin 0 0 0 -sin60
cos60 0 0
0 0 cos 0 sin 0
0 0-sin0 cos 0
1 0 0 0 0 1 0 0 0 0 1 0 0 0 1
1 0 0 0 0 1 0 0 0 0 1 0 0 0 1
UA VA UB VB25 0 -25 0 UA0 0 0 0 VA
-250 025,00
0 0 UB0 0 0 0 VB
UA VA UB VB UC VC
FA 31,25010,82
5 -25 0 -6,250
-10,82
5 UA
GA 10,82518,75
0 0 0-
10,825
-18,75
0 VA
FB=
-25 0 31,250-
10,825 -6,25010,82
5 UB
GB 0 0-
10,825 18,750 10,825
-18,75
0 VB
FC -6,250
-10,82
5 -6,250 10,825 12,500 0,000 UC
GC-
10,825
-18,75
0 10,825-
18,750 0,00037,50
0 VC
UA VA UB VB UC VC
FA 31,25010,82
5 -25 0 -6,250
-10,82
5 0
GA 10,82518,75
0 0 0-
10,825
-18,75
0 0
0=
-25 0 31,250-
10,825 -6,25010,82
5 UB
GB 0 0-
10,825 18,750 10,825
-18,75
0 0
5 -6,250
-10,82
5 -6,250 10,825 12,500 0,000 UC
0-
10,825
-18,75
0 10,825-
18,750 0,00037,50
0 VC
REARRANGEMENT
UC VC UB VB UA VA
5 12,500 0,000 -6,250 10,825 -6,250
-10,825 UC
0= 0,000 37,500 10,825
-18,750
-10,825
-18,750 VC
0 -6,250 10,825 31,250
-10,825
-25,000 0,000 UB
GB 10,825
-18,750
-10,825 18,750 0,000 0,000 0
FA -6,250
-10,825
-25,000 0,000 31,250 10,825 0
GA-
10,825
-18,750 0,000 0,000 10,825 18,750 0
Displacements and reactions
5=
12,500 0,000 -6,250 UC0 0,000 37,500 10,825 VC0 -6,250 10,825 31,250 UB
UC 12,500 0,000 -6,250 -1 5VC = 0,000 37,500 10,825 0UB -6,250 10,825 31,250 0
UC 0,090 -0,006 0,020 5VC = -0,006 0,030 -0,012 0UB 0,020 -0,012 0,040 0
UC0,45
0
VC =
-0,02
9
UB0,10
0
FA -6,250 -10,825 - 0,45
25,000 0
GA = -10,825 -18,750 0,000
-0,02
9
GB 10,825 -18,750-
10,825 0,10
0
MEMBER FORCES
Elemen 1 (nodal i=A, dan j= c)
= [T1] [Kg1] { U1}
fA 0,500
0,866 0 0 6,250 10,825
-6,250
-10,82
5 0
gA =
-0,866
0,500 0 0 10,825 18,750
-10,82
5
-18,75
0 0fC 0 0
0,500
0,866 -6,250
-10,825 6,250
10,825
0,450
gC 0 0
-0,86
60,500
-10,825
-18,750
10,825
18,750
-0,029
fA -5gA = 0fC 5gC 0
FA -5
GA =-
4,33GB 4,33
fAgAfCgC
Elemen 2 ( nodal i=B, dan j=C)
= [T2] [Kg2] { U2}
fB
-0,500
0,866 0 0 6,250
-10,82
5-
6,25010,82
5 0,1
gB =
-0,866
-0,500 0 0
-10,82
518,75
010,82
5
-18,75
0 0
fC 0 0
-0,500
0,866
-6,250
10,825 6,250
-10,82
5 0,450
gC 0 0
-0,866
-0,500
10,825
-18,75
0
-10,82
518,75
0
-0,029
fB 5gB = 0fC -5gC 0
elemen 3 ( nodal i=A, dan j=B )
= [T2] [Kg2] { U2}
fA 1 0 0 0 25 0 -25 0 0gA = 0 1 0 0 0 0 0 0 0
