JHON AYALA CARDOZO
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Transcript of JHON AYALA CARDOZO
TRABAJO DE INGENIERIA ANTISISMICACALCULO DE RIGIDEZ LATERAL
V1 V2 V3
3C2 C2 C2 C2V1 V2 V3
3C2 C2 C2 C2V1 V2 V3
3.5C1 C1 C1 C1
4 5 7PredimensionamientoLuces:Nombre: Jhon = 4Apellido Paterno: Ayala = 5Apellido Materno: Cardozo = 7
Vigas:
V1: Medidas Constructivash = L/12 = 0.333 m = 0.35 m
b= h/2 = 0.175 m = 0.25 m (ancho minimo E.060)
V2: Medidas Constructivash = L/12 = 0.417 m = 0.45 m
b= h/2 = 0.225 m = 0.25 m (ancho minimo E.060)
V3: Medidas Constructivash = L/12 = 0.583 m = 0.6 m
b= h/2 = 0.3 m = 0.3 m
Columna:b= 0.3 mh= 0.4 m
Datos:f'c = 210Ec= 15000√f'c = 217370.65 Kg/cm2
2173706.5119 Tn/m2
Calculo de Inercias:
I colum= bxh3/12 = 160000.00 cm4 = 0.0016 m4I v1= bxh3/12 = 89322.92 cm4 = 0.00089323 m5I v2= bxh3/12 = 189843.75 cm4 = 0.00189844 m6I v3= bxh3/12 = 540000.00 cm4 = 0.0054 m7
A. METODO DE CROSSa1) Calculo de Rigideces: K= EI
L
Como "E" es constante solo calculamos la relacion I/LEn vigas: En columnas:
Kv1=I
= 223.31cm3
Kc1=I
= 457.14cm3
L L
Kv2=I
= 379.69cm3
Kc2=I
= 533.33cm3
L L
Kv3= I = 771.43 cm3L
a1) Calculo de los Factores de Distribución:NUDOS
V1 V2 V34 8 12 16
C2 C2 C2 C2V1 V2 V3
3 7 11 15C2 C2 C2 C2
V1 V2 V32 6 10 14
C1 C1 C1 C1
1 5 9 13
NUDO 2457.14 = 0.3766
457.14 + 533.33 + 223.31
533.33 = 0.4394457.14 + 533.33 + 223.31
FD2-1 =
FD2-3 =
3
12
bhI
223.31 = 0.1840457.14 + 533.33 + 223.31
NUDO 3533.33 = 0.4134
533.33 + 533.33 + 223.31
533.33 = 0.4134533.33 + 533.33 + 223.31
223.31 = 0.1731533.33 + 533.33 + 223.31
NUDO 4533.33 = 0.7049
533.33 + 223.31
223.31 = 0.2951533.33 + 223.31
NUDO 6223.31 = 0.1401
223.31 + 533.33 + 379.69 + 457.14
533.33 = 0.3347223.31 + 533.33 + 379.69 + 457.14
379.69 = 0.2383223.31 + 533.33 + 379.69 + 457.14
457.14 = 0.2869223.31 + 533.33 + 379.69 + 457.14
NUDO 7223.31 = 0.1337
223.31 + 533.33 + 379.69 + 533.33
533.33 = 0.3194223.31 + 533.33 + 379.69 + 533.33
379.69 = 0.2274223.31 + 533.33 + 379.69 + 533.33
FD2-6 =
FD3-2 =
FD3-4 =
FD3-7 =
FD4-3=
FD4-8=
FD6-2 =
FD6-7 =
FD6-10 =
FD6-5 =
FD7-3 =
FD7-8 =
FD7-11 =
533.33 = 0.3194223.31 + 533.33 + 379.69 + 533.33
NUDO 8223.31 = 0.1965
223.31 + 379.69 + 533.33
379.69 = 0.3341223.31 + 379.69 + 533.33
533.33= 0.4693
223.31 + 379.69 + 533.33
NUDO 10379.69 = 0.1773
379.69 + 533.33 + 771.43 + 457.14
533.33 = 0.2490379.69 + 533.33 + 771.43 + 457.14
771.43 = 0.3602379.69 + 533.33 + 771.43 + 457.14
457.14 = 0.2135379.69 + 533.33 + 771.43 + 457.14
