70
4.2.5 Langkah Kelima : Menghitung Tegangan-Tegangan Yang Terjadi
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⎭ ⎪
⎪ ⎬
⎪ ⎪
⎫
3000 mm 500 mm
400 kN
500 mm 500 mm
500 mm 500 mm
500 mm 500 mm
500 mm
500 mm
500 mm
500 mm
500 mm 1
2 3
4 5
7 8
9 10
11
6 12
13 14
400 kN
15 16
17 18
19 21
22 23
24 25
20 26
27 28
29 30
31 32
33 35
36 37
38 39
34 40
41 42
43 44
45 46
47 48
49 A
A B
B C
C D
D E
E F
F
Gambar 4.4 Pengambilan nilai tegangan pada potongan melintang A,B,C,D,E,F
Universitas Sumatera Utara
71
4.2.5.1 Tegangan pada potongan A---A Elemen 1,3,5,7,9,11
Pada jendela microsoft excel 2010:
Elemen 1
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27813186.8
8343956.044 -0.66667
0.666667 d1x
-1.67319E-07 [ σ ] =
8343956.04 27813186.81
-0.66667 0.666667
d1y 7.03675E-08
0 9734615 -0.66667 -0.66667
0.666667 0.666667 d2x
-1.28488E-07 d2y
2.41837E-07 d3x
-1.23455E-07 d3y
7.06207E-08
σ
x 2.58875E-08
0.721423
σ
y 1.68752E-10
0.220698 kNm2
σ
xy 1.43556E-07
1.397458 m=3
i=1 j=2
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Universitas Sumatera Utara
72
Elemen 3
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27813187
8343956 -0.66667
0.666667 d3x
-1.28488E-07 [ σ ] =
8343956 27813187 -0.66667
0.666667 d3y
2.41837E-07 9734615
-0.66667 -0.66667 0.666667 0.666667
d4x -1.23455E-07
d4y 7.06207E-08
d5x -1.03921E-07
d5y 5.46972E-07
σ
x 3.36E-09
1.790671
σ
y 2.03E-07
5.685843 kNm2
σ
xy -9.8E-08
-0.95172 m=5
i=3 j=4
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Universitas Sumatera Utara
73
Elemen 5
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27813187 8343956
-0.66667 0.666667
d5x -1.0392E-07
[ σ ] = 8343956 27813187
-0.66667 0.666667
d5y 5.46972E-07
0 9734615 -0.66667 -0.66667
0.666667 0.666667 d6x
-7.8364E-08 d6y
1.2231E-07 d7x
-5.0937E-08 d7y
7.39768E-07
σ
x 1.7E-08
1.546348
σ
y 1.29E-07
3.717027 kNm2
σ
xy -2.5E-07
-2.4121 m=7
i=5 j=6
y
x
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1−� 2
Universitas Sumatera Utara
74
Elemen 7
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27813187 8343956
-0.66667 0.666667
d7x -5.09369E-08
[ σ ] = 8343956 27813187
-0.66667 0.666667
d7y 7.39768E-07
0 9734615 -0.66667 -0.66667
0.666667 0.666667 d8x
-1.01412E-07 d8y
1.25217E-07 d9x
3.01403E-07 d9y
1.36595E-06
σ
x -3.4E-08
2.547297
σ
y 4.17E-07
11.32994 kNm2
σ
xy -1.7E-07
-1.70169 m=9
i=7 j=8
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Universitas Sumatera Utara
75
Elemen 9
m = 11
0.5 m
i = 9 0.5 m
j = 10 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27813187 8343956
-0.66667 0.666667
d9x 3.01403E-07
[ σ ] = 8343956 27813187
-0.66667 0.666667
d9y 1.36595E-06
0 9734615 -0.66667 -0.66667
0.666667 0.666667 d10x
4.67537E-08 d10y
3.45144E-08 d11x
1.91169E-06 d11y
2.54742E-06
σ
x -1.7E-07
1.850344
σ
y 7.88E-07
20.49042 kNm2
σ
xy 1.86E-07
1.809679 y
x
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1−� 2
Universitas Sumatera Utara
76
Elemen 11
m = 13
0.5 m
i = 11 0.5 m
j = 12 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27813187 8343956
-0.66667 0.666667
d11x 1.91169E-06
[ σ ] = 8343956 27813187
-0.66667 0.666667
d11y 2.54742E-06
0 9734615 -0.66667 -0.66667
0.666667 0.666667 d12x
1.05247E-06 d12y
-2.97732E-07 d13x
8.15901E-06 d13y
3.63921E-06
σ
x -5.7E-07
-9.85845
σ
y 7.28E-07
15.46465 kNm2
σ
xy 2.27E-06
22.07924 y
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Universitas Sumatera Utara
77
4.2.5.2 Tegangan σx pada potongan B—B Elemen
5,4,6,8,10,15
Pada jendela microsoft excel 2010:
Elemen 2
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
-0.5 0.5
1 0.75
-0.5 -0.5
0.5 0.5
m
1 0.3
[ D ] = 25332084.4
0.3 1
Mpa 0.91
0.35 27837455.4
8351237 -0.66667
0.666667 d2x
-1.6732E-07 [ σ ] =
8351236.62 27837455 -0.66667 -0.66667
0.666667 d2y
7.03675E-08 9743109
-0.66667 -0.66667 0.666667 0.666667
d4x -1.2346E-07
d4y 7.06207E-08
d3x -1.2849E-07
d3y 2.41837E-07
σ
x 2.92E-08
2.700244
σ
y 2.26E-07
6.531554 kNm2
σ
xy 2.61E-08
0.253869 m=3
i=1 j=2
y
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Universitas Sumatera Utara
78
Elemen 4
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25332084.4
0.3 1
Mpa 0.91
0.35 27837455.38
8351237 -0.66667
0.666667 d4x
-1.2346E-07 [ σ ] =
8351236.615 27837455 -0.66667
0.666667 d4y
7.06207E-08 9743109
-0.66667 -0.66667 0.666667 0.666667
d6x -7.8364E-08
d6y 1.2231E-07
d5x -1.0392E-07
d5y 5.46972E-07
σ
x 3.01E-08
3.488905
σ
y 3.18E-07
9.091315 kNm2
σ
xy 4.75E-08
0.462622 m=5
i=3 j=4
y
x
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Universitas Sumatera Utara
79
Elemen 6
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25332084.4
0.3 1