fBgBfCgC
fBgBfCgC
A
C
B
P = 5 t
5 t
4,33 t
4,33 t
5 t
5 t
3 t
P1 = 3 t
P2 = 9 t
2
4
5 73
B C
fB 0 0 1 0 -25 0 25 0 0,1gB 0 0 0 1 0 0 0 0 0
fB -3gB = 0fC 3gC 0
HASIL ANALIS
P3 = 5 t
1 6A D E
3
3
A = 100 cm2
E = 300 t/m2
P1= 3 t
P2= 9 t
P3= 5 t
AB = 1/2ADcos60
AD = 1,5cos60
AD = 3M
AD= BD =DC =CE
MATRIK KEKAKUAN ELEMEN
L = 300 cm
A = 100 cm2
E = 300 t/m2
[Kl1] = AEL [10−100000
−10100000 ]
[Kl1] = 100X300300 [10−100000
−10100000 ]
[Kl1] =
[T1] =
[T1] =
[T1]t =
[Kg1] = [T1]t [Kl1] [T1]
[Kg1] =
ELEMEN 2 ( NODAL i= A, dan j= B )
L = 300 cm
100 0 -100 0 0 0 0 0
-100 0 100 0 0 0 0 0
cos 0 sin 0 0 0 -sin0 cos 0 0 0
0 0 cos 0sin0
0 0-sin0
cos0
1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
UA VA UD VD100 0 -100 0 UA0 0 0 0 VA
-100 0 100 0 UD0 0 0 0 VD
[Kl2] = AEL [10−100000
−10100000 ]
[Kl2] = 100x300300 [10−100000
−10100000 ]
[Kl2] =
[T2] =
[T2] =
[T2]t =
[Kg2] = [T2]t [Kl2] [T2]
[Kg2] =
100 0 -100 0 0 0 0 0
-100 0 100 0 0 0 0 0
cos60
sin60 0 0
-sin60
cos60 0 0
0 0cos60
sin60
0 0-sin60
cos60
0,5 0,866 0 0 -
0,866 0,500 0 0
0 0 0,50,866
0 0-
0,866 0,5 0,5-
0,866 0 0 0,866 0,5 0 0
0 0 0,5-
0,866 0 0 0,866 0,5
UA VA UB VB
2543,30
1 -25
-43,30
1 UA
43,301 75
-43,30
1 -75 VA
-25
-43,30
1 2543,30
1 UB-
43,301 -75
43,301 75 VB
ELEMEN 3 ( nodal i= D dan j=B )
L = 300 cm
[Kl3] = AEL [10−100000
−10100000 ]
[Kl3] = 100x300300 [10−100000
−10100000 ]
[Kl3] =
[T3] =
100 0 -100 0 0 0 0 0
-100 0 100 0 0 0 0 0
cos120
sin120 0 0
-sin120
cos120 0 0
0 0cos120
sin120
0 0-sin120
cos120
[T3] =
[T3]t =
[Kg3] = [T3]t [Kl3] [T3]
[Kg3] =
ELEMEN 4 (nodal i=B, dan j=C )
L = 300 cm
[Kl4] = AEL [10−100000
−10100000 ]
-0,5 0,866 0 0 -
0,866-
0,500 0 0 0 0 -0,5 0,866
0 0-
0,866 -0,5 -0,5
-0,866 0 0
0,866 -0,5 0 0
0 0 -0,5-
0,866 0 0 0,866 -0,5
UD VD UB VB
25
-43,301 -25
43,301 UD
-43,30
1 7543,30
1 -75 VD
-2543,301 25
-43,30
1 UB
43,301 -75
-43,30
1 75 VB
X
Xi=D
j=C
YY
[Kl4] = 100x300300 [10−100000
−10100000 ]
[Kl4] =
[T4] =
[T4] =
[T4]t =
[Kg4] = [T4]t [Kl4] [T4]
[Kg4] =
ELEMEN 5 ( NODAL i= D, dan j= C )
L = 300 cm
100 0 -100 0 0 0 0 0
-100 0 100 0 0 0 0 0
cos 0 sin 0 0 0 -sin0 cos 0 0 0
0 0 cos 0sin0
0 0-sin0
cos0
