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
Tangki
Portal bidang
Portal Ruang
Dome
Portal ruang
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.
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.
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 cablestayed 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
Reaksi tumpuan (V, H, M).
Gaya-gaya dalam (M, L, N, T)
Displacement (translasi, rotasi)
MANUAL
SOFTWARE APLIKASI
(M.Matrik, Takabeya, Cross, dll)
(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 :
13
12
13
11
8
6
12
9
10
7
11
8
9
5
10
6
2
3
7
5
4
1
1
2
3
4
KOORDINAT GLOBAL
• Koordinat dalam tiga dimensi, mengikuti
aturan tangan kanan (right handed), dan
merupakan koordinat Cartesian (segiempat).
• 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.