NUDO 11379.69 = 0.1712
379.69 + 533.33 + 771.43 + 533.33
533.33 = 0.2405379.69 + 533.33 + 771.43 + 533.33
771.43 = 0.3478379.69 + 533.33 + 771.43 + 533.33
533.33 = 0.2405379.69 + 533.33 + 771.43 + 533.33
NUDO 12379.69 = 0.2254
379.69 + 771.43 + 533.33
FD7-6 =
FD8-4 =
FD8-12 =
FD8-7 =
FD10-6 =
FD10-11=
FD10-14 =
FD10-9 =
FD11-7 =
FD11-12=
FD11-15 =
FD11-10 =
FD12-8 =
771.43 = 0.4580379.69 + 771.43 + 533.33
533.33 = 0.3166379.69 + 771.43 + 533.33
NUDO 14771.43
= 0.4378771.43 + 533.33 + 457.14
533.33= 0.3027
771.43 + 533.33 + 457.14
457.14 = 0.2595771.43 + 533.33 + 457.14
NUDO 15771.43 = 0.4197
771.43 + 533.33 + 533.33
533.33 = 0.2902771.43 + 533.33 + 533.33
533.33 = 0.2902771.43 + 533.33 + 533.33
NUDO 16771.43 = 0.5912
771.43 + 533.33
533.33 = 0.4088771.43 + 533.33
FD12-16 =
FD12-11 =
FD14-10 =
FD14-15=
FD14-13=
FD15-11 =
FD15-16=
FD15-14=
FD16-12=
FD16-15=
a3)PORTICO A RESOLVER CON FUERZAS HORIZONTALES3
4 8 12 16
2 37 11 15
1 26 10 14
1 5 9 13
Panteo de la Ecuación:
-2.30026 + 15.60046 + -19.369 = 1
15.86785 + -1.31233 + -7.79987 = 2
-4.45667 + 13.95081 + -11.1282 = 3
Resolviendo:0.440
0.763
0.511
CALCULO DE LOS MOMENTOS FINALES en TN.m
NUDO 1 2 3 4 5MIEMBRO 1--2 2--1 2--6 2--3 3--2 3--7 3--4 4--3 4--8 5--6
-4.45 -4.58 -0.11 4.70 3.43 -1.36 -2.07 -0.32 0.32 -4.451.34 2.63 1.72 -4.35 -5.68 0.08 5.60 2.70 -2.70 0.90-0.20 -0.21 -0.16 0.37 1.34 0.94 -2.28 -1.59 1.59 -0.12
NUDO 6 7 8 9MIEMBRO 6--2 6--5 6--10 6--7 7--3 7--6 7--11 7--8 8--4 8--7 8--12 9--10
X1 X2 X3
X1 X2 X3
X1 X2 X3
X1=
X2=
X3=
∆1 (X1)
∆2(X2)
∆3(X3)
-0.13 -4.62 -0.23 4.98 -1.14 4.30 -1.53 -1.63 0.09 -0.01 -0.08 -4.451.59 1.92 2.09 -5.60 -0.13 -7.10 -0.35 7.58 -2.18 4.63 -2.45 0.60-0.17 -0.15 -0.18 0.50 0.93 1.47 1.40 -3.81 1.40 -3.14 1.74 -0.07
NUDO 10 11 12 13MIEMBRO 10--6 10--1110--14 10--9 11--7 11--1211--1511--10 12--8 12--1612--1113--14
-0.11 5.21 -0.48 -4.63 -0.96 -1.08 -2.71 4.74 0.06 0.37 -0.43 -4.461.25 -6.09 3.55 1.29 -0.14 6.98 0.09 -6.93 -2.07 -4.02 6.08 0.81-0.12 0.34 -0.20 -0.02 0.81 -3.79 2.08 0.90 1.35 2.40 -3.74 -0.10
NUDO 14 15 16MIEMBRO 14--1014--1514--1315--1115--1615--1416--1216--15
-0.44 5.06 -4.62 -2.99 -1.38 4.37 0.47 -0.473.88 -5.59 1.70 0.13 6.49 -6.62 -4.93 4.93-0.26 0.35 -0.09 2.22 -3.28 1.06 2.95 -2.95
4 0.80 8 1.48 12 1.91 16 1.51
3 1.25 2.14 2.11 1.83
-0.90 7 -1.33 11 -1.28 15 -1.19
2 0.71 -0.12 -0.54 -0.17
-2.16 6 -2.86 10 -3.36 14 -3.00
-3.31 -3.67 -3.91 -3.74
1 5 9 13
Calculando las cortantes en Tn.