Mpa 0.91
0.35 27837455.38
8351237 -0.66667
0.666667 d6x
-7.8364E-08 [ σ ] =
8351236.615 27837455 -0.66667
0.666667 d6y
1.2231E-07 9743109
-0.66667 -0.66667 0.666667 0.666667
d8x -1.0141E-07
d8y 1.25217E-07
d7x -5.0937E-08
d7y 7.39768E-07
σ
x -1.5E-08
3.009954
σ
y 4.12E-07
11.33067 kNm2
σ
xy 2.02E-08
0.197032 m=7
i=5 j=6
y
x
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Universitas Sumatera Utara
80
Elemen 8
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25332084.4
0.3 1
Mpa 0.91
0.35 27837455.38
8351237 -0.66667
0.666667 d8x
-1.01412E-07 [ σ ] =
8351236.615 27837455 -0.66667
0.666667 d8y
1.25217E-07 9743109
-0.66667 -0.66667 0.666667 0.666667
d10x 4.67537E-08
d10y 3.45144E-08
d9x 3.01403E-07
d9y 1.36595E-06
σ
x 9.88E-08
9.657472
σ
y 8.27E-07
23.85079 kNm2
σ
xy 2.08E-07
2.027298
m=9
i=7 j=8
y
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Universitas Sumatera Utara
81
Elemen 10
m = 11
0.5 m
i = 9 0.5 m
j = 10 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25332084.4
0.3 1
Mpa 0.91
0.35 27837455.38
8351237 -0.66667
0.666667 d10x
4.67537E-08 [ σ ] =
8351236.615 27837455 -0.66667
0.666667 d10y
3.45144E-08 9743109
-0.66667 -0.66667 0.666667 0.666667
d12x 1.05247E-06
d12y -2.97732E-07
d11x 1.91169E-06
d11y 2.54742E-06
σ
x 6.7E-07
32.65502
σ
y 1.68E-06
52.23456 kNm2
σ
xy 1.02E-06
9.955442 y
x
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Universitas Sumatera Utara
82
Elemen 12
m = 13
0.5 m
i = 11 0.5 m
j = 12 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25332084.4
0.3 1
Mpa 0.91
0.35 27837455.38
8351237 -0.66667
0.666667 d12x
1.05247E-06 [ σ ] =
8351236.615 27837455 -0.66667
0.666667 d12y
-2.97732E-07 9743109
-0.66667 -0.66667 0.666667 0.666667
d14x 1.23616E-05
d14y 7.19496E-07
d13x 8.15901E-06
d13y 3.63921E-06
σ
x 7.54E-06
231.7971
σ
y 2.62E-06
136.0265 kNm2
σ
xy 5.42E-06
52.76718 y
x
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Universitas Sumatera Utara
83
4.2.5.3 Tegangan pada potongan C—C 14,16,18,50,55,54
Pada jendela microsoft excel 2010:
Elemen 14
m = 4 j = 17
0.5 m
0.5 m i = 15
0.5-0.5 = 0.5-0 =
0.5 0-0.5 =
-0.5 0-0.5 =
-0.5 0.5 - 0 =
0.5 0.5- 0.5 =
0.5 -0.5
-0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
0.5 0.5
-0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.75
0.35 27837455.4
8351236.615 0.666667 -0.66667 -0.66667
d15x -1.97538E-07
[ σ ] = 8351236.62
27837455.38 -0.66667
0.666667 d15y
-1.89149E-07 9743109
-0.66667 0.666667 0.666667
-0.66667 d17x
-6.88378E-07 d17y
-7.2339E-07 d4x
-1.23455E-07 d4y
7.06207E-08
σ
x 1.05645E-07
-0.0335
σ
y -3.56161E-07
-9.03234 kNm2
σ
xy -8.56567E-07
-8.34563 y
x
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1 �
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1−� 2
Universitas Sumatera Utara
84
Elemen 16
m = 6 j = 19
0.5 m
0.5 m i = 17
0.5-0.5 = 0.5-0 =
0.5 0-0.5 =
-0.5 0-0.5 =
-0.5 0.5 - 0 =
0.5 0.5- 0.5 =
0.5 -0.5
-0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
0.5 0.5
-0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.75
0.35 27837455
8351237 0.666667 -0.66667 -0.66667
d17x -6.88378E-07
[ σ ] = 8351237 27837455
-0.66667 0.666667
d17y -7.2339E-07
9743109 -0.66667
0.666667 0.666667 -0.66667
d19x -1.65079E-06
d19y -1.64978E-06
d6x -7.83636E-08
d6y 1.2231E-07
σ
x 5.16E-08
-3.72219
σ
y -6.2E-07
-16.7616 kNm2
σ
xy -1.8E-06
-17.7617 y
x �
�
= �
�
− �
�
= �
�
= �
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− �
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= �
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− �
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− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
85
Elemen 18
m = 8 j =
21
0.5 m
0.5 m
i =
19 0.5-0.5 =
0.5-0 = 0.5
0-0.5 = -0.5
0-0.5 = -0.5
0.5 - 0 = 0.5
0.5- 0.5 = 0.5
-0.5 -0.5
[ β ] = 1
-0.5 0.5
1 0.75
-0.5 0.5
0.5 -0.5
m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.75
0.35 27837455
8351237 0.666667 -0.66667 -0.66667
d19x -1.6508E-06
[ σ ] = 8351237 27837455
-0.66667 0.666667
d19y -1.6498E-06
9743109 -0.66667
0.666667 0.666667 -0.66667
d21x -1.5442E-06
d21y -3.6332E-06
d8x -1.0141E-07
d8y 1.25217E-07
σ
x 1.46E-06
29.60747
σ
y -1.3E-06
-24.6142 kNm2
σ
xy -2.4E-06
-23.7204 y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
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= �
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− �
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= �
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− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�2
1 �
� 1
1−� 2
Universitas Sumatera Utara
86
Elemen 20
m = 10 j =
23
0.5 m
0.5 m
i =
21 0.5-0.5 =
0.5-0 = 0.5
