portal 2 dimensi - Universitas Brawijaya

Dalam bentuk matriks:jijjjiiiCosSinSinCosCosSinSinCosvuvujjiiVUVU1000000000000000010000000000Vektor perpindahanpada koordinat lokalMatrikstransformasiVektor perpindahanpada koordinat global )()()( eeeUTu

Untuk vektor gaya, juga berlaku hubungan transformasi yang sama: f Cosig i Sin mi 0 f j 0gj 0 mj 0SinCos0000001000Cos000Sin0000SinCos00Fi0G0M0 Fj0Gj1MiijVektor gaya padakoordinat lokalMatrikstransformasif( e)T( e) F( e)Vektor gaya padakoordinat globalMatriks kekakuan elemen dalam koordinat global: ( e) ( ) ( ) ( ) e T e eK T k Tg

Contoh Soal….Diketahui struktur Portal Bidang sbb :E = 2100 t/cm 2I 1 = 5000 cm 4A 1 = 100 cm 2I 2 = 1000 cm 4A 2 = 40 cm 2Tentukan :a. Matriks Kekakuan Globalb. Perpindahan dan Reaksi yangtidak diketahuic. Gaya tiap batangd. Diagram M, D, N

ReactionO,5 tO,5 tEquivalent JointLoad

MatriksKekakuan: LEILEILEILEILEILEILEILEILAELAELEILEILEILEILEILEILEILEILAELAEK460260612061200000260460612061200000222323222323MatriksTransformasi 1000000000000000010000000000CosSinSinCosCosSinSinCosT

a). Penentuan Matriks Kekakuan Global# Matriks Kekakuan Batang 1 (node 1 – 2)0 36.874200420 0 001.008 10 252 84000 0 252 420001k; T01.00825202520 25242000 42004200001.00801.008 25202520 25284000 0.8 0.6 0 0 0 00.60.800000010000000.8 0.600000.60.8000000111kTgT 11 . k.Tkg1 269.29201.08151.13 269.29201.08151.13201.08151.71201.65 201.08151.71201.65151.13201.6584000151.13 201.6542000 269.29 201.08151.13269.29201.08151.13 201.08151.71 201.65201.08151.71 201.65151.13201.6542000 151.13 201.6584000

# Matriks Kekakuan Elemen 2 (node 1 – 2) →0 902800280 0 000.933 20 140 28000 0 140140002k; T0 0.9331400140014014000 2800280000 0.93300.93314001400 1402800001000010000000100000001000010000000122kTgT 22 . k.Tkg2 0.9330 140 0.933 0 140028000 2800140028000140014000 0.93301400.93301400 280002800140 0140001400 28000

# Overall Stiffness Matrix

# Penataan Ulang

c). Mencari Gaya Tiap Batang (Member Forces)# Element 1

c). Mencari Gaya Tiap Batang (Member Forces)# Element 2

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