Aplikasi Perhitungan Data- data struktur

BAB IV APLIKASI ANALISA P C

ollapse PADA GABLE FRAME

4.1. Aplikasi Perhitungan

Dalam tugas akhir ini maka diberikan suatu contoh perhitungan untuk mencari factor beban runtuhnya collapse load factor, � � akibat struktur mengalami mekanisme keruntuhan dengan jumlah sendi plastis yang terbentuk sebelum mengalami keruntuhan. Selain itu beban runtuh Pkritis dapat diperoleh dengan melacak keadaan pembebanan portal dan dengan melakukan analisa elastis pada struktur yang dimodifikasi akibat terbentuknya sendi plastis yang baru dengan jumlah sendi palstis yang diijinkan sebelum mengalami keruntuhan. beban runtuh Pkritis dan factor beban runtuhnya collapse load factor, � � akan diperoleh dengan metode finite element. Untuk perhitungan tabel-tabel dilakukan dengan bantuan program Microsoft Excel 2007. Data-data yang digunakan dalam aplikasi adalah sebagai berikut : Gambar 4.1. Struktur gable frame dan pembebanannya 4Pc Pc 3Pc a b c d h 1 h 2 h 3 h 4 h 5 h 6 h 7 b a c d e f g 10m 1 2 3 4 5 6 7 8 10m 20m 10m 10m 3m 3m 10m 6m 3m 17m Universitas Sumatera Utara

4.2. Data- data struktur

• Langkah I : menentukan model yaitu nomor simpul dan element � = 4175000 �� 2 Element I m 4 �� � L m � Kuadran ��� � ��� � a 0.1440 0.2044 10 90 I 1.000 0.000 b 0.1440 0.2044 10 90 I 1.000 0.000 c 0.2464 0.3266 10.44 16.69 I 0.287 0.958 d 0.2464 0.3266 10.44 16.69 I 0.287 0.958 e 0.1934 0.2653 20.88 343.31 IV -0.287 0.958 f 0.1934 0.2653 10.44 343.31 IV -0.287 0.958 g 0.1140 0.1716 17 270 III -1.000 0.000 Element ��� � � ��� � � ��� � ��� � �� � ���� � � ��� � � a 1.000 0.000 0.000 85337 7214.4 36072 b 1.000 0.000 0.000 85337 7214.4 36072 c 0.082 0.918 0.275 130608.716 10848.68085 56630.114 d 0.082 0.918 0.275 130608.716 10848.68085 56630.114 e 0.082 0.918 -0.275 53047.2941 1064.394723 11112.281 f 0.082 0.918 -0.275 106094.588 8515.157781 44449.124 g 1.000 0.000 0.000 42142.9412 1162.507633 9881.3149 Universitas Sumatera Utara Element ��� � ��� � � � ��� � + ��� � � � � � � � ��� � + ��� � � � � � � � �� − ��� � � � �� a 240480 120240 7214.400 85337.000 0.000 b 240480 120240 7214.400 85337.000 0.000 c 394145.594 197072.797 120730.907 20726.491 32945.344 d 394145.594 197072.797 120730.907 20726.491 32945.344 e 154682.95 77341.4751 48759.744 5351.945 -14300.217 f 309365.9 154682.95 98046.235 16563.511 -26843.579 g 111988.235 55994.1176 1162.508 42142.941 0.000 Element ��� � � � ��� � � � Ujung batang Kapasitas momen plastis Mp a 36072 0.000 1 765.0 2 765.0 b 36072 0.000 1 765.0 2 765.0 c 16263.792 54244.437 1 1275.0 2 1275.0 d 