0-0.5 = -0.5
0-0.5 = -0.5
0.5 - 0 = 0.5
0.5- 0.5 = 0.5
-0.5 -0.5
[ β ] = 1
-0.5 0.5
1 0.75
-0.5 0.5
0.5 -0.5
m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.75
0.35 27837455
8351237 0.666667 -0.66667 -0.66667
d21x -1.54423E-06
[ σ ] = 8351237 27837455
-0.66667 0.666667
d21y -3.63322E-06
9743109 -0.66667
0.666667 0.666667 -0.66667
d23x -2.69777E-06
d23y -7.73805E-06
d10x 4.67537E-08
d10y 3.45144E-08
σ
x 3.33E-06
69.81785
σ
y -2.7E-06
-48.3772 kNm2
σ
xy -6E-06
-57.9787 y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
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− �
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= �
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= �
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− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
87
Elemen 22
m = 12 j = 25
0.5 m
0.5 m i = 23
0.5-0.5 = 0.5-0 =
0.5 0-0.5 =
-0.5 0-0.5 =
-0.5 0.5 - 0 =
0.5 0.5- 0.5 =
0.5 -0.5
-0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
0.5 0.5
-0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.75
0.35 27837455
8351237 0.666667 -0.66667 -0.66667
d23x -2.69777E-06
[ σ ] = 8351237 27837455
-0.66667 0.666667
d23y -7.73805E-06
9743109 -0.66667
0.666667 0.666667 -0.66667
d25x -4.14917E-06
d25y -1.91127E-05
d12x 1.05247E-06
d12y -2.97732E-07
σ
x 9.27E-06
194.8368
σ
y -7.6E-06
-133.644 kNm2
σ
xy -1.4E-05
-131.638 y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
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= �
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− �
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= �
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= �
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− �
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= �
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= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
88
Elemen 24
m = 14 j = 27
0.5 m
0.5 m i = 25
0.5-0.5 = 0.5-0 =
0.5 0-0.5 =
-0.5 0-0.5 =
-0.5 0.5 - 0 =
0.5 0.5- 0.5 =
0.5 -0.5
-0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
0.5 0.5
-0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.75
0.35 27837455
8351237 0.666667 -0.66667 -0.66667
d25x -4.14917E-06
[ σ ] = 8351237 27837455
-0.66667 0.666667
d25y -1.91127E-05
9743109 -0.66667
0.666667 0.666667 -0.66667
d27x 1.7642E-06
d27y -4.97496E-05
d14x 1.23616E-05
d14y 7.19496E-07
σ
x 2.61E-05
556.0279
σ
y -2E-05
-350.591 kNm2
σ
xy -3E-05
-289.408 y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
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= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
89
4.2.5.4 Tegangan pada potongan D—D 55,57,59,31,33,35
Pada jendela microsoft excel 2010:
Elemen 25
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455.38 8351236.62
-0.66667 0.666667
d15x -1.97538E-07
[ σ ] = 8351236.615 27837455.4
-0.66667 0.666667
d15y -1.89149E-07
9743109 -0.66667 -0.66667
0.666667 0.666667 d16x
2.31103E-07 d16y
-6.20872E-08 d17x
-6.88378E-07 d17y
-7.2339E-07
σ
x 2.8576E-07
4.980465
σ
y -3.5616E-07
-7.52815 kNm2
σ
xy -2.4252E-07
-2.36289 m=3
i=1 j=2
y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
90
Elemen 27
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455.38 8351236.615
-0.66667 0.666667
d17x -6.8838E-07
[ σ ] = 8351236.615 27837455.38
-0.66667 0.666667
d17y -7.2339E-07
9743109 -0.66667 -0.66667
0.666667 0.666667 d18x
-4.616E-07 d18y
-1.7628E-07 d19x
-1.6508E-06 d19y
-1.6498E-06
σ
x 1.51183E-07
-0.94912
σ
y -6.17593E-07
-15.9297 kNm2
σ
xy -2.76871E-07
-2.69759 m=5
i=3 j=4
y
x
�
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
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= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
91
Elemen 29
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455.4
8351236.615 -0.66667
0.666667 d19x
-1.65079E-06 [ σ ] =
8351236.62 27837455.38
-0.66667 0.666667
d19y -1.64978E-06
9743109 -0.66667 -0.66667
0.666667 0.666667 d20x
-2.1905E-06 d20y
-6.32891E-07 d21x
-1.54423E-06 d21y
-3.63322E-06
σ
x -3.59805E-07
-21.0589
σ
y -1.3223E-06
-39.8141 kNm2
σ
xy 7.48971E-07
7.297306
m=7
i=5 j=6
y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
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= �
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− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
92
Elemen 31
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455.38
8351236.615 -0.66667
0.666667 d21x
-1.54423E-06 [ σ ] =
8351236.615 27837455.38
-0.66667 0.666667
d21y -3.63322E-06
9743109 -0.66667 -0.66667
0.666667 0.666667 d22x
-1.08142E-06 d22y
-2.48947E-06 d23x
