Analisis Estructural I
= 4700 4700 ´ ´
´ = 21
Solucion Ev =
21,538.00 Mpa
Ec =
21,538.00 Mpa VIGA [4-1]
A= Ev =
0.18
m2
21,538,000.00 kN/m2
L=
6.00
I=
0.0054
m m4 COLUMNAS
A= Ec =
0.12
m2
21,538,000.00 kN/m2
COLUMNAS
A= Ec =
0.12
m2
21,538,000.00 kN/m2
L=
3.00
m
L=
4.00
m
I=
0.0016
m4
I=
0.0016
m4
A=
0.18
VIGA [1-2]
Ev = L
m2
21,538,000.00 kN/m2
4 00
Analisis Estructural I
Elemento
L (m)
A (m2)
I
[4-1]
6
0.18
0.0054
[1-2]
4
0.18
0.0054
[5-1]
3
0.12
[3-2]
4
0.12
E(kN/m^2)
AE
EI
AE/L
12EI/L^3
6EI/L^2
21,538,000.00 3,876,840.000
116,305.200
21,538,000.00 3,876,840.000
116,305.200
0.001600
21,538,000.00 2,584,560.000
0.00160
21,538,000.00 2,584,560.000
646,140.000
6,461.400
19,384.200
77,536.800
38,768.400
969,210.000
21,807.225
43,614.450
116,305.200
5 8,152.600
3 4,460.800
861,520.000
15,315.911
22,973.867
45,947.733
22,973.867
34,460.800
646,140.000
6,461.400
12,922.800
34,460.800
17,230.400
Xij
Xji
-40.00
-40.00
1.- Determinando las fuerzas reactivas de empotramiento Tramo
Yij
Yji
Mij
Mji
[4-1]
180.00
180.00
180.00
-180.00
[1-2]
96.00
64.00
58.667
-48.00
0.00
0.00
30.00
-30.00
0.00
0.00
0.00
0.00
[5-1] [3-2] [2vol]
20.00
13.333
4EI/L
2EI/L
Analisis Estructural I
2.-
Planteando las matrices de rigideces para cada tramo: VIGA [4-1] u4
v4
θ 4
u1
v1
θ 1
X41
646,140.000
0.00
0.00
-646,140.000
0.00
0.00
u4
Y41
0.00
6,461.400
19,384.200
0.00
-6,461.400
19,384.200
v4
0.00
19,384.200
77,536.800
0.00
-19,384.200
38,768.4000
θ 4
M41
=
0
180.00 +
180.00
X14
-646,140.000
0.00
0.00
646,140.000
0.00
0.00
u1
Y14
0.00
-6,461.400
-19,384.200
0.00
6,461.400
-19,384.200
v1
180.00
0
M14
0.00
19,384.200
38,768.400
0.00
-19,384.200
77,536.800
θ 1
-180.00
u5
v5
θ 5
u1
-40.00
COLUMNA [5-1] v1
θ 1
X51
15,315.911
0.00
-22,973.867
-15,315.911
0.00
-22,973.867
u5
Y51
0.00
861,520.000
0.00
0.00
-861,520.000
0.00
v5
M51
-22,973.867
0.00
45,947.733
22,973.867
0.00
22,973.867
θ 5
X15
=
-15,315.911
0.00
22,973.867
15,315.911
0.00
22,973.867
u1
Y15
0.00
-861,520.000
0.00
0.00
861,520.000
0.00
v1
M15
-22,973.867
0.00
22,973.867
22,973.867
0.00
45,947.733
θ 1
u1
v1
θ 1
u2
v2
θ 2
969,210.000
0.00
0.00
-969,210.000
0.00
0.00
0 +
30.00
-40.00
-30.00
0
VIGA [1-2] X12
0
u1
Y12
0.00
21,807.225
43,614.450
0.00
-21,807.225
43,614.450
v1
96.00
M12
0.00
43,614.450
116,305.200
0.00
-43,614.450
58,152.600
θ 1
58.667
X21
=
-969,210.000
0.00
0.00
969,210.000
0.00
0.00
u2
Y21
0.00
-21,807.225
-43,614.450
0.00
21,807.225
-43,614.450
v2
64.00
M21
0.00
43,614.450
58,152.600
0.00
-43,614.450
116,305.200
θ 2
-48.00
+
0
Analisis Estructural I
COLUMNA [3-2] u3
v3
θ 3
u2
X32
6,461.400
0.000
-12,922.800
-6,461.400
0.000
-12,922.800
Y32
0.000
646,140.000
0.000
0.000
-646,140.000
0.000
v3
M32
-12,922.800
0.000
34,460.800
12,922.800
0.000
17,230.400
θ 3
-6,461.400
0.000
12,922.800
6,461.400
0.000
12,922.800
u2
Y23
0.000
-646,140.000
0.000
0.000
646,140.000
0.000
v2
M23
-12,922.800
0.000
17,230.400
12,922.800
0.000
34,460.800
θ 2
X23
3.-
=
Ensamblamiento de la matriz de rigidez Planteamiento de ecuaciones
X14+X12+X15=0 Y14+Y12+Y15=0 M14+M12+M15=0 X21+X23+X2ol = 0 Y21+Y23+Y2ol = 0 M21+M23+M2ol = 0 M32 = 0 X32 = X3 Y32 = Y3 X41 = X4 Y41 = Y4 M41 = M4 X51 = X5 Y51 = Y5 M51 = M5
v2
θ 2
u3
