ANALISIS STRUKTUR DENGAN METODE MATRIK KEKAKUAN Oleh : RIZKI ZULKIFLI

STRUKTUR??? Suatu sistem yang mengambil tempat dalam ruang, dengan komponen atau bagian yang memiliki ukuran tertentu

TIPE-TIPE STRUKTUR Berdasarkan kegunaan sistem Struktur jembatan, tangki, gedung, bendungan, atau pesawat udara Berdasarkan derajat ketidaktentuannya Struktur statis tertentu Struktur statis tak tentu Berdasarkan fungsi sistem menerima beban luar Struktur kerangka Mis : Balok Menerus, Portal Bidang, Portal Ruang, Rangka Batang Bidang, Rangka Batang Ruang, Grid Struktur kontinum Mis : Pelat, cangkang, tangki

Balok menerus Portal bidang Portal ruang Portal Bidang Portal Ruang Tangki Dome

Sydney Opera House, Australia The shell-shaped Sydney Opera House is one of the most famous pieces of modern architecture in the world. It was designed by Jørn Utzon and completed in 1973. Sydney is the capital of New South Wales, which is located on the southeastern coast of Australia. Sydney is the largest city in Australia and the country’s cultural center. Petronas Towers, Kuala Lumpur Completed in 1998, the Petronas Towers, in Kuala Lumpur, Malaysia, stand 452 m (1,483 ft) tall at their pinnacles. The towers are connected by a skyway at the 41st and 42nd floors. The architect, Argentine American Cesar Pelli, found inspiration for the buildings’ design in traditional Malaysian Islamic architecture.

Astoria Bridge Constructed of continuous trusses, this interstate bridge over the meandering Columbia River connects Astoria, Oregon, to Megler, Washington. The bridge was named for Fort Astor, a fur-trading post established in 1811 by John Jacob Astor's Pacific Fur Company.

Yokohama Bay Bridge The 860-meter (2,822-foot) Yokohama Bay Bridge crosses part of Tokyo Bay. The cable-stayed bridge reflects the modern character of the city of Yokohama, which was almost completely rebuilt after an earthquake caused widespread destruction in 1923. The city is now an industrial center and leading seaport for Japan. Golden Gate Bridge, San Francisco The Golden Gate Bridge links the city of San Francisco with Marin County to the north. The suspension bridge was opened in 1937 and since then has been one of the principal landmarks of both San Francisco and California

Saint Peter’s Basilica, Rome In 1506 architect Donato Bramante, under commission from Pope Julius II, designed Saint Peter’s, located in Vatican City, within the city of Rome. Bramante died before completing the church, so Florentine artist Michelangelo assumed the supervisory role in 1546. Michelangelo’s innovative design for the enormous ribbed dome of Saint Peter’s influenced dome design and construction for the next 300 years. The dome, which was completed after the death of Michelangelo, preserves the essential elements of his design but is taller and more elongated than he planned. Geodesic Dome This geodesic dome was built for the United States pavilion at Expo ’67, the world’s fair in Montréal, Canada. Geodesic domes have no internal supports, making them ideal structures for holding large groups of people. They are made up of standardized, interlocking shapes that can be assembled and taken apart quickly.

STRUKTUR ANALISIS STRUKTUR DESAIN Reaksi tumpuan (V, H, M). Gaya-gaya dalam (M, L, N, T) Displacement (translasi, rotasi) MANUAL (M.Matrik, Takabeya, Cross, dll) SOFTWARE APLIKASI (SAP, ETABS, SANS, dll) DESAIN

JOIN & DERAJAT KEBEBASAN Joint : titik kumpul yang menghubungkan antara elemen, dan merupakan titik pada struktur yang displacement-nya diketahui atau akan dihitung. Komponen displacement pada joint : translasi dan rotasi Jumlah displacement bebas  derajad kebebasan atau DOF (Degree of Freedom).

Penentuan Jumlah derajat kebebasan Struktur NX = 3NJ – 3NFJ – 2NPJ – NR Dimana : NJ = jumlah total titik kumpul (termasuk perletakan) NFJ = jumlah titik yang sifatnya JEPIT NPJ = jumlah titik yang sifatnya SENDI NR = jumlah titik yang sifatnya ROL

Contoh : 1 2 3 4 5 6 7 8 9 10 11 12 13

KOORDINAT GLOBAL Koordinat dalam tiga dimensi, mengikuti aturan tangan kanan (right handed), dan merupakan koordinat Cartesian (segi-empat). Tiga sumbu dengan notasi X, Y, dan Z ialah sumbu yang saling tegak lurus sesuai dengan aturan tangan kanan.

KOORDINAT LOKAL Digunakan untuk menentukan potongan property, beban dan gaya-gaya keluaran. Sumbu-sumbunya dinyatakan dengan simbol 1,2 dan 3. Sumbu 1 arahnya searah sumbu elemen, dua sumbu yang lain tegak lurus dengan elemen tersebut dan arahnya dapat ditentukan sendiri oleh pengguna.