16263.792 54244.437 1 1275.0 2 1275.0 e -3191.3731 10644.150 1 1015.0 2 1015.0 f -12765.492 42576.599 1 1015.0 2 1015.0 g -9881.3149 0.000 1 616.0 2 616.0 Universitas Sumatera Utara • Langkah II : menentukan matriks kekakuan lokal element [ �] = ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ �� � 12 �� � 3 6 �� � 2 6 �� � 2 4 �� � − �� � − 12 �� � 3 6 �� � 2 − 6 �� � 2 2 �� � − �� � − 12 �� � 3 − 6 �� � 2 6 �� � 2 2 �� � �� � 12 �� � 3 − 6 �� � 2 − 6 �� � 2 4 �� � ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ Element a : [ � � ] = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 85337.00 0.00 0.00 −85337.00 0.00 0.00 0.00 7214.40 36072.00 0.00 7214.40 36072.00 0.00 36072.00 240480.00 0.00 −36072.00 120240.00 −85337.00 0.00 0.00 85337.00 0.00 0.00 0.00 −7214.40 −36072.00 0.00 7214.40 −36072.00 0.00 36072.00 120240.00 0.00 −36072.00 240480.00 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ Element b : [ � � ] = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 85337.00 0.00 0.00 −85337.00 0.00 0.00 0.00 7214.40 36072.00 0.00 −7214.40 36072.00 0.00 36072.00 240480.00 0.00 −36072.00 120240.00 −85337.00 0.00 0.00 85337.00 0.00 0.00 0.00 −7214.40 −36072.00 0.00 7214.40 −36072.00 0.00 36072.00 120240.00 0.00 −36072.00 240480.00 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ Element c : [ � � ] = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 130608.72 0.00 0.00 −130608.72 0.00 0.00 0.00 10848.68 56630.11 0.00 10848.68 56630.11 0.00 56630.11 394145.59 0.00 −56630.11 197072.80 −130608.72 0.00 0.00 130608.72 0.00 0.00 0.00 −10848.68 −56630.11 0.00 10848.68 −56630.11 0.00 56630.11 197072.80 0.00 −56630.11 394145.59 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ Element d : [ � � ] = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 130608.72 0.00 0.00 −130608.72 0.00 0.00 0.00 10848.68 56630.11 0.00 −10848.68 56630.11 0.00 56630.11 394145.59 0.00 −56630.11 197072.80 −130608.72 0.00 0.00 130608.72 0.00 0.00 0.00 −10848.68 −56630.11 0.00 10848.68 −56630.11 0.00 56630.11 197072.80 0.00 −56630.11 394145.59 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ Universitas Sumatera Utara Element e : [ � � ] = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 53047.29 0.00 0.00 −53047.29 0.00 0.00 0.00 1064.39 11112.28 0.00 −1064.39 11112.28 0.00 11112.28 154682.95 0.00 −11112.28 77341.48 −53047.29 0.00 0.00 53047.29 0.00 0.00 0.00 −1064.39 −11112.28 0.00 1064.39 −11112.28 0.00 11112.28 77341.48 0.00 −11112.28 154682.95 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ Element f : �� � � = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 106094.59 0.00 0.00 −106094.59 0.00 0.00 0.00 8515.16 44449.12 0.00 −8515.16 44449.12 0.00 44449.12 309365.90 0.00 −44449.12 154682.95 −106094.59 0.00 0.00 106094.59 0.00 0.00 0.00 −8515.16 −44449.12 0.00 8515.16 −44449.12 0.00 44449.12 154682.95 0.00 −44449.12 309365.90 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ Element g : �� � � = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 42142.94 0.00 0.00 −42142.94 0.00 0.00 0.00 1162.51 9881.31 0.00 −1162.51 9881.31 0.00 9881.31 111988.24 0.00 −9881.31 55994.12 −42142.94 0.00 0.00 42142.94 0.00 0.00 0.00 −1162.51 −9881.31 0.00 1162.51 −9881.31 0.00 9881.31 55994.12 0.00 −9881.31 111988.24⎦ ⎥ ⎥ ⎥ ⎥ ⎤ • Langkah III : menentukan matriks kekakuan global element ���� = [�][�][�] −1 ��� � � = � � ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ �� 2 + 12 � � 2 � 2 �� − 12 � � 2 � �� − 6 � � � �� − 12 � � 2 � �� �� 2 + 12 � � 2 � 2 6 � � � − 6 � � � 6 � � � 4 � − ��� 2 + 12 � � 2 � 2 � − �� − 12 � � 2 � �� − 6 � � � − �� − 12 � � 2 � �� − ��� 2 + 12 � � 2 � 2 � 6 � � � 6 � � � − 6 � � � 2 � − ��� 2 + 12 � � 2 � 2 � − �� − 12 � � 2 � �� 6 � � � − �� − 12 � � 2 � �� − ��� 2 + 12 � � 2 � 2 � − 6 � � � − 6 � � � 6 � � � 2 � �� 2 + 12 � � 2 � 2 �� − 12 � � 2 � �� − 6 � � � �� − 12 � � 2 � �� �� 2 + 12 � � 2 � 2 − 6 � � � − 6 � � � − 6 � � � 4 � ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ Element a : [ � � ] = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 7214.400 0.000 −36072 −7214.400 0.000 −36072 0.000 85337.000 0.000 0.000 −85337.000 0.000 −36072 0.000 24048 36072 0.000 120240 −7214.400 0.000 36072 7214.400 0.000 −36072 0.000 −85337.000 0.000 0.000 85337.000 0.000 −36072 0.000 120240 −36072 0.000 24048 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ Universitas Sumatera Utara Element b : [ � � ] = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 7214.400 0.000 −36072 −7214.400 0.000 −36072 0.000 85337.000 0.000 0.000 −85337.000 0.000 −36072 0.000 240480 36072 0.000 120240 −7214.400 0.000 36072 7214.400 0.000 −36072 0.000 −85337.000 0.000 0.000 85337.000 0.000 −36072 0.000 120240 −36072 0.000 240480 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ Element c : [ � � ] = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 120730.907 120730.907 −16263.792 −120730.907 −32945.344 −16263.792 32945.344 20726.491 54244.437 −32945.344 −20726.491 54244.437 −16263.792 54244.437 394145.594 16263.7918 −54244.437 197072.797 −120730.907 −32945.344 16263.7918 120730.907 32945.344 −16263.792 −32945.344 −20726.491 −54244.437 32945.344 