-2.69777E-06 d23y
-7.73805E-06
σ
x 3.08537E-07
-14.2647
σ
y -2.73655E-06
-73.602 kNm2
σ
xy -6.52291E-09
-0.06355
m=9
i=7 j=8
y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
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= �
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− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
93
Elemen 33
m = 11
0.5 m
i = 9 0.5 m
j = 10 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455.38 8351236.615
-0.66667 0.666667
d23x -2.69777E-06
[ σ ] = 8351236.615 27837455.38
-0.66667 0.666667
d23y -7.73805E-06
9743109 -0.66667 -0.66667
0.666667 0.666667 d24x
5.39637E-08 d24y
-5.4225E-06 d25x
-4.14917E-06 d25y
-1.91127E-05
σ
x 1.83449E-06
-12.2606
σ
y -7.5831E-06
-195.773 kNm2
σ
xy 5.76094E-07
5.612951 y
x
�
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
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= �
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− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
94
Elemen 35
m = 13
0.5 m
i =
11 0.5 m
j =
12 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455.38
8351236.615 -0.66667
0.666667 d25x
-4.14917E-06 [ σ ] =
8351236.615 27837455.38
-0.66667 0.666667
d25y -1.91127E-05
9743109 -0.66667 -0.66667
0.666667 0.666667 d26x
3.19857E-06 d26y
-1.10742E-05 d27x
1.7642E-06 d27y
-4.97496E-05
σ
x 4.89849E-06
-34.2095
σ
y -2.04246E-05
-527.662 kNm2
σ
xy 9.30125E-06
90.62311 y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
95
4.2.5.5 Tegangan pada potongan E –E Elemen56,58,30,35,34,36
Pada jendela microsoft excel 2010:
Elemen 26
m = 17 j = 18
0.5 m
0.5 m i = 16
0.5-0.5 = 0.5-0 =
0.5 0-0.5 =
-0.5 0-0.5 =
-0.5 0.5 - 0 =
0.5 0.5- 0.5 =
0.5 -0.5
-0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
0.5 0.5
-0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.75
0.35 27837455.4
8351236.615 0.666667 -0.66667 -0.66667
d16x 2.31103E-07
[ σ ] = 8351236.62
27837455.38 -0.66667
0.666667 d16y
-6.20872E-08 9743109
-0.66667 0.666667 0.666667
-0.66667 d18x
-4.61603E-07 d18y
-1.76281E-07 d17x
-6.88378E-07 d17y
-7.2339E-07
σ
x 2.68704E-07
6.844261
σ
y -7.61294E-08
0.124762 kNm2
σ
xy -9.7065E-08
-0.94572 y
x
�
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
96
Elemen 28
m = 19 j = 20
0.5 m
0.5 m i = 18
0.5-0.5 = 0.5-0 =
0.5 0-0.5 =
-0.5 0-0.5 =
-0.5 0.5 - 0 =
0.5 0.5- 0.5 =
0.5 -0.5
-0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
0.5 0.5
-0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.75
0.35 27837455
8351237 0.666667 -0.66667 -0.66667
d18x -4.61603E-07
[ σ ] = 8351237 27837455
-0.66667 0.666667
d18y -1.76281E-07
9743109 -0.66667
0.666667 0.666667 -0.66667
d20x -2.1905E-06
d20y -6.32891E-07
d19x -1.65079E-06
d19y -1.64978E-06
σ
x 6.21E-08
-0.81285
σ
y -3E-07
-7.95511 kNm2
σ
xy -4.7E-07
-4.62479 y
x
[D] =
� 1−�
2
1 �
� 1
1−� 2
�
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
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− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
Universitas Sumatera Utara
97
Elemen 30
m = 21 j =
22
0.5 m
0.5 m
i =
20 0.5-0.5 =
0.5-0 = 0.5
0-0.5 = -0.5
0-0.5 = -0.5
0.5 - 0 = 0.5
0.5- 0.5 = 0.5
-0.5 -0.5
[ β ] = 1
-0.5 0.5
1 0.75
-0.5 0.5
0.5 -0.5
m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.75
0.35 27837455
8351237 0.666667 -0.66667 -0.66667
d20x -2.1905E-06
[ σ ] = 8351237 27837455
-0.66667 0.666667
d20y -6.3289E-07
9743109 -0.66667
0.666667 0.666667 -0.66667
d22x -1.0814E-06
d22y -2.4895E-06
d21x -1.5442E-06
d21y -3.6332E-06
σ
x 1.97E-06
44.45269
σ
y -1.2E-06
-18.0181 kNm2
σ
xy 1.5E-06
14.63309 y
x
[D] =
� 1−�2
1 �
� 1
1−� 2
�
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
Universitas Sumatera Utara
98
Elemen 32
m = 23 j =
24
0.5 m
0.5 m
i =
22 0.5-0.5 =
0.5-0 = 0.5
0-0.5 = -0.5
0-0.5 = -0.5
0.5 - 0 = 0.5
0.5- 0.5 = 0.5
-0.5 -0.5
[ β ] = 1
-0.5 0.5
1 0.75
-0.5 0.5
0.5 -0.5
m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.75
0.35 27837455
8351237 0.666667 -0.66667 -0.66667
d22x -1.08142E-06
[ σ ] = 8351237 27837455
-0.66667 0.666667
d22y -2.48947E-06
9743109 -0.66667
0.666667 0.666667 -0.66667
d24x 5.39637E-08
d24y -5.4225E-06
d23x -2.69777E-06
d23y -7.73805E-06
σ
x 5.45E-06
135.3702
σ
y -2E-06
-8.92218 kNm2
σ
xy 2.3E-06
22.41521 y
x
[D] =
� 1−�
2
1 �
� 1
1−� 2
�
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
Universitas Sumatera Utara
99
Elemen 34
m = 25 j =
26
0.5 m
0.5 m
i =
24 0.5-0.5 =
0.5-0 = 0.5
0-0.5 = -0.5
0-0.5 = -0.5
0.5 - 0 = 0.5
0.5- 0.5 = 0.5
-0.5 -0.5
[ β ] = 1
-0.5 0.5
1 0.75
-0.5 0.5
0.5 -0.5
m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.75
0.35 27837455
8351237 0.666667 -0.66667 -0.66667
d24x 5.39637E-08