0.681127 1.204505 1.341155 1.114368
-0.06398 -0.48144 -0.60834 -0.45459
-1.56327 -1.8653 -2.07749 -1.92761
Calculando las deformaciones
E= 2173706.51 Tn/m2I= 0.0016 m4
∆1 (X1)
∆2(X2)
∆3(X3)
∆1 (X1)
∆2(X2)
∆3(X3)
∆1 (X1)
∆2(X2)
∆3(X3)
M4-3= M8-7= M12-11= M16-15=
M3-4= M7-8= M11-12= M15-16=
M3-2= M7-6= M11-10= M15-14=
M2-3= M6-7= M10-11= M14-15=
M2-1= M6-5= M10-9= M14-13=
M1-2= M5-6= M9-10= M13-14=
V4-3=V3-4= V8-7=V7-8= V12-11=V11-12= V16-15=V15-16=
V3-2=V2-3= V7-6=V6-7= V11-10=V10-11= V15-14=V14-15=
V2-1=V1-2= V6-5=V5-6= V10-9=V9-10= V14-13=V13-14=
EI
ML
L
EIM
6
6
2
2
-0.00679888 + -0.00444289 = -0.01124177 m-0.00754263 + -0.00587107 = -0.0134137 m-0.00804366 + -0.00689594 = -0.0149396 m-0.00768865 + -0.00617311 = -0.01386175 m
∆PISO 1= -0.05345683 m
0.00092136 + -0.00116968 = -0.00024833 m-0.00015028 + -0.00171848 = -0.00186876 m-0.00070075 + -0.00166061 = -0.00236136 m-0.00022394 + -0.00154059 = -0.00176453 m
∆PISO 2= -0.00624298 m
0.00161274 + 0.00103114 = 0.00264387 m0.002764 + 0.00191143 = 0.00467543 m
0.00273463 + 0.00247122 = 0.00520585 m0.00236921 + 0.00195635 = 0.00432555 m
∆PISO 2= 0.01685071 m
∆1-2= ∆2-1=∆5-6= ∆6-5=∆9-10 = ∆10-9=∆13-14= ∆14-13=
∆2-3= ∆3-2=∆6-7= ∆7-6=∆10-11 = ∆11-10=∆14-15= ∆15-14=
∆3-4= ∆4-3=∆7-8= ∆8-7=∆11-12= ∆12-11=∆15-16= ∆16-15=
1 a2)Calculo de los Momentos:SISTEMA MO
4 8 12 16
37 11 15
26 10 14
1 5 9 13
NO EXISTEN MOMENTOS DE EMPOTRAMIENTO PERFECTO
SISTEMA M3
4 8 12 16
37 11 15
26 10 14
1 5 9 13
-10 Tn.m
= M2= -10.00 Tn.m
Haciendo M3-4 =
M3-4 = M4-3 = M7-8 = M8-7 = M11-12 = M12-11 = M15-16 = M16-15
1TN
3TN
2TN
M3-4
M4-3
M7-8
M8-7
M11-12
M12-11
M15-16
M16-15
2CALCULO DE FUERZAS HORIZONTALES: Momentos calculados en "crossmovnivel3"
Sentido Positivo Sentido Negativo
4 8 12 16
-3.11 -6.15 -7.33 -5.77
-4.47 -7.46 -7.43 -6.423 7 11 15
-3 Tn -5 Tn 0 Tn -4 Tn
F3= -11.1282 Tn
3 7 11 152.63 2.89 1.76 2.08
0.72 0.98 0.66 0.692 6 10 14
1 Tn 1 Tn 0 Tn 1 Tn
F2= -7.79987 Tn
2 6 10 14
-0.41 -0.29 -0.04 -0.18
-0.39 -0.23 -0.13 -0.191 5 9 13
0 Tn 0 Tn 0 Tn 0 Tn
F1= -19.369 Tn
M4-3= M8-7= M12-11= M16-15=
M3-4= M7-8= M11-12= M15-16=
F3-4= F7-8= F11-12= F15-16=
M3-2= M7-6= M11-10= M15-14=
M2-3= M6-7= M10-11= M14-15=
F3-4= F7-8= F11-12= F15-16=
M2-1= M6-5= M10-9= M14-13=
M1-2= M5-6= M9-10= M13-14=
F3-4= F7-8= F11-12= F15-16=
F3
F3
F2
F3
F2
F1
