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INGENIERIA SISMICAMATRICES DE RIGIDEZ
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TRABAJO DOMICILIARIO DE INGENIERIA SISMICA
K11 = K1+K2
K21 = -K2
K31 = 0
K12 = - K2
K22 = K2+K3
K32 = -K3
K12 = - K2
K22 = K2+K3
K32 = -K3
V=12 EI
h3
(KL)P =
CALCULO DE RIGIDECES LATERALES DE LOS PORTICOS
PORTICO “A”
EIC1 ¿2x 106 x 0.30 x0.453
12=4556.25
EIC1¿2x 106 x 0.30 x0.553
12=8318.75
K1¿2x 12x 4556.25
4.103+2 x12 x 8318.75
4.103=4483.39 TN/M
K1¿4483.39 TN/M
4,483.39 0.00 0.00
[ KL ]A = 0.00 0.00 0.00
0.00 0.00 0.00
PORTICO “B”
EIC3 ¿2x 106 x 0.65 x0.303
12=2950.00
EIC4 ¿2x 106 x 0.35 x0.753
12=2409.38
K1¿2x 12x 2950
4.103+ 2 x12 x24609.38
4.103=¿9,588.15 TN/M
K1¿9,588.15 TN/M
K2¿2x 12x 2950
33+ 2 x12 x24609.38
33=¿24,475.00 TN/M
K2¿24,475.00 TN/M
K3¿24,475.00 TN/M
34,063.15 -24,475.00 0.00
[ KL ]B ,C = -24,475.00 48,950.00 -24,475.00
0.00 -24,475.00 24,475.00
PORTICO “D”
EIC1 ¿2x 106 x 0.45 x0.303
12=2025.00
EIC4 ¿2x 106 x 0.35 x0.753
12=2406.38
EIC3 ¿2x 106 x 0.65 x0.303
12=2925.00
K1¿2x 12x 24609.38
4.103+ 12 x2025
4.103+12 x2925
4.103=¿9,431.45 TN/M
K1¿9,431.45
K2¿2x 12x 24609.38
33+ 12 x2025
33+12 x2925
33=24075.00 TN/M
K3¿24075.00 TN/M
33,506.45 -24,075.00 0.00
[ KL ]D =-24,075.00 48,150.00 -24,075.00
0.00 -24,075.00 24,075.00
PORTICO “E”
EIC1 ¿4556.25
EIC2 ¿8318.75
K1¿2x 12
4.103(4556.25+8318.75)=¿4,483.39
K1¿4,483.39
K2¿2x 12
33(4556.25+8318.75)=11444.44 TN/M
K2¿11444.44 TN/M
K3¿11444.44 TN/M
15,927.84 -11,444.44 0.00
[ KL ]E =-11,444.44 22,888.89 -11,444.44
0.00 -11,444.44 11,444.44
PORTICO 1
EIC1 ¿2x 106 x 0.45 x0.303
12=2025.00
EIC1* ¿
2x 106 x 0.30 x0.453
12=4556.25
EIC3 ¿2x 106 x 0.30 x0.653
12=13731.25
K1¿2x 12x 2025
4.103+ 2 x12 x13731.25
4.103+12 x 4556.25
4.103=¿6,280.02 TN/M
K1¿6,280.02
K2¿2x 12x 13731.25
33+ 12x 4556.25
33+ 12x 4556.25
33=15130.56 TN/M
K2¿15130.56 TN/M
K3¿15130.56 TN/M
21,410.57 -15,130.56 0.00
[ KL ]1 =-15,130.56 30,261.11 -15,130.56
0.00 -15,130.56 15,130.56
PORTICO 2 Y 3
EIC1 ¿2x 106 x 0.55 x0.303
12=2475.00
EIC4 ¿2x 106 x 0.75 x0.353
12=5359.38
K1¿2x 12x 2475
4.103+ 3 x12 x5359.38
4.103=¿3,661.26 TN/M
K1¿3,661.26 TN/M
K2¿2x 12x 2475
33+ 3 x12 x5359.38
33=8245.84 TN/M
K3¿8245.84 TN/M
PORTICO – 4
EIC1 ¿2x 106 x 0.45 x0.303
12=2025.00
EIC3 ¿2x 106 x 0.30 x0.653
12=13731.25
K1¿2x 12x 2025
4.103+ 3 x12 x13731.25
4.103=¿7,877.50
K2¿12x 2025
33+ 3 x12 x13731.25
33=19208.33
K2¿19208.33
K3¿19208.33
11,907.09 -8,245.83 0.00
[ KL ]2,3 =-8,245.83 16,491.67 -8,245.83
0.00 -8,245.83 8,245.83
27,085.83 -19,208.33 0.00
[ KL ]4 =-19,208.33 38,416.67 -19,208.33