[ σ ] = 8351237 27837455
-0.66667 0.666667
d24y -5.4225E-06
9743109 -0.66667
0.666667 0.666667 -0.66667
d26x 3.19857E-06
d26y -1.10742E-05
d25x -4.14917E-06
d25y -1.91127E-05
σ
x 1.23E-05
310.4136
σ
y -3.8E-06
-2.32139 kNm2
σ
xy 7.46E-06
72.63883 y
x
[D] =
� 1−�
2
1 �
� 1
1−� 2
�
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
Universitas Sumatera Utara
100
Elemen 36
m = 27 j = 28
0.5 m
0.5 m i = 26
0.5-0.5 = 0.5-0 =
0.5 0-0.5 =
-0.5 0-0.5 =
-0.5 0.5 - 0 =
0.5 0.5- 0.5 =
0.5 -0.5
-0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
0.5 0.5
-0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.75
0.35 27837455
8351237 0.666667 -0.66667 -0.66667
d26x 3.19857E-06
[ σ ] = 8351237 27837455
-0.66667 0.666667
d26y -1.10742E-05
9743109 -0.66667
0.666667 0.666667 -0.66667
d27x 1.7642E-06
d27y -4.97496E-05
d28x 6.65225E-06
d28y -1.68695E-05
σ
x 2.99E-05
617.2295
σ
y -2.6E-05
-467.985 kNm2
σ
xy -2.3E-05
-222.887 y
x
[D] =
� 1−�
2
1 �
� 1
1−� 2
�
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
Universitas Sumatera Utara
101
4.2.5.6 Tegangan Pada potongan potongan F—F elemen37,39,41,43,45,47
Pada jendela microsoft excel 2010:
Elemen 37
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25332084.4
0.3 1
Mpa 0.91
0.35 27837455.38 8351236.62
-0.66667 0.666667
d16x -6.20872E-08
[ σ ] = 8351236.615 27837455.4
-0.66667 0.666667
d16y -6.88378E-07
9743109 -0.66667 -0.66667
0.666667 0.666667 d29x
6.23046E-07 d29y
5.83427E-07 d18x
-4.61603E-07 d18y
-1.76281E-07
σ
x 4.5676E-07
15.566
σ
y 3.414E-07
13.31812 kNm2
σ
xy 5.8153E-07
5.665874 m=3
i=1 j=2
y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
102
Elemen 39
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25332084.4
0.3 1
Mpa 0.91
0.35 27837455.38 8351236.615
-0.66667 0.666667
d18x -4.616E-07
[ σ ] = 8351236.615 27837455.38
-0.66667 0.666667
d18y -1.7628E-07
9743109 -0.66667 -0.66667
0.666667 0.666667 d31x
3.80907E-07 d31y
5.93875E-07 d20x
-2.1905E-06 d20y
-6.3289E-07
σ
x 5.61674E-07
13.09339
σ
y -3.04407E-07
-3.78324 kNm2
σ
xy -6.39161E-07
-6.22742 m=5
i=3 j=4
y
x
�
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
103
Elemen 41
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25332084.4
0.3 1
Mpa 0.91
0.35 27837455.4
8351236.615 -0.66667
0.666667 d20x
-2.1905E-06 [ σ ] =
8351236.62 27837455.38
-0.66667 0.666667
d20y -6.32891E-07
9743109 -0.66667 -0.66667
0.666667 0.666667 d33x
-3.11473E-06 d33y
1.28862E-06 d22x
-1.08142E-06 d22y
-2.48947E-06
σ
x -6.16153E-07
-27.4886
σ
y -1.23772E-06
-39.6005 kNm2
σ
xy 2.02039E-06
19.68492
m=7
i=5 j=6
y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
104
Elemen 43
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25332084.4
0.3 1
Mpa 0.91
0.35 27837455.38
8351236.615 -0.66667
0.666667 d22x
-1.08142E-06 [ σ ] =
8351236.615 27837455.38
-0.66667 0.666667
d22y -2.48947E-06
9743109 -0.66667 -0.66667
0.666667 0.666667 d35x
-1.03281E-06 d35y
-2.24053E-06 d24x
5.39637E-08 d24y
-5.4225E-06
σ
x 3.24098E-08
-15.4274
σ
y -1.95536E-06
-54.1615 kNm2
σ
xy 9.22878E-07
8.991696
m=9
i=7 j=8
y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
105
Elemen 45
m = 11
0.5 m
i = 9 0.5 m
j = 10 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25332084.4
0.3 1
Mpa 0.91
0.35 27837455.38 8351236.615
-0.66667 0.666667
d24x 5.39637E-08
[ σ ] = 8351236.615 27837455.38
-0.66667 0.666667
d24y -5.4225E-06
9743109 -0.66667 -0.66667
0.666667 0.666667 d37x
-8.97067E-07 d37y
-7.27857E-06 d26x
3.19857E-06 d26y
-1.10742E-05
σ
x -6.3402E-07
-49.115
σ
y -3.7678E-06
-110.18 kNm2
σ
xy 8.59021E-07
8.369532 y
x
�
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
106
Elemen 47
m = 13
0.5 m
i =
11 0.5 m
j =
12 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25332084.4
0.3 1
Mpa 0.91
0.35 27837455.38
8351236.615 -0.66667
0.666667 d26x
3.19857E-06 [ σ ] =
8351236.615 27837455.38
-0.66667 0.666667
d26y -1.10742E-05
9743109 -0.66667 -0.66667
0.666667 0.666667 d39x
-2.41307E-06 d39y
-1.89712E-05 d28x
6.65225E-06 d28y
-1.68695E-05
σ
x -3.74109E-06
-136.408
σ
y -3.86354E-06
-138.794 kNm2
σ
xy -2.96224E-06
-28.8614 y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
107
0.72 1.79
1.55 2.55
1.85 -9.87
50 100
150 200
250 300
-15 -10
-5 5
tinggi lenga
n cm
tegangan kNm2
tegangan σx pada potongan A---A
2.70 3.49
3.01 9.66
32.66 231.80
500 1000
1500 2000
2500 3000
50 100
150 200
250
tegangan kNm2
tegangan σx potongan B--B
-0.03 -3.72
29.61 69.82
194.84 556.03
50 100
150 200
250 300
-200 200
400 600
tegangan kNm2
tegangan σx pada potongan C--C
4.98 -0.95
-21.06 -14.26
-12.26 -34.21
50 100
150 200
250 300
-40 -20
20
tegangan kNm2 tegangan
σx potongan D--D