3 SISTEMA M2
4 8 12 16
37 11 15
26 10 14
1 5 9 13
-10 Tn.m
= M2= -10.00 Tn.m
= M2= 10.00 Tn.m
Haciendo M2-3 =
M2-3 = M3-2 = M6-7 = M7-6 = M10-11 = M11-10 = M14-15 = M15-14
M3-4 = M4-3 = M7-8 = M8-7 = M11-12 = M12-11 = M15-16 = M16-15
M2-3
M3-2
M3-4
M4-3
M6-7
M7-6
M8-7
M7-8
M10-11
M11-10
M11-12
M12-11
M14-15
M15-14
M15-16
M16-15
4CALCULO DE FUERZAS HORIZONTALES: Momentos calculados en "crossmovnivel2"
Sentido Positivo Sentido Negativo
4 8 12 16
3.54 6.07 7.97 6.46
7.34 9.93 9.15 8.503 7 11 15
4 Tn 5 Tn 0 Tn 5 Tn
F3= 13.95081 Tn
3 7 11 15-7.44 -9.31 -9.08 -8.68
-5.70 -7.34 -7.98 -7.322 6 10 14
-4 Tn -6 Tn 0 Tn -5 Tn
F2= -1.31233 Tn
2 6 10 143.45 2.51 1.69 2.23
1.75 1.18 0.79 1.061 5 9 13
2 Tn 1 Tn 0 Tn 0 Tn
M4-3= M8-7= M12-11= M16-15=
M3-4= M7-8= M11-12= M15-16=
F3-4= F7-8= F11-12= F15-16=
M3-2= M7-6= M11-10= M15-14=
M2-3= M6-7= M10-11= M14-15=
F3-4= F7-8= F11-12= F15-16=
M2-1= M6-5= M10-9= M14-13=
M1-2= M5-6= M9-10= M13-14=
F3-4= F7-8= F11-12= F15-16=
F3
F3
F2
F3
F2
F1
F1= 15.60046 Tn
5 SISTEMA M1
4 8 12 16
37 11 15
26 10 14
1 5 9 13
-10 Tn.m
Como EI es constante para las columnas:
= -10.00 Tn.m
= 13.61 Tn.m
Haciendo M1-2 =
M1-2 = M2-1 = M5-6 = M6-5 = M9-10 = M10-9 = M13-14 = M14-13
M2-3 = M3-2 = M6-7 = M7-6 = M10-11 = M11-10 = M14-15 = M15-14
M1-2
M2-1
M2-3
M3-2
M5-6
M6-5
M7-6
M6-7
M9-10
M10-9
M10-11
M11-10
M13-14
M14-13
M14-15
M15-14
221
22121
)(
)(
YX
YXYX
LEI
LEIMM
2
22121
YX
YXL
LMM
12CALCULO DE FUERZAS HORIZONTALES: Momentos calculados en "crossmovnivel1"
Sentido Positivo Sentido Negativo
4 8 12 16
-0.73 -0.03 -0.98 -1.07
-4.70 -3.71 -2.45 -3.13
3 7 11 15-2 Tn -1 Tn 0 Tn -1 Tn
F3= -4.45667 Tn
3 7 11 157.80 9.77 10.78 9.93
10.67 11.32 11.84 11.492 6 10 14
6 Tn 7 Tn 0 Tn 7 Tn
F2= 15.86785 Tn
2 6 10 14
M4-3= M8-7= M12-11= M16-15=
M3-4= M7-8= M11-12= M15-16=
F3-4= F7-8= F11-12= F15-16=
M3-2= M7-6= M11-10= M15-14=
M2-3= M6-7= M10-11= M14-15=
F3-4= F7-8= F11-12= F15-16=
F3
F3
F2
F3
F2
F1
-10.41 -10.51 -10.51 -10.51
-10.10 -10.11 -10.11 -10.111 5 9 13
-7 Tn -7 Tn 0 Tn 0 Tn
F1= -2.30026 Tn
13
k3a k3b k3c k4d
k2a k2b k2c k2d
k1a k1b k1c k1d
Calculando las rigideces laterales
k1a = 157.1366 Tn/m k2a = 174.568996 Tn/mk1b = 157.1366 Tn/m k2b = 174.568996 Tn/mk1c = 157.1366 Tn/m k2c = 174.568996 Tn/mk1d = 157.1366 Tn/m k2d = 174.568996 Tn/m
