The document presents stiffness matrices for different structural elements:
1) Frames, with matrices given for elements parallel to the X and Y axes.
2) Trusses, with a general stiffness matrix given.
3) Grillages, with general notation and matrix presented for elements parallel to X and Y.
The matrices relate the stiffness of each element to displacement and force terms using structural properties like length, cross sectional area, and moments of inertia.
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Matrices
1. MATRIZ DE RIGIDEZ PARA PORTICOS
EA EI EI EI
K= K1 = 12 K2 = 6 K3 = 4
L L3 L2 L
General
A = γ 12 K + γ 2 K1
2
B = γ 1γ 2 ( K − K1 ) C = γ 2 K2
D = γ 2 K + γ 12 K1
2
E = γ 1K 2
A B C A B C
B D E B D E
K3
C E K3 C E 2
K
A B C A B C
B D E B D E
K3
C E 2
C E K 3
Barra paralela a ''X''
K 0 0 K 0 0
0 K1 K2 0 K 1 K2
K3
0 K2 K3 0 K 2 2
K
K 0 0 K 0 0
0 K 1 K 2 0 K1 K 2
K3
0 K2 2
0 K 2 K3
Barra paralela a ''Y''
K1 0 K 2 K 1 0 K 2
0 K 0 0 K 0
K3
K 2 0 K3 K2 0 2
K
K 1 0 K2 K1 0 K2
0 K 0 0 K 0
K3
K 2 0 2
K2 0 K3
MATRIZ DE RIGIDEZ PARA RETICULADOS
2
1 1 2 2
1 1 2
1 2 2
2 1 2 2
2
KK
2
1 1 2 2
1 1 2
1 2 2
2 1 2 2
2
2. MATRIZ DE RIGIDEZ PARA EMPARRILLADOS
GJ EI EI EI
K= K1 = 12 K2 = 6 K3 = 4
L L3 L2 L
General
A 2 K 2 C 2 K 2 K 3
1 2 E 2 K 2 K 3
2 1 G 2 K 2 K 3
1 2 2
K3
B 1 K 2 D 1 2 K K 3 F 1 2 K 2
H 2 K 2 K 3
2 1 2
K1 A B K 1 A B
A C D A G F
B D E B F H
K
K 1 A B K 1 A B
A G F A C D
B F H B D E
Barra paralela a ''X''
K1 0 K 2 K 1 0 K 2
0 K 0 0 K 0
K3
K 2 0 K3 K2 0 2
K
K 1 0 K2 K1 0 K2
0 K 0 0 K 0
K3
K 2 0 2
K2 0 K3
Barra paralela a ''Y''
K1 K2 0 K 1 K2 0
K3
K2 K3 0 K 2 2
0
0 0 K 0 0 K
K
K 1 K 2 0 K1 K 2 0
K3
K2 2
0 K 2 K3 0
0 0 K 0 0 K