6.84 -0.81
44.45 135.37
310.41 617.23
50 100
150 200
250 300
-200 200
400 600
800
tegangan kNm2 tegangan
σx pada potongan E--E
15.57 13.09
-27.49 -15.43
-49.12 -136.41
50 100
150 200
250 300
-150 -100
-50 50
tegangan kNm2
tegangan σx pada potongan F--F
-0.22 -5.69
-3.72 -11.33
-20.49 -15.46
50 100
150 200
250 300
-30 -20
-10
ti n
g g
i len
g a
n cm
tegangan kNm2
tegangan σy pada potongan A---A
-13.31 3.78
39.57 54.11
110.08 138.67
50 100
150 200
250 300
-50 50
100 150
tegangan kNm2
tegangan σy pada potongan
B--B
9.02 16.75
24.59 48.34
133.53 350.28
50 100
150 200
250 300
100 200
300 400
tegangan kNm2
tegangan σy pada
potongan C--C
7.52 15.92
39.78 73.54
195.60 527.20
50 100
150 200
250 300
200 400
600
tegangan kNm2
tegangan σy pada potongan
D--D
-0.12 7.95
18.00 8.91
2.32 467.58
50 100
150 200
250 300
-200 200
400 600
tegangan kNm2
tegangan σy pada potongan E--E
tengah bentang
-13.31 3.78
39.57 54.11
110.08 138.67
50 100
150 200
250 300
-50 50
100 150
ting g
i leng
a n
c m
tegangan kNm2
tegangan σy pada potongan F--F
Grafik 4.1 Tegangan σ
x
pada potongan potongan melintang A,B,C,D,E,F
Grafik 4.2 Tegangan σ
y
pada potongan potongan melintang A,B,C,D,E,F
Universitas Sumatera Utara
108 -1.40
0.95 2.41
1.70 -1.81
-22.08
50 100
150 200
250 300
-30 -20
-10 10
ti n
g g
i len
g a
n cm
tegangan kNm2
tegangan τxy pada potongan
A---A
-1.40 0.95
2.41 1.70
-1.81 -22.08
50 100
150 200
250 300
-30 -20
-10 10
tegangan kNm2
tegangan τxy pada
potongan B--B
8.34 17.75
23.70 57.93
131.52 289.16
50 100
150 200
250 300
100 200
300 400
tegangan kNm2
tegangan τxy pada
potongan C--C
2.36 2.70
-7.29 0.06
-5.61 -90.54
50 100
150 200
250 300
-100 -50
50
tegangan kNm2
tegangan Ϯxy pada potongan
D--D
0.94 4.62
-14.62 -22.40
-72.58 222.69
50 100
150 200
250 300
-100 100
200 300
tegangan kNm2
tegangan τxy pada potongan
E--E tengah bentang
-5.66 6.22
-19.67 -8.98
-8.36 28.84
50 100
150 200
250 300
-40 -20
20 40
tegangan kNm2 tegangan
τxy pada potongan F--F
Grafik 4.3 Tegangan τ
xy
pada potongan potongan melintang A,B,C,D,E,F
Universitas Sumatera Utara
109
1 1
2 2
3 3
Gambar 4.5 Pengambilan nilai tegangan pada potongan memanjang 1,5,3
Tegangan pada arah y diambil 3 potongan yang mewakili,
Universitas Sumatera Utara
110
4.2.5.7 Tegangan Pada potongan potongan 1-- 1 elemen 15,54,36,48,60,75
Pada jendela microsoft excel 2010:
Elemen 12
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d12x
1.05247E-06 [ σ ] =
8351237 27837455 -0.66667
0.666667 d12y
-2.97732E-07 9743109
-0.66667 -0.66667 0.666667 0.666667
d14x 1.23616E-05
d14y 7.19496E-07
d13x 8.15901E-06
d13y 3.63921E-06
σ
x 7.54E-06
231.7971
σ
y 2.62E-06
136.0265 kNm2
σ
xy 5.42E-06
52.76718 m=3
i=1 j=2
y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
111
Elemen 24
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d25x
-4.14917E-06 [ σ ] =
8351237 27837455 -0.66667
0.666667 d25y
-1.91127E-05 9743109
-0.66667 -0.66667 0.666667 0.666667
d27x 1.7642E-06
d27y -4.97496E-05
d14x 1.23616E-05
d14y 7.19496E-07
σ
x 3.94E-06
220.1575
σ
y 1.32E-05
400.9738 kNm2
σ
xy -9.4E-06
-91.7554 m=5
i=3 j=4
y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
112
Elemen 36
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d26x
3.19857E-06 [ σ ] =
8351237 27837455 -0.66667
0.666667 d26y
-1.10742E-05 9743109
-0.66667 -0.66667 0.666667 0.666667
d28x 6.65225E-06
d28y -1.68695E-05
d27x 1.7642E-06
d27y -4.97496E-05
σ
x 2.3E-06
-151.231
σ
y -2.6E-05
-698.523 kNm2
σ
xy -4.8E-06
-46.9596 m=7
i=5 j=6
y
x
�
�
= �
�
− �
�
= �
�
= �
�
− �
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= �
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− �
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− �
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= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
113
Elemen 48
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d39x
-2.41307E-06 [ σ ] =
8351237 27837455 -0.66667
0.666667 d39y
-1.89712E-05 9743109
-0.66667 -0.66667 0.666667 0.666667
d41x -3.99519E-06
d41y -4.90167E-05
d28x 6.65225E-06
d28y -1.68695E-05
σ
x -1.1E-06
-17.66
σ
y 1.4E-06
30.19631 kNm2
σ
xy -1.4E-05
-136.275 m=9
i=7 j=8
y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
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= �
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− �
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= �
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= �
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− �
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= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
114
Elemen 48