0.00 -19,208.33 19,208.33
CENTRO DE GRAVEDAD
PISO Nº 01:
X=ΣAi∗XiΣAi
Y= ΣAi∗YiΣAi
Ai (m2) Xi (m) Ai*Xi (m3) 1 344.00 8.00 2,752.00 2 8.00 5.33 42.673 21.50 16.67 358.334 -30.00 2.50 -75.00𝛴 343.50 3,078.00
X1 = 8.96 m
Ai (m2) Yi (m) Ai*Yi (m3)1 344.00 10.75 3,698.002 8.00 21.83 174.673 21.50 7.17 154.084 -30.00 7.50 -225.00𝛴 343.50 3,801.75
Y1 = 11.07 m
PISO Nº 02 Y 03:
X=ΣAi∗XiΣAi
Ai (m2) Xi (m) Ai*Xi (m3)1 271.76 8.24 2,237.903 12.62 16.98 214.334 -30.00 2.50 -75.00𝛴 254.38 2,377.23
X2,3 = 9.35 m
Y= ΣAi∗YiΣAi
Ai (m2) Yi (m) Ai*Yi (m3)1 271.76 8.25 2,241.983 12.62 5.50 69.424 -30.00 7.50 -225.00𝛴 254.38 2,086.40
Y2,3 = 8.20 m
P α (°) α (rad) cos α sen αA 176.42 3.0791 -0.9980 0.062B 0.00 0.0000 1.0000 0.000C 0.00 0.0000 1.0000 0.000D 0.00 0.0000 1.0000 0.000E 0.00 0.0000 1.0000 0.0001 90.00 1.5708 0.0000 1.0002 90.00 1.5708 0.0000 1.0003 90.00 1.5708 0.0000 1.0004 95.31 1.6635 -0.0925 0.996
PRIMER PISODIST. AL CM (0,0) R1
A 10.87 10.851B 5.43 -5.43C -0.57 0.57D -6.57 6.57E -11.07 11.071 -8.96 -8.962 -3.96 -3.963 1.54 1.544 8.01 -7.975
SEGUNDO Y TERCER PISODIST. AL CM
(0,0) R2 Y R3
A - 0.000
B 8.30 -8.300
C 2.30 -2.300
D -3.70 3.700E -8.20 8.2001 -9.35 -9.350
2 -4.35 -4.350
3 1.15 1.150
4 7.89 7.856
MATRICES DE COMPATIBILIDAD
1 0 0
I 0 1 0 A [I]cosα [I]senα R
0 0 1
PORTICOS EN EL EJE X
1 2 3 4 5 6 7 8 9
-0.998 0.000 0.000 0.062 0.000 0.000 10.851 0.000 0.000 1
AA 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 3
1.000 0.000 0.000 0.000 0.000 0.000 -5.430 0.000 0.000
AB 0.000 1.000 0.000 0.000 0.000 0.000 0.000 -8.300 0.000
0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 -8.300
1.000 0.000 0.000 0.000 0.000 0.000 0.570 0.000 0.000
AC 0.000 1.000 0.000 0.000 0.000 0.000 0.000 -2.300 0.000
0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 -2.300
1.000 0.000 0.000 0.000 0.000 0.000 6.570 0.000 0.000
AD
0.000 1.000 0.000 0.000 0.000 0.000 0.000 3.700 0.000
0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 3.700
1.000 0.000 0.000 0.000 0.000 0.000 11.070 0.000 0.000
AE 0.000 1.000 0.000 0.000 0.000 0.000 0.000 8.200 0.000
0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 8.200
PORTICOS EN EL EJE Y
0.000 0.000 0.000 1.000 0.000 0.000 -8.960 0.000 0.000
A1 0.000 0.000 0.000 0.000 1.000 0.000 0.000 -9.350 0.000
0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 -9.350
0.000 0.000 0.000 1.000 0.000 0.000 -3.960 0.000 0.000
A2 0.000 0.000 0.000 0.000 1.000 0.000 0.000 -4.350 0.000
0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 -4.350
0.000 0.000 0.000 1.000 0.000 0.000 1.540 0.000 0.000
A3 0.000 0.000 0.000 0.000 1.000 0.000 0.000 1.150 0.000
