Langkah Kelima : Menghitung Tegangan-Tegangan Yang Terjadi

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4.2.5 Langkah Kelima : Menghitung Tegangan-Tegangan Yang Terjadi

{ �} = [�][�]{�} � � � � � � �� � = � 1 − � 2 � 1 � � 1 1 − � 2 � � � 1 2 �� � � 1 � 3 � 2 � 1 � 3 � 2 � 1 � 1 � 3 � 3 � 2 � 2 � ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ � 1 � � 1 � � 3 � � 3 � � 2 � � 2 � ⎭ ⎪ ⎪ ⎬ ⎪ ⎪ ⎫ 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 y x � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [D] = � 1−� 2 1 � 0 � 1 0 0 0 1−� 2 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 y x � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [D] = � 1−� 2 1 � � 1 0 0 1−� 2 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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [D] = � 1−� 2 1 � 0 � 1 0 0 0 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 y x � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [D] = � 1−� 2 1 � � 1 0 0 0 1−� 2 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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [D] = � 1−� 2 1 � 0 � 1 0 0 0 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 x � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [D] = � 1−� 2 1 � 0 � 1 0 0 0 1−� 2 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 x � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = 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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = 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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = 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 x � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = 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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = 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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = 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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [D] = � 1−� 2 1 � � 1 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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = 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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = � � = � � − � � = [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 Universitas Sumatera Utara 128 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 Universitas Sumatera Utara 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 Universitas Sumatera Utara 130

4.3 Dengan metode Heft 540 sebagai control