K 1 PISO = 6285.46344 Kg/cm K2PISO = 6982.75984 Kg/cm
k3a = 174.568996 Tn/mk3b = 174.568996 Tn/mk3c = 174.568996 Tn/mk3d = 174.568996 Tn/m
K3PISO = 6982.75984 Kg/cm
Calculando Rigidez lateral total:
M2-1= M6-5= M10-9= M14-13=
M1-2= M5-6= M9-10= M13-14=
F3-4= F7-8= F11-12= F15-16=
F1
V
M
3
1
2
1
1
11
KKK
K
K= 2244.583454 Tn/m
14
3
1
2
1
1
11
KKK
K
6
M15-16
7
-5.77
-6.42
2.08
0.69
8
M14-15
9
6.46
8.50
-8.68
-7.32
10
11
-1.07
-3.13
9.93
11.49
15
DESARRO
LLO D
EL METO
DO
CROS PARA U
N D
ESPLAZAMIEN
TO EN
EL PISO 3 D
EBIDO
A UN
MO
MEN
TO CO
NO
CIDO
DE -10Tn.m
0.72 -4.47 -3.110.43 0.68 0.79-0.87 -1.07 -0.87-0.91 -1.73 -2.152.07 3.52 2.070.00 4.13 7.05
1 2 0.00 3 -10.00 -10.00 40.4394 0.4134 0.7049
0 0.3766
0.18400.000.000.00-0.38-0.110.18-0.31
0.4134 0.17310.001.73
0.67-0.73-0.120.281.84
3.110.33
-0.26-0.900.982.950.00
0.29510.00 0.00 0.000.00 0.00 4.130.00 0.00 0.000.00 -0.78 -1.73-0.39 0.00 -0.450.00 0.37 0.68
-0.39 -0.41 2.63
-0.29 2.89 -6.150.16 0.51 0.650.00 -0.27 -0.27-0.46 -0.55 -1.220.00
-0.334
0.00
1.823
0.00
2.751
0.00 0.14010.00
0.0000.00
-0.22-0.190.08
3.19 0.13370.00
1.3370.87
-0.23-0.360.21
4.69 0.19650.001.971.48
-0.51-0.450.27
5 6 0.00 7 0.00 -10.000.2869 0.3194 0.4693
0
-0.35 0.14-0.11-0.380.000.000.00
0.2383
0.3347
2.750.36
-0.35-0.390.862.270.00
0.2274
0.3194
3.400.46
-0.66-0.871.133.340.00
0.3341
8
0.00 0.00 -10.000.00 0.00 3.190.00 1.60 0.000.00 -0.53 -0.55-0.23 -0.27 -0.610.00 0.19 0.51
-0.23 0.98 -7.46-0.04 1.76 -7.33
0.21 0.50 0.640.00 -0.15 -0.49-0.26 -0.99 -1.850.00
-0.226
0.00
1.594
1.20
2.635
0.00 0.1773 00.000
0.00-0.21-0.190.18
2.40 0.17120.00
1.7120.43
-0.70-0.200.35
3.17 0.22540.002.251.67
-1.31-0.430.46
9 10 0.00 11 0.00 -10.000.2135 0.2405 0.3166
0
-0.39 0.36-0.32-0.430.000.000.00
0.3602
0.2490
4.070.72
-0.79-1.432.103.480.00
0.3478
0.2405
4.690.93
-1.11-2.672.964.580.00
0.4580
12
0.00 0.00 -10.000.00 0.00 2.400.00 1.20 1.580.00 -0.30 -0.99-0.13 -0.49 -0.920.00 0.25 0.50
-0.13 0.66 -7.43-0.18 2.08 -5.77
0.20 0.49 0.770.00 -0.22 -0.55
-0.38 -1.10 -1.530.00
-0.517
0.00
4.35
1.45
5.77
0.00 0.43780.000.000.00
-0.64-0.220.34
2.90 0.41970.004.201.74
-1.59-0.710.71
4.09 0.59120.005.912.29
-2.21-1.331.11
13 0.00 0.00 -10.000.2595 0.2902 0.4088
0 14 0.3027 15 0.2902 16
0.00 0.00 -10.000.00 0.00 2.900.00 1.45 2.040.00 -0.44 -1.10-0.19 -0.55 -0.760.00 0.23 0.49