0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 1.150
-0.093 0.000 0.000 0.996 0.000 0.000 -7.975 0.000 0.000
A4 0.000 -0.093 0.000 0.000 0.996 0.000 0.000 7.856 0.000
0.000 0.000 -0.093 0.000 0.000 0.996 0.000 0.000 7.856
TRASPUESTA DE LA MATRIZ DE COMPATIBILIDAD
1 2 3
-0.998 0.000 0.000 1 0.000 0.000 0.000
0.000 0.000 0.000 2 0.000 0.000 0.000
0.000 0.000 0.000 3 0.000 0.000 0.000
0.062 0.000 0.000 4 1.000 0.000 0.000
AT 0.000 0.000 0.000 5 1T 0.000 1.000 0.000
0.000 0.000 0.000 6 0.000 0.000 1.000
10.851 0.000 0.000 7 -8.960 0.000 0.000
0.000 0.000 0.000 8 0.000 -9.350 0.000
0.000 0.000 0.000 9 0.000 0.000 -9.350
1.000 0.000 0.000 0.000 0.000 0.000
0.000 1.000 0.000 0.000 0.000 0.000
0.000 0.000 1.000 0.000 0.000 0.000
0.000 0.000 0.000 1.000 0.000 0.000
BT 0.000 0.000 0.000 2T 0.000 1.000 0.000
0.000 0.000 0.000 0.000 0.000 1.000
-5.430 0.000 0.000 -3.960 0.000 0.000
0.000 -8.300 0.000 0.000 -4.350 0.000
0.000 0.000 -8.300 0.000 0.000 -4.350
1.000 0.000 0.000 0.000 0.000 0.000
0.000 1.000 0.000 0.000 0.000 0.000
0.000 0.000 1.000 0.000 0.000 0.000
0.000 0.000 0.000 1.000 0.000 0.000
CT 0.000 0.000 0.000 3T 0.000 1.000 0.000
0.000 0.000 0.000 0.000 0.000 1.000
0.570 0.000 0.000 1.540 0.000 0.000
0.000 -2.300 0.000 0.000 1.150 0.000
0.000 0.000 -2.300 0.000 0.000 1.150
1.000 0.000 0.000 -0.093 0.000 0.000
0.000 1.000 0.000 0.000 -0.093 0.000
0.000 0.000 1.000 0.000 0.000 -0.093
0.000 0.000 0.000 0.996 0.000 0.000
DT 0.000 0.000 0.000 4T 0.000 0.996 0.000
0.000 0.000 0.000 0.000 0.000 0.996
6.570 0.000 0.000 -7.975 0.000 0.000
0.000 3.700 0.000 0.000 7.856 0.000
0.000 0.000 3.700 0.000 0.000 7.856
1.000 0.000 0.000
0.000 1.000 0.000
0.000 0.000 1.000
0.000 0.000 0.000
ET 0.000 0.000 0.000
0.000 0.000 0.000
11.070 0.000 0.000
0.000 8.200 0.000
0.000 0.000 8.200
MATRIZ DEL EDIFICIO
122,258.5 -84,634.0 0.0 -2,775.3 1,770.0 0.0 202,348.4 90,478.3 0.0
-84,634.0 169,267.9 -84,634.0 1,770.0 -3,540.0 1,770.0 -180,091.5 -180,956.6 90,478.3
0.0 -84,634.0 84,634.0 0.0 1,770.0 -1,770.0 0.0 90,478.3 -90,478.3
-2,775.3 1,770.0 0.0 72,096.1 -50,666.0 0.0 -432,708.7 17,601.6 0.0
1,770.0 -3,540.0 1,770.0 -50,666.0 101,332.1 -50,666.0 308,061.0 -35,203.2 17,601.6
0.0 1,770.0 -1,770.0 0.0 -50,666.0 50,666.0 0.0 17,601.6 -17,601.6
202,348.4 -180,091.5 0.0 -432,708.7 308,061.0 0.0 8,598,166.8 -2,915,786.7 0.0
90,478.3 -180,956.6 90,478.3 17,601.6 -35,203.2 17,601.6 -2,915,786.7 11,179,745.3 -5,589,872.6
0.0 90,478.3 -90,478.3 0.0 17,601.6 -17,601.6 0.0 -5,589,872.6 5,589,872.6
MOMENTO TORSOR
CM=CG EXCENTRICIDAD SENTIDO DEL M.T.
