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Programa para cálculos de armaduras:
Cálculo de de longitudes de elementos:
XY ---> Coordenadas
CON---> Matriz de conectividad
CalculoLongitudes ≔
XY ,CON
Nele ←rows
CON
for ∊
i 1 ‥Nele
NI ←CON
i , 2
NJ ←CON
i , 3
y2 ←XY
NJ , 2
y1 ←XY
NI , 2
x2 ←XY
NJ , 1
x1 ←XY
NI , 1
L ←
i , 1
y2 - y
2 ( ( x2 - x
2
L
Matriz de Transformación
MatrizBeta ≔
( XY ,CON ,L
Nele ←rows
(CON
for ∊
i 1 ‥Nele
NI ←CON
i , 2
NJ ←CON
i , 3
y2 ←XY
NJ , 2
y1 ←XY
NI , 2
x2 ←XY
NJ , 1
x1 ←XY
NI , 1
cθ ←―――
x2 - x
L
i , 1
sθ ←―――
y2 - y
L
i , 1
β ←
i , 1
cθ sθ 0 0
0 0 cθ sθ
0 0 - sθ cθ
⎤ ⎥ ⎥ ⎥ ⎦ β
Matriz de Colocación
MatrizColocacion ≔
CON ,XY
GDLnodo ← 2
GDL ←rows ⋅
XY
GDLnodo
Nele ←rows
CON
for ∊
i 1 ‥Nele
NI ←CON
i , 2
NJ ←CON
i , 3
f ←
x ,y
L ←
i , 1
matrix
2 ⋅GDLnodo ,GDL ,f
for ∊
j 1 ‥GDLnodo
L
i , 1
j ,GDLnodo ⋅ + ( ( NI - 1 ) ) j
L
i , 1
j +GDLnodo ,GDLnodo ⋅ + ( ( NJ - 1 ) ) j
L
Matriz de Rigidez ejes y dimensiones Globales de cada elemento
MatrizKelemento ≔
Long ,β ,L ,CON ,MAT ,PROP
Nele ←rows
CON
for ∊
i 1 ‥Nele
IdenA ←CON
i , 5
IdenM ←CON
i , 4
E ←
i , 1
MAT
IdenM , 2
if
else
E ＝
i , 1
k ←
i , 1
MAT ⋅
IdenM , 4
A ←
i , 1
PROP
IdenA , 2
k ←
i , 1
E ⋅
i , 1
A
i , 1
Long
i , 1
K_E ←
i , 1
T
L
i , 1
T
β
i , 1
k
i , 1
β
i , 1
L
i , 1
K_E
Vector de Fuerzas de Empotramiento (Femp):
Fempotramiento ≔
femp ,XY
GDLnodo ← 2
Nele ←rows
femp
GDL ←rows ⋅
XY
GDLnodo
f ←
x ,y
Femp ←matrix
GDL , 1 ,f
for ∊
i 1 ‥Nele
Femp ←Femp +femp
i , 1
Femp
Vector de Restricciones
VectorRestricciones ≔
R ,XY
GDLnodo ← 2
GDL ←rows ⋅
XY
GDLnodo
f ←
x ,y
R2 ←matrix
GDL , 1 ,f
Nrest ←rows
R
for ∊
i 1 ‥Nrest
for ∊
j 1 ‥GDLnodo
N ←R
i , 1
R2 ←
2 ⋅N - 2 +j , 1
R
i ,j + 1
R
Vector de fuerzas nodales:
FuerzasNodales ≔
( R ,XY
GDLnodo ← 2
GDL ←rows ⋅
(XY
) GDLnodo
f ←
x ,y
VectorR ←matrix
GDL , 1 ,f
Nrest ←rows
R
for ∊
i 1 ‥Nrest
for ∊
j 1 ‥GDLnodo
N ←R
i , 1
VectorR ←
2 N - 2 +j , 1
R
i ,j + 1
VectorR
Partición de Matrices
MatrizKpp ≔ ( ( K ,p ) )
‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖
‖
| | | | | | | | | | | | |
|
GDLp ←rows ( ( p ) )
for ∊ | | | | | | | | | | i 1 ‥GDLp
‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖
for ∊
| | | | | | | | j 1 ‥GDLp
‖ ‖ ‖ ‖ ‖ ‖ ‖
f ←p
i , 1
c ←p
j , 1
Kpp ←
i ,j
K
f ,c
Kpp
MatrizKss ≔ ( ( K ,s ) )
‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖
‖
| | | | | | | | | | | | |
|
GDLs ←rows ( ( s ) )
for ∊ | | | | | | | | | | i 1 ‥GDLs
‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖
for ∊ | | | | | | | | j 1 ‥GDLs
‖ ‖ ‖ ‖ ‖ ‖ ‖
f ←s
i , 1
c ←s
j , 1
Kss ←
i ,j
K
f ,c
Kss
MatrizKps ≔ ( ( K ,p ,s ) )
‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖
‖
| | | | | | | | | | | | | |
|
GDLp ←rows ( ( p ) )
for ∊ | | | | | | | | | | |
|
i 1 ‥GDLp
‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖
GDLs ←rows ( ( s ) )
for ∊ | | | | | | | | j 1 ‥GDLs
‖ ‖ ‖ ‖ ‖ ‖ ‖
f ←p
i , 1
c ←s
j , 1
Kps ←
i ,j
K
f ,c
Kps
MatrizKsp ≔ ( ( K ,s ,p ) )
‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖
‖
| | | | | | | | | | | | | |
|
GDLs ←rows ( ( s ) )
for ∊
| | | | | | | | | | |
|
i 1 ‥GDLs
‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖
GDLp ←rows
( (p
) )
for ∊ | | | | | | | | j 1 ‥GDLs
‖ ‖ ‖ ‖ ‖ ‖ ‖
f ←s
i , 1
c ←p
j , 1
Ksp ←
i ,j
K
f ,c
Ksp
MatrizFp ≔ ( ( F ,p ) )
‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ ‖ | | | | | | | | |
GDLp ←rows ( ( p ) )
for ∊ | | | | | | i 1 ‥GDLp
‖
‖
‖
‖
‖
f ←p
i , 1
Fp ←
i , 1
F
f , 1
Fp
