STRUKTUR PORTAL BIDANG
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JOINT-I ADALAH SENDI
jiE, A, I, L
Kekakuan elemen pada sumbu lokal
Kekakuan elemen pada sumbu
global
sb-x ; u , f
sb-y ; v , g
JOINT-J ADALAH SENDI
ji E, A, I, L
Kekakuan elemen pada sumbu lokal
Kekakuan elemen pada sumbu
global
sb-x ; u , f
sb-y ; v , g
j
j
i
i
j
j
i
i
V
U
V
U
kkkk
kkkk
kkkk
kkkk
G
F
G
F
44434241
34333231
24232221
14131211
OVER-ALL STIFFNESS MATRIX
n
n
i
i
mnnmmm
nmnmmm
nn
nn
n
n
i
i
V
U
V
U
kkkk
kkkk
kkkk
kkkk
G
F
G
F
...
...
...
..........
......
...
...
...
..........
..........
..
..
..
)1(21
)1()1)(1(2)1(1)1(
2)1(22221
1)1(11211
..... .... ........... ... .... .... ........... ... .... .... .......... ...
....untuk 1 elemen dengan node i dan j
......untuk rangka bidang dengan
node sejumlah n
BOUNDARY CONDITIONS
k
u
r
e
U
U
K
K
K
K
F
F
22
12
21
11
{Fe} = “Prescribed external force vector”
{Fr} = “Un-known reaction vector”
{Uu} = “Un-known displacement vector”
{Uk} = “Known displacement vector “given by boundary condition.
[Kij] = “Sub-matrix of overall stiffness matrix”.
X
Stiffness by Definition vs Direct Stiffness
K
K completed
Uunknown
FunknownUknown
Fknown=
=X
Reactions
Zero Unless Settlement
Occurs
kue UKUKF 1211
UN-KNOWN DISPLACEMENT & REACTION
kur UKUKF 2221
keu UKFKU 121
11
SEHINGGA DIPEROLEH ;
TUMPUAN)PADA SETTLEMENTTIDAK ADA (JIKA 0KU