X Y ex= YR-X positivoantihorario
8.96 11.07 ey= XR-Y negativo horario
PORTICO
KL(tm/m) BRAZO(m)
Mparcial CR(XR,YR)
CM(X,Y)
e MOMENTO
sentido
EJE X(XR)
A 4,483.39 22.46 100,697.03 YR Y ey Vx*ey
7.98B 9,588.15 16.50
158,204.50
10.70 11.07 0.37 7.98C 9,588.15 10.50 100,675.59
D 9,431.45 4.50 42,441.53E 4,483.39 0.00 0.00
TOTAL 37,574.54
402,018.65
EJE Y(YR)
1 6,280.02 0.00 0.00 XR X ex Vy*ex
-11.042 3,661.26 5.00 18,306.29
8.45 8.96 0.51 11.043 3,661.26 10.50 38,443.20
4 7,877.50 15.84 124,779.56
TOTAL 21,480.03
181,529.04
M1 (tn.m)
momento torsor final -3.06
PISO Nº 01
CM=CG EXCENTRICIDAD SENTIDO DEL M.T.X Y ex= YR-X positivo antihorario
9.35 8.20 ey= XR-Y negativo horario
PORTICO KL(tm/m) BRAZO(m) Mparcial CR(XR,YR) CM(X,Y) DELTA MOMENTO sentido
EJE X(XR)
B 24,475.00 16.50 403,837.50 YR Y ey Vx*ey
-25.78C 24,475.00 10.50 256,987.50
9.11 8.20 0.91 25.78D 24,075.00 4.50 108,337.50E 11,444.44 0.00 0.00
TOTAL 84,469.44 769,162.50
EJE Y(YR)
1 15,130.56 0.00 0.00 XR X ex Vy*ex
-23.842 8,245.83 5.00 41,229.17
8.50 9.35 0.85 23.843 8,245.83 10.50 86,581.254 19,208.33 15.84 304,260.00
TOTAL 50,830.56 432,070.42 M2 momento torsor final -49.63
PISO Nº 02
PISO Nº 03
CM=CG EXCENTRICIDAD SENTIDO DEL M.T.
X Y ex= YR-X positivo antihorario
9.35 8.20 ey= XR-Y negativo horario
PORTICO KL(tm/m) BRAZO(m
) Mparcial CR(XR,YR)
CM(X,Y)
DELTA
MOMENTO sentido
EJE X(XR
)
B24,475.0
0 16.50403,837.5
0 YR Y ey Vx*ey
-32.37C
24,475.00
10.50256,987.5
0
9.11 8.20 0.91 32.37D 24,075.00
4.50 108,337.50
E 11,444.44 0.00 0.00
TOTAL 84,469.44
769,162.50
EJE Y(YR)
115,130.5
6 0.00 0.00 XR X ex Vy*ex
-29.942 8,245.83 5.00 41,229.17
8.50 9.35 0.85 29.943 8,245.83 10.50 86,581.25
4 19,208.33
15.84 304,260.00
TOTAL 50,830.56
432,070.42
M3 momento torsor final
-62.31
LAS EXCENTRICIDADES
PISO Nº 01
PISO Nº 02
PISO Nº 03
21.67 Vx1
28.22 Vx235.43 Vx321.67 Vy1
Q9x1= 28.22 Vy2
35.43 Vy3-3.06 M1
-49.63 M2-62.31 M3
DESPLAZAMIENTOS
{Q }2nx1=⌈ K EDIF ⌉2nX2n {D }2nx 1
2.356E-03 m3.253E-03 m3.684E-03 m4.364E-03 m
LUEGO D9x1= 5.374E-03 m
6.088E-03 m4.693E-05 rad2.214E-05 rad2.023E-05 rad
Direccion X
-1.57E-03
dA 0.00E+00
0.00E+00
2.10E-03
dB 3.07E-03
3.52E-03
2.38E-03
dC 3.20E-03
3.64E-03
2.66E-03
dD 3.33E-03
3.76E-03
2.88E-03
dE 3.43E-03
3.85E-03
Direccion Y
3.94E-03
d1 5.17E-03
5.90E-03
4.18E-03
d2 5.28E-03
6.00E-03
4.44E-03
d3 5.40E-03
6.11E-03
3.75E-03
d4 5.22E-03
5.88E-03