1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
UB VB UC VC100 0 -100 0 UB0 0 0 0 VB
-100 0 100 0 UC0 0 0 0 VC
i=D
[Kl5] = AEL [10−100000
−10100000 ]
[Kl5] = 100x300300 [10−100000
−10100000 ]
[Kl5] =
[T5] =
[T5] =
100 0 -100 0 0 0 0 0
-100 0 100 0 0 0 0 0
cos60
sin60 0 0
-sin60
cos60 0 0
0 0cos60
sin60
0 0-sin60
cos60
0,5 0,866 0 0 -
0,866 0,500 0 0
0 0 0,50,866
0 0-
0,866 0,5
0,5-
0,866 0 0 0,866 0,5 0 0
0 0 0,5-
0,866 0 0 0,866 0,5
YY
X X0ºi=
Dj=E
[T5]t =
[Kg5] = [T2]t [Kl2] [T2]
[Kg5] =
ELEMEN 6 ( nodal i=D, dan j=E )
L = 300 cm
[Kl6] = AEL [10−100000
−10100000 ]
UD VD UC VC
2543,30
1 -25
-43,30
1 UD
43,301 75
-43,30
1 -75 VD
-25
-43,30
1 2543,30
1 UC-
43,301 -75
43,301 75 VC
Xi=E
Y
y
Xj=C
[Kl6] = 100x300300 [10−100000
−10100000 ]
[Kl6] =
[T6] =
[T6] =
[T6]t =
[Kg6] = [T4]t [Kl4] [T4]
[Kg6] =
ELEMEN 7 ( NODAL i= E, dan j=C )
L = 300 cm
100 0 -100 0 0 0 0 0
-100 0 100 0 0 0 0 0
cos 0 sin 0 0 0 -sin0 cos 0 0 0
0 0 cos 0sin0
0 0-sin0
cos0
1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
UD VD UE VE100 0 -100 0 UD0 0 0 0 VD
-100 0 100 0 UE0 0 0 0 VE
y
[Kl7] = AEL [10−100000
−10100000 ]
[Kl7] = 100x300300 [10−100000
−10100000 ]
[Kl7] =
[T7] =
[T7] =
[T7]t =
100 0 -100 0 0 0 0 0
-100 0 100 0 0 0 0 0
cos120
sin120 0 0
-sin120
cos120 0 0
0 0cos120
sin120
0 0-sin120
cos120 -0,5 0,866 0 0
-0,866
-0,500 0 0
0 0 -0,5 0,866
0 0-
0,866 -0,5
-0,5-
0,866 0 0 0,866 -0,5 0 0
0 0 -0,5-
0,866 0 0 0,866 -0,5
[Kg7] = [T7]t [Kl7] [T7]
[Kg7] =
Overal stiffness matrix
UA VA UB VB UC VC UD VD UE VE
FA125 43,30
1 -25-
43,301
0 0 -100 0 0 0 UA
GA43,301 75 -43,301 -75 0 0 0 0 0 0 VA
FB-25
-43,301
150 0 -100 0 -25 43,301 0 0
UB
GB
-43,301
-75 0 150 0 0 43,301 -75 0 0
VB
FC =0 0 -100 0 150
-86,603
-25 43,301 -25 43,30
1 UC
GC0 0 0 0
-86,603
150 43,301 -75 43,30
1 -75 VC
FD-100 0 -25 43,30
1 -25 43,301 250
-86,60
3-100 0
UD
GD0 0 43,301 -75 43,30
1 -75-
86,603
150 0 0 VD
FE0 0 0 0 -25 43,30
1 -100 0 125-
43,301 UE
GE0 0 0 0 43,30
1 -75 0 0-
43,301
75 VE
UB VB UC VC UD VD UE VE UA VA
3 150 0 -100 0 -25 43,30 0 0 -25 - UB
UE VE UC VC
25
-43,301 -25
43,301 UE
-43,30
1 7543,30
1 -75 VE
-2543,301 25
-43,30
1 UC
43,301 -75
-43,30
1 75 VC
143,30
1
0 0 150 0 043,301 -75 0 0