20726.491 −54244.437 −16263.792 54244.437 197072.8 −16263.792 −54244.437 394145.59 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ Element c : [ � � ] = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 120730.907 32945.344 −16263.792 −120730.907 −32945.34 −16263.792 32945.344 20726.491 54244.437 −32945.344 −20726.491 54244.437 −16263.792 54244.437 394145.594 16263.7918 −54244.437 197072.797 −120730.907 −32945.344 16263.7918 120730.907 32945.344 −16263.792 −32945.344 −20726.491 −54244.437 32945.344 20726.491 −54244.437 −16263.792 54244.437 197072.8 16263.792 −16263.792 394145.59 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ Element d : [ � � ] = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 120730.907 32945.344 −16263.79 −120730.907 −32945.344 −16263.792 32945.344 20726.491 54244.437 −32945.344 −20726.491 54244.437 −16263.792 54244.437 394145.594 16263.7918 −54244.437 197072.797 −120730.907 −32945.344 16263.7918 120730.907 32945.344 −16263.792 −32945.344 −20726.491 −54244.437 32945.344 20726.491 −54244.437 −16263.792 54244.437 197072.8 −16263.792 −54244.437 394145.59 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ Element e : [ � � ] = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 98046.235 −26843.579 12765.4924 −98046.235 26843.579 12765.4924 −26843.579 16563.511 42576.599 26843.579 −16563.511 42576.599 12765.4924 42576.599 309365.9 −12765.492 −42576.599 154682.95 −98046.235 26843.579 −12765.492 98046.235 −26843.579 12765.4924 26843.579 −16563.511 −42576.599 −26843.579 16563.511 −42576.599 12765.492 42576.599 154682.95 12765.492 −42576.59 309365.9 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ Element f: �� � � = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 98046.235 −26843.579 12765.4924 −98046.235 26843.579 12765.4924 −26843.579 16563.511 42576.599 26843.579 −16563.511 42576.599 12765.4924 42576.599 309365.9 −12765.492 −42576.599 154682.95 −98046.235 26843.579 −12765.492 98046.235 −26843.579 12765.4924 26843.579 −16563.511 −42576.599 −26843.579 16563.511 −42576.599 12765.492 42576.599 154682.95 12765.492 −42576.599 309365.9 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ Universitas Sumatera Utara Element g: �� � � = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 1162.508 0.000 9881.31488 −1162.508 0.000 9881.31488 0.000 42142.941 0.000 0.000 −42142.941 0.000 9881.31488 0.000 111988.235 −9881.3149 0.000 55994.1176 −1162.508 0.000 −9881.3149 1162.508 0.000 9881.31488 0.000 −42142.941 0.000 0.000 42142.941 0.000 9881.3149 0.000 55994.118 9881.3149 0.000 111988.24 