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d39x
-2.41307E-06 [ σ ] =
8351237 27837455 -0.66667
0.666667 d39y
-1.89712E-05 9743109
-0.66667 -0.66667 0.666667 0.666667
d41x -3.99519E-06
d41y -4.90167E-05
d28x 6.65225E-06
d28y -1.68695E-05
σ
x -1.1E-06
-17.66
σ
y 1.4E-06
30.19631 kNm2
σ
xy -1.4E-05
-136.275 m=9
i=7 j=8
y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
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= �
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− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
115
Elemen 60
m = 11
0.5 m
i =
9 0.5 m
j =
10 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d40x
8.02304E-06 [ σ ] =
8351237 27837455 -0.66667
0.666667 d40y
-2.85984E-06 9743109
-0.66667 -0.66667 0.666667 0.666667
d42x 1.7273E-05
d42y -5.32159E-06
d41x -3.99519E-06
d41y -4.90167E-05
σ
x 6.17E-06
-85.3137
σ
y -3.1E-05
-805.094 kNm2
σ
xy -9.7E-06
-94.0534 y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
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= �
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− �
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− �
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= �
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= �
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− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
116
Elemen 72
m = 13
0.5 m
i = 11 0.5 m
j = 12 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d48x
3.15487E-06 [ σ ] =
8351237 27837455 -0.66667
0.666667 d48y
-1.9951E-06 9743109
-0.66667 -0.66667 0.666667 0.666667
d49x 5.14461E-06
d49y -2.9966E-06
d42x 1.7273E-05
d42y -5.3216E-06
σ
x 1.33E-06
18.40599
σ
y -2.2E-06
-50.6566 kNm2
σ
xy 8.74E-06
85.19823 y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
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= �
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= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
117
4.2.5.8 Tegangan Pada potongan potongan 2-- 2 elemen 7,19,31,43,55,63
Pada jendela microsoft excel 2010:
Elemen 7
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d7x
-5.09369E-08 [ σ ] =
8351237 27837455 -0.66667
0.666667 d7y
7.39768E-07 9743109
-0.66667 -0.66667 0.666667 0.666667
d8x -1.01412E-07
d8y 1.25217E-07
d9x 3.01403E-07
d9y 1.36595E-06
σ
x -3.4E-08
2.54952
σ
y 4.17E-07
11.33983 kNm2
σ
xy -1.7E-07
-1.70317 m=3
i=1 j=2
y
x
�
�
= �
�
− �
�
= �
�
= �
�
− �
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= �
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= �
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− �
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− �
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= �
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= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
118
Elemen 19
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d8x
-1.01412E-07 [ σ ] =
8351237 27837455 -0.66667
0.666667 d8y
1.25217E-07 9743109
-0.66667 -0.66667 0.666667 0.666667
d21x -1.54423E-06
d21y -3.63322E-06
d10x 4.67537E-08
d10y 3.45144E-08
σ
x -9.6E-07
-27.2812
σ
y -6E-08
-9.71614 kNm2
σ
xy -2.4E-06
-23.4502 m=5
i=3 j=4
y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
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= �
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− �
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�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
119
Elemen 31
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d21x
-1.54423E-06 [ σ ] =
8351237 27837455 -0.66667
0.666667 d21y
-3.63322E-06 9743109
-0.66667 -0.66667 0.666667 0.666667
d22x -1.08142E-06
d22y -2.48947E-06
d23x -2.69777E-06
d23y -7.73805E-06
σ
x 3.09E-07
-14.2647
σ
y -2.7E-06
-73.602 kNm2
σ
xy -6.5E-09
-0.06355 m=7
i=5 j=6
y
x
�
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
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= �
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− �
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− �
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− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
120
Elemen 43
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d22x
-1.08142E-06 [ σ ] =
8351237 27837455 -0.66667
0.666667 d22y
-2.48947E-06 9743109
-0.66667 -0.66667 0.666667 0.666667
d35x -1.03281E-06
d35y -2.24053E-06
d24x 5.39637E-08
d24y -5.4225E-06
σ
x 3.24E-08
-15.4274
σ
y -2E-06
-54.1615 kNm2
σ
xy 9.23E-07
8.991696
m=9
i=7 j=8
y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
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= �
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− �
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= �
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= �
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− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
121
Elemen 55
m = 11
0.5 m
i = 9 0.5 m
j = 10 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d35x
-1.03281E-06 [ σ ] =
8351237 27837455 -0.66667
0.666667 d35y
-2.24053E-06 9743109
-0.66667 -0.66667 0.666667 0.666667
d36x 1.31006E-06
d36y -7.0422E-08
d37x -8.97067E-07
d37y -7.27857E-06
σ
x 1.56E-06
15.43044
σ
y -3.4E-06
-80.4535 kNm2
σ
xy 1.54E-06
14.97745 y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
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= �
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− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
122
Elemen 63
m = 13
0.5 m
i =
11 0.5 m
j =
12 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d36x
1.31006E-06 [ σ ] =
8351237 27837455 -0.66667
0.666667 d36y
-7.0422E-08 9743109
-0.66667 -0.66667 0.666667 0.666667
d46x 5.23274E-07
d46y 2.18616E-07
d38x 3.66206E-06
d38y -1.0878E-06
σ
x -5.2E-07
-20.2655
σ
y -6.8E-07
-23.2607 kNm2
σ
xy 1.76E-06
17.15462 y
x
Universitas Sumatera Utara
123
4.2.5.9 Tegangan Pada potongan potongan 3-- 3 elemen 1,13,25,37,49,61
Pada jendela microsoft excel 2010:
Elemen 1
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d1x
[ σ ] = 8351237 27837455
-0.66667 0.666667
d1y 9743109
-0.66667 -0.66667 0.666667 0.666667
d2x -1.67319E-07
d2y 7.03675E-08
d3x -1.28488E-07
d3y 2.41837E-07
σ
x -1.1E-07
-1.75874
σ
y 1.61E-07
3.556535 kNm2
σ
xy -3.9E-08
-0.37752 m=3
i=1 j=2
y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
124
Elemen 13
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d2x
-1.67319E-07 [ σ ] =
8351237 27837455 -0.66667
0.666667 d2y
7.03675E-08 9743109
-0.66667 -0.66667 0.666667 0.666667
d15x -1.97538E-07
d15y -1.89149E-07
d4x -1.23455E-07
d4y 7.06207E-08
σ
x -2E-08
-0.5594
σ
y 1.69E-10
-0.16354 kNm2
σ
xy -1.4E-07
-1.40075 m=5
i=3 j=4
y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
125
Elemen 25
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d15x
-1.97538E-07 [ σ ] =
8351237 27837455 -0.66667
0.666667 d15y
-1.89149E-07 9743109
-0.66667 -0.66667 0.666667 0.666667
d16x 2.31103E-07
d16y -6.20872E-08
d17x -6.88378E-07
d17y -7.2339E-07
σ
x 2.86E-07
4.980465
σ
y -3.6E-07
-7.52815 kNm2
σ
xy -2.4E-07
-2.36289 m=7
i=5 j=6
y
x
�
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
126
Elemen 37
0.5 m
0.5 m 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d16x
2.31103E-07 [ σ ] =
8351237 27837455 -0.66667
0.666667 d16y
-6.20872E-08 9743109
-0.66667 -0.66667 0.666667 0.666667
d29x 6.23046E-07
d29y 5.83427E-07
d18x -4.61603E-07
d18y -1.76281E-07
σ
x 2.61E-07
6.638015
σ
y -7.6E-08
0.062889 kNm2
σ
xy -3.1E-08
-0.30653
m=9
i=7 j=8
y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
Universitas Sumatera Utara
127
Elemen 49
m = 11
0.5 m
i =
9 0.5 m
j =
10 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d29x
6.23046E-07 [ σ ] =
8351237 27837455 -0.66667
0.666667 d29y
5.83427E-07 9743109
-0.66667 -0.66667 0.666667 0.666667
d30x 8.05836E-07
d30y 5.61995E-07
d31x 3.80907E-07
d31y 5.93875E-07
σ
x 1.22E-07
3.450457
σ
y 6.97E-09
1.21158 kNm2
σ
xy -1.8E-07
-1.712 y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
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Elemen 61
m = 13
0.5 m
i =
11 0.5 m
j =
12 0-0.5 =
-0.5 0.5-0 =
0.5 0-0 =
0-0.5 = -0.5
0-0 = 0.5-0 =
0.5 -0.5
0.5 [ β ] =
1 -0.5
0.5 1
0.75 -0.5
-0.5 0.5
0.5 m
1 0.3
[ D ] = 25310000
0.3 1
Mpa 0.91
0.35 27837455
8351237 -0.66667
0.666667 d30x
8.05836E-07 [ σ ] =
8351237 27837455 -0.66667
0.666667 d30y
5.61995E-07 9743109
-0.66667 -0.66667 0.666667 0.666667
d43x d43y
d32x 1.22374E-06
d32y 4.97918E-07
σ
x -5.4E-07
-15.3117
σ
y -4.3E-08
-5.67564 kNm2
σ
xy -9.6E-08
-0.93596 y
x �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
= �
�
= �
�
− �
�
=
[D] =
� 1−�
2
1 �
� 1
1−� 2
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129
Grafik 4.4
Tegangan τ
xy
pada potongan potongan memanjang 1,5,3
16.67 66.67
116.67 166.67
216.67 266.67
-1000 1000
50 100
150 200
250 300
ti n
g g
i l e
n g
a n
c m
tegangan kNm2 tegangan
σy pada potongan 1--1
33.33 83.33
133.33 183.33
233.33 283.33
-100 -50
50
50 100
150 200
250 300
ti n
g g
i len
g a
n cm
tegangan kNm2
tegangan σy pada potongan 2--2
33.33 83.33
133.33 183.33
233.33
283.33 -10
-5 5
50 100
150 200
250 300
ti n
g g
i len
g a
n cm
tegangan kNm2 tegangan
σy pada potongan 3--3
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4.3 Dengan metode Heft 540 sebagai control