-43,301 -75 VB
0-100 0 150
-86,60
3-25 43,30
1 -25 43,301 0 0
UC
-9 0 0 -86,603 150 43,30
1 -75 43,301 -75 0 0 VC
0 =-25 43,30
1 -25 43,301 250
-86,603
-100 0 -100 0UD
-543 -75 43,30
1 -75-
86,603
150 0 0 0 0VD
00 0 -25 43,30
1 -100 0 125-
43,301
0 0UE
GE0 0 43,30
1 -75 0 0-
43,301
75 0 00
FA-25
-43,301
0 0 -100 0 0 0 125 43,301 0
GA-
43,301 -75 0 0 0 0 0 0 43,301 75 0
REARRANGEMENT
3 150 0 -100 0 -25 43,301 0 -1 UB
0 0 150 0 0 43,301 -75 0 VB
0-100 0 150
-86,60
3-25 43,30
1 -25 UC
-9 =0 0
-86,603
150 43,301 -75 43,3
01 VC
0-25 43,3
01 -25 43,301 250
-86,60
3-100
UD
-5
43,301 -75 43,3
01 -75-
86,603
150 0 VD
0 0 0 -25 43,301 -100 0 125 UE
UB 0,045
-0,014
0,045 0,009
0,005
-0,026
0,010 3
VB-
0,0140,015
-0,014 0,002
-0,003 0,015
-0,006 0
UC 0,045
-0,014
0,055 0,014
0,005
-0,026
0,010 0
VC = 0,0090,002
0,014 0,018
-0,003 0,002
-0,006 -9
UD 0,005
-0,003
0,005
-0,003
0,010 0,000
0,010 0
VD-
0,0260,015
-0,026 0,002
0,000 0,030
-0,006 -5
UE 0,010
-0,006
0,010
-0,006
0,010
-0,006
0,020 0
UB0,187
0
VB
-0,133
3
UC0,135
0
VC =
-0,147
4
UD0,041
0
VD
-0,242
9
UE0,110
8
0,1870-
0,1333
FA-25
-43,301
0 0 -100 0 0 0,1350
GA = -43,301 -75 0 0 0 0 0 -
0,1474
0 0 43,301 -75 0 0
-43,301 0,0410
-0,24290,1108
FA-3 =RHA
GA =1,902RFA
GE12,098
RFE
MEMBER FORCES
Elemen 1 ( nodal i=A, dan j=D )
= [T1] [Kg1] { U1}
fA 1 0 0 0 25 -43 -25 43 0gA = 0 1 0 0 -43 75 43 -75 0fD 0 0 1 0 -25 43 25 -43 0,041
gD 0 0 0 1 43 -75 -43 75 -
0,243
fA-
11,544
gA=
20
fD 11,544
gD -20
Elemen 2 ( nodal i=A, dan j=B )
= [T2] [Kg2] { U2}
fA 0,5
0,866 0 0 25
43,301 -25
-43,301 0
gA
= -0,86
0,5 0 0 43,301 75 -43,30
-75 0
fAgAfDgD
fAgAfBgB
6 1
fB 0 0 0,5
0,866 -25
-43,301 25
43,301
0,187
gB 0 0
-0,866 0,5
-43,301 -75
43,301 75
-0,133
fA
2,196
gA
=0
fB
-2,196
gB 0
Elemen 3 ( nodal i=D, dan j=B )
= [T3] [Kg3] { U3}
fD -0,50,866 0 0 25 -43,301 -25
43,301 0,041
gD=
-0,866
-0,5 0 0 -43,301 75
43,301 -75
-0,243
FB 0 0 -0,50,866 -25 43,301 25
-43,30
1 0,187
gB0 0
-0,866
-0,5 43,301 -75
-43,30
1 75-
0,133
fD -2,196
gD = 0fB 2,196gB 0
Elemen 4 ( nodal i=B, dan j=C )
fDgDfBgB
fBgBfCgC
= [T4] [Kg4] { U4}
fB 1 0 0 0 100 0 -100 0 0,187gB
= 0 1 0 0 0 0 0 0 -0,133fc 0 0 1 0 -100 0 100 0 0,135gc 0 0 0 1 0 0 0 0 -0,147