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ • Langkah IV : Menentukan matriks kekakuan struktur  ��̅ 1 � = ��� � 11 ���̅ 1 � + ��� � 12 ���̅ 2 �  ��̅ 2 � = ��� � 21 ���̅ 1 � + ��� � 22 ���̅ 2 � + ��� � 22 ���̅ 2 � + ��� � 23 ���̅ 3 �  ��̅ 3 � = ��� � 32 ���̅ 2 � + ��� � 33 ���̅ 3 � + ��� � 33 ���̅ 3 � + ��� � 34 ���̅ 4 �  ��̅ 4 � = ��� � 43 ���̅ 3 � + ��� � 44 ���̅ 4 � + ��� � 44 ���̅ 4 � + ��� � 45 ���̅ 5 �  ��̅ 5 � = ��� � 54 ���̅ 4 � + ��� � 55 ���̅ 5 � + ��� � 55 ���̅ 5 � + ��� � 56 ���̅ 6 �  ��̅ 6 � = ��� � 65 ���̅ 5 � + ��� � 66 ���̅ 6 � + ��� � 66 ���̅ 6 � + ��� � 67 ���̅ 7 �  ��̅ 7 � = ��� � 76 ���̅ 6 � + ��� � 77 ���̅ 7 � + ��� � 77 ���̅ 7 � + ��� � 78 ���̅ 8 �  ��̅ 8 � = ��� � 87 ���̅ 7 � + ��� � 88 ���̅ 8 � ⎩ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎧� ̅ 1 �̅ 2 �̅ 3 �̅ 4 �̅ 5 �̅ 6 �̅ 7 �̅ 8 ⎭ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎫ = ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡�� �11 �� �21 �� �12 �� �22 + �� �22 �� �32 �� �23 �� �33 + �� �33 �� �43 �� �34 �� �44 + �� �44 �� �54 �� �45 �� �55 + �� �55 �� �65 �� �56 �� �66 + �� �66 �� �76 �� �67 �� �77 + �� �77 �� �87 �� �78 �� �88 ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ ⎩ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎧� ̅ 1 �̅ 2 �̅ 3 �̅ 4 �̅ 5 �̅ 6 �̅ 7 �̅ 8 ⎭ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎫ • Langkah V : Menentukan kondisi-kondisi batas Boundary condition Dengan meninjau kondisi batas pada kedua simpul 1 dan 8 merupakan jepit sehingga pada kedua simpul ini tidak akan terjadi perpindahan sehingga : • �̅ 1 = 0 • �̅ 8 = 0 Universitas Sumatera Utara ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧� ̅ 2 �̅ 3 �̅ 4 �̅ 5 �̅ 6 �̅ 7 ⎭ ⎪ ⎪ ⎬ ⎪ ⎪ ⎫ = ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡�� �22 + �� �22 �� �32 �� �23 �� �33 + �� �33 �� �43 �� �34 �� �44 + �� �44 �� �54 �� �45 �� �55 + �� �55 �� �65 �� �56 �� �66 + �� �66 �� �76 �� �67 �� �77 + �� �77 ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧� ̅ 2 �̅ 3 �̅ 4 �̅ 5 �̅ 6 �̅ 7 ⎭ ⎪ ⎪ ⎬ ⎪ ⎪ ⎫ ⎩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎧ 1 −4 −3 0 ⎭ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎫ = ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ 14428.80 −72144.00 −7214.40 −36072.00 170674.00 −85337.00 −72144.00 480960.00 36072.00 120240.00 −7214.40 36072.00 127945.31 32945.34 −52335.79 −120730.91 −32945.34 −16263.79 −85337.00 32945.34 106063.49 54244.44 −32945.34 −20726.49 54244.44 −36072.00 120240.00 −52335.79 54244.44 634625.59 16263.79 −54244.44 197072.80 − 120730.91 −32945.34 16263.79 241461.81 65890.69 −32527.58 −120730.91 −32945.34 −16263.79 −32945.34 −20726.49 −54244.44 65890.69 41452.98 −32945.34 −20726.49 54244.44 −16263.79 54244.44 197072.80 −32527.58 788291.19 16263.79 −54244.44 197072.80 −120730.91 −32945.34 16263.79 169490.65 18645.13 −13072.42 −48759.74 14300.22 3191.37 −32945.34 −20726.49 −54244.44 18645.13 26078.44 −43600.29 14300.22 −5351.95 10644.15 −16263.79 54244.44 197072.80 −13072.42 −43600.29 548828.54 −3191.37 −10644.15 77341.48 −48759.74 14300.22 −3191.37 146805.98 −41143.80 15956.87 −98046.24 26843.58 12765.49 14300.22 −5351.95 −10644.15 −41143.80 21915.46 31932.45 26843.58 −16563.51 42576.60 3191.37 10644.15 77341.48 15956.87 31932.45 464048.85 −12765.49 −42576.60 154682.95 −98046.24 26843.58 −12765.49 99208.74 −26843.58 22646.81 26843.58 −16563.51 −42576.60 −26843.58 58706.45 −42576.60 12765.49 42576.60 154682.95 22646.81 −42576.60 421354.14 ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ ⎩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎧ �� 2 �̅ 2 �̅ 2 �� 3 �̅ 3 �̅ 3 �� 4 �̅ 4 �̅ 4 �� 5 �̅ 5 �̅ 5 �� 6 �̅ 6 �̅ 6 �� 7 �̅ 7 �̅ 7 ⎭ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎫ • Langkah VI : Menghitung besar perpindahan Setelah memasukkan nilai-nilai syarat-syarat batas maka, Penyelesaian matriks di atas menghasilkan o �� 2 = 3.69139 x 10 -4 m o �� 5 = 3.74576x 10 -5 m o �̅ 2 = -1.27499 x 10 -5 m o �̅ 5 =-7.43508x 10 -5 m o �̅ 2 = 4.86912 x 10 -5 rad o �̅ 5 = 6.00802x 10 -6 rad o �� 3 = -4.16775x 10 -5 m o �� 6 = 3.48351x 10 -5 m o �̅ 3 =-2.54998x 10 -5 m o �̅ 6 = 2.66999 x 10 -4 m o �̅ 3 =-1.42155x 10 -5 rad o �̅ 6 = 1.45380x 10 -5 rad Universitas Sumatera Utara o �� 4 = 3.151116x 10 -5 m o �� 7 = 2.95123x 10 -5 m o �̅ 4 =-4.05023x 10 -5 m o �̅ 7 =-2.16397x 10 -5 m o �̅ 4 =-3.87754x 10 -6 rad o �̅ 7 =-1.89250x 10 -5 rad • Langkah VII : Menentukan perpindahan lokal { �} = [�] −1 ��̅� Element a : ⎩ ⎪ ⎨ ⎪ ⎧ � 1 � 1 � 1 � 2 � 2 � 2 ⎭ ⎪ ⎬ ⎪ ⎫ = ⎣ ⎢ ⎢ ⎢ ⎡ −1 1 1 −1 1 1⎦ ⎥ ⎥ ⎥ ⎤ ⎩ ⎪ ⎨ ⎪ ⎧ 3.69139 x 10 −4 −127499 x 10 −5 4.86912 x 10 −5 ⎭ ⎪ ⎬ ⎪ ⎫ = ⎩ ⎪ ⎨ ⎪ ⎧ −1.27499 x 10 −5 −369139 x 10 −4 4.86912 x 10 −5 ⎭ ⎪ ⎬ ⎪ ⎫ Element b : ⎩ ⎪ ⎨ ⎪ ⎧ � 2 � 2 � 2 � 3 � 3 � 3 ⎭ ⎪ ⎬ ⎪ ⎫ = ⎣ ⎢ ⎢ ⎢ ⎡ −1 1 1 −1 1 1⎦ ⎥ ⎥ ⎥ ⎤ ⎩ ⎪ ⎨ ⎪ ⎧ 3.69139 x 10 −4 −1.27499 x 10 −5 4.86912 x 10 −5 4.16775 x 10 −5 −1.08452 x 10 −4 −4.10282 x 10 −5 ⎭ ⎪ ⎬ ⎪ ⎫ = ⎩ ⎪ ⎨ ⎪ ⎧− 5.42259 x 10 −5 −2.58694 x 10 −4 2.10694 x 10 −5 −1.08452 x 10 −4 −3.73223 x 10 −4 −4.10282 x 10 −5 ⎭ ⎪ ⎬ ⎪ ⎫ Element c : ⎩ ⎪ ⎨ ⎪ ⎧ � 3 � 3 � 3 � 4 � 4 � 4 ⎭ ⎪ ⎬ ⎪ ⎫ = ⎣ ⎢ ⎢ ⎢ ⎡ 0.958 −0.287 0.287 0.958 1 0.958 −0.287 0.287 0.958 1⎦ ⎥ ⎥ ⎥ ⎤ ⎩ ⎪ ⎨ ⎪ ⎧ 3.73223 x 10 −4 −1.08452 x 10 −4 −4.10282 x 10 −5 6.85091 x 10 −4 −1.10575 x 10 −3 −6.53135 x 10 −5 ⎭ ⎪ ⎬ ⎪ ⎫ = ⎩ ⎪ ⎨ ⎪ ⎧ 3.26353 x 10 −4 −2.11070 x 10 −4 −4.10282 x 10 −5 3.38665 x 10 −4 −1.25592 x 10 −3 −6.53135 x 10 −5 ⎭ ⎪ ⎬ ⎪ ⎫ Element d : ⎩ ⎪ ⎨ ⎪ ⎧ � 4 � 4 � 4 � 5 � 5 � 5 ⎭ ⎪ ⎬ ⎪ ⎫ = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 0.958 −0.287 0.287 0.958 1 0.958 −0.287 0.287 0.958 1 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ ⎩ ⎪ ⎨ ⎪ ⎧ 6.85091 x 10 −4 −1.10575 x 10 −3 −6.53135 x 10 −5 7.58800 x 10 −4 −1.22384 x 10 −3 7.65260 x 10 −5 ⎭ ⎪ ⎬ ⎪ ⎫ = ⎩ ⎪ ⎨ ⎪ ⎧ 3.38665 x 10 −4 −1.25592 x 10 −3 −6.53135 x 10 −5 3.75354 x 10 −4 −1.39021 x 10 −3 7.65260 x 10 −5 ⎭ ⎪ ⎬ ⎪ ⎫ Universitas Sumatera Utara Element e : ⎩ ⎪ ⎨ ⎪ ⎧ � 5 � 5 � 5 � 6 � 6 � 6 ⎭ ⎪ ⎬ ⎪ ⎫ = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 0.958 0.287 −0.287 0.958 1 0.958 0.287 −0.287 0.958 1 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ ⎩ ⎪ ⎨ ⎪ ⎧ 7.58800 x 10 −4 −1.22384 x 10 −3 7.65260 x 10 −5 1.18990 x 10 −3 3.22993 x 10 −5 3.48524 x 10 −5 ⎭ ⎪ ⎬ ⎪ ⎫ = ⎩ ⎪ ⎨ ⎪ ⎧ 1.07831 x 10 −3 −9.54364 x 10 −4 7.65260 x 10 −5 1.13049 x 10 −3 3.72669 x 10 −4 3.48524 x 10 −5 ⎭ ⎪ ⎬ ⎪ ⎫ Element f : ⎩ ⎪ ⎨ ⎪ ⎧ � 6 � 6 � 6 � 7 � 7 � 7 ⎭ ⎪ ⎬ ⎪ ⎫ = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 0.958 0.287 −0.287 0.958 1 0.958 0.287 −0.287 0.958 1 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ ⎩ ⎪ ⎨ ⎪ ⎧ 1.18990 x 10 −3 3.22993 x 10 −5 3.48524 x 10 −5 1.18419 x 10 −3 −5.62971 x 10 −5 −1.21444 x 10 −4 ⎭ ⎪ ⎬ ⎪ ⎫ = ⎩ ⎪ ⎨ ⎪ ⎧ 1.13049 x 10 −3 3.72669 x 10 −4 3.48524 x 10 −5 1.15047 x 10 −3 2.86165 x 10 −4 −1.21444 x 10 −4 ⎭ ⎪ ⎬ ⎪ ⎫ Element g : ⎩ ⎪ ⎨ ⎪ ⎧ � 7 � 7 � 7 � 8 � 8 � 8 ⎭ ⎪ ⎬ ⎪ ⎫ = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 1 −1 1 1 −1 1⎦ ⎥ ⎥ ⎥ ⎥ ⎤ ⎩ ⎪ ⎨ ⎪ ⎧ 1.18419 x 10 −3 −5.62971 x 10 −5 −1.21444 x 10 −4 ⎭ ⎪ ⎬ ⎪ ⎫ = ⎩ ⎪ ⎨ ⎪ ⎧ 5.62971 x 10 −5 1.18419 x 10 −3 −1.21444 x 10 −4 ⎭ ⎪ ⎬ ⎪ ⎫ • Langkah VIII : Menentukan gaya-gaya dalam lokal masing-masing element { �} = [�]{�} Universitas Sumatera Utara hasil perhitungan gaya –gaya dalam masing –masing element dapat dilihat pada tabel berikut ini: tabel 4.1 Gaya –gaya dalam masing –masing element Element Ujung batang Gaya Normal Ton Gaya lintang Ton Momen Tonm A 1 1.09 4.42 7.51 2 -109 -4.42 0.56 B 2 1.09 -0.09 -0.56 3 -1.09 0.09 18.69 C 3 1.38 0.72 -18.69 4 -1.38 -0.72 -12.95 D 4 0.98 -0.98 12.95 5 -0.98 0.20 -4.59 E 5 0.74 0.31 4.59 6 -0.74 -0.31 -9.61 F 6 0.94 -0.67 9.61 7 -0.94 0.67 17.88 G 7 0.91 0.22 -17.88 8 -0.91 -0.22 -12.94 4.2 gambar bidang momen Universitas Sumatera Utara

4.3. Memodifikasi kekakuan batang akibat terbentuknya sendi plastis