fB 5,196
gB
=0
fc
-5,196
gc 0
Elemen 5 ( nodal i=D, dan j=C )
= [T5] [Kg5] { U5}
fD0,5
0,866 0 0 25,000
-43,30
1
-25,00
043,30
1
0,041
gD
=
-0,866 0,5 0 0 -43,301
75,000
43,301
-75,00
0
-0,243
fc 0 0 0,50,866 -25,000
43,301
25,000
-43,30
1
0,135
gc0 0
-0,866 0,5 43,301
-75,00
0
-43,30
175,00
0
-0,147
fD -1,789
gD=
-3,098
fc 1,789gc 3,098
fDgDfCgC
Elemen 6 ( nodal i=D, dan j=E )
= [T6] [Kg6] { U6}
fD 1 0 0 0 100 0 -100 0 0,041gD
= 0 1 0 0 0 0 0,00 0 -0,243fE 0 0 1 0 -100 0 100 0 0,111gE 0 0 0 1 0 0 0 0 0
fD-
6,9848
gD=
0
fE6,98483
gE 0
Elemen 7 ( nodal i=E, dan j=C )
= [T7] [Kg7] { U7}
fE -0,50,866 0 0 25,00
-43,30
-25,00 43,30 0,111
gE=
-0,866 -0,5 0 0 -43,30 75,00 43,30
-75,00 0
fc 0 0 -0,50,866 -25,00 43,30 25,00
-43,30 0,135
gc0 0
-0,866
-0,5 43,30
-75,00
-43,30 75,00
-0,147
fE13,9
70gE
=0
fc
-13,9
70gc 0
fDgDfEgE
fEgEfCgC
q = 5 t/m
AB
CP= 2 t
D
HASIL ANALISIS
A= 100 cm
I= 5000 cm4
E = 2100 t/cm2
P = 8 t
q= 5 t/m
MATRIK KEKAKUAN ELEMEN
Elemen 1 ( nodal i= A dan j=B )
L = 400 cm
A = 100 cm
I =5000 cm4
E = 2100 t/cm2
525 0 0 -525 0 00 2 393,750 0 -1,969 393,750
KL1 = 0393,750 105000 0
-393,750 52500
-525 0 0 525 0 0
0-
1,969-
393,750 0 1,969 -393,750
0393,750 52500 0
-393,750 105000
cos120
sin120 0 0 0 0
-sin120
cos120 0 0 0 0
T 1=0 0 1 0 0 0
0 0 0 cos120
sin120 0
0 0 0 -sin cos 0
AE/L 0 0 -AE/L 0 0
0 12EI/L3 6EI/L2 0
-12EI/L3
6EI/L2
KL1=
0 6EI/L2 4EI/L 0 -6EI/L2 2EI/L
-AE/L 0 0 AE/L 0 0
0-
12EI/L3
-6EI/L2 0 12EI/
L3-
6EI/L2
0 6EI/L2 2EI/L 0 -6EI/L2 4EI/L
120 1200 0 0 0 0 1
1,000 0,000 0 0 0 00,000 1,000 0 0 0 0
T1T= 0 0 1 0 0 00 0 0 1,000 0,000 00 0 0 0,000 1,000 00 0 0 0 0 1
[Kg7] = [T7]t [Kl7] [T7]
UA VA ΦA UB VB ѲB
525,00 0,00 0,00
-525,0
0 0,00 0,00 0,00 1,97 393,75 0,00 -1,97 393,75
Kg = 0,00
393,75
105000,00 0,00
-393,7
552500,0
0 -
525,00 0,00 0,00
525,00 0,00 0,00
0,00 -1,97 -393,75 0,00 1,97 -393,75
0,00393,7
552500,0
0 0,00
-393,7
5105000,
00
1,000 0,000 0 0 0 00,000 1,000 0 0 0 0
T1= 0 0 1 0 0 00 0 0 1,000 0,000 00 0 0 0,000 1,000 00 0 0 0 0 1
![IAC 8/8/12 Revenue[701] Ch 86, p.1](https://static.fdokumen.com/doc/165x107/6324d2c4051fac18490cf637/iac-8812-revenue701-ch-86-p1.jpg)