-0.19 0.69 -6.42
DESARRO
LLO D
EL METO
DO
CROS PARA U
N D
ESPLAZAMIEN
TO EN
EL PISO 3 D
EBIDO
A UN
MO
MEN
TO CO
NO
CIDO
DE -10Tn.m
DESARRO
LLO D
EL METO
DO
CROS PARA U
N D
ESPLAZAMIEN
TO EN
EL PISO 2 D
EBIDO
A UN
MO
MEN
TO CO
NO
CIDO
DE -10Tn.m
-5.70 7.34 3.54-0.06 -0.03 -0.370.27 0.35 0.27-0.31 0.55 0.690.00 -3.52 0.004.39 0.00 -7.05
1 2 -10.00 3 10.00 10.00 40.4394 0.4134 0.7049
0 0.3766
0.18400.001.840.70-0.13-0.13-0.032.26 0.4134 0.1731
0.000.00
0.000.23-0.11-0.010.10
-3.54 -0.160.260.29
-0.98-2.950.00
0.29510.00 0.00 -10.000.00 3.77 0.001.88 0.00 2.200.00 -0.26 0.55-0.13 0.00 -0.150.00 -0.06 -0.03
1.75 3.45 -7.44
2.51 -9.31 6.070.16 -0.14 -0.190.00 -0.30 -0.27-0.52 -0.53 1.220.00
2.083
1.67
-0.169
0.00
-2.863
2.87 0.14010.00
1.4010.92
-0.25-0.060.08
0.00 0.13370.00
0.0000.00
-0.220.11
-0.06
-4.69 0.19650.00
-1.97-1.480.510.14
-0.08
5 6 0.00 7 -10.00 10.000.2869 0.3194 0.4693
0
2.740.13
-0.23-0.430.892.380.00
0.2383
0.3347
-0.45 -0.100.03
-0.380.000.000.00
0.2274
0.3194
-3.21 -0.130.520.87
-1.13-3.340.00
0.3341
8
0.00 -10.00 10.000.00 3.35 0.001.43 0.00 0.000.00 -0.60 -0.53-0.26 -0.27 0.610.00 0.19 -0.14
1.18 -7.34 9.931.69 -9.08 7.97
0.12 -0.08 -0.360.00 -0.33 0.04-0.56 0.08 1.460.00
1.635
1.25
-0.188
0.00
-2.707
2.13 0.1773 01.773
0.44-0.47-0.220.10
0.00 0.17120.00
0.0000.000.06
-0.19-0.06
-3.17 0.22540.00
-2.25-1.671.040.43
-0.26
9 10 0.00 11 -10.00 10.000.2135 0.2405 0.3166
0
4.650.20
-0.39-0.952.193.600.00
0.3602
0.2490
0.12 -0.110.110.120.000.000.00
0.3478
0.2405
-5.27 -0.530.682.12
-2.96-4.580.00
0.4580
12
0.00 -10.00 10.000.00 2.49 0.001.07 0.00 -1.580.00 -0.66 0.08-0.28 0.04 0.730.00 0.14 -0.08
0.79 -7.98 9.152.23 -8.68 6.46
0.10 -0.07 -0.460.00 -0.27 0.08
-0.47 0.15 0.940.00
5.091
1.51
0.17
0.00
-6.46
2.59 0.43780.004.381.80
-0.79-0.470.17
0.00 0.41970.000.000.000.220.06
-0.11
-4.09 0.59120.00
-5.91-2.291.351.06
-0.67
13 0.00 -10.00 10.000.2595 0.2902 0.4088
0 14 0.3027 15 0.2902 16
0.00 -10.00 10.000.00 3.03 0.001.30 0.00 -2.040.00 -0.55 0.15-0.23 0.08 0.470.00 0.12 -0.07
1.06 -7.32 8.50
DESARRO
LLO D
EL METO
DO
CROS PARA U
N D
ESPLAZAMIEN
TO EN
EL PISO 2 D
EBIDO
A UN
MO
MEN
TO CO
NO
CIDO
DE -10Tn.m
DESARRO
LLO D
EL METO
DO
CROS PARA U
N D
ESPLAZAMIEN
TO EN
EL PISO 1 D
EBIDO
A UN
MO
MEN
TO CO
NO
CIDO
DE -10Tn.m
10.67 -4.70 -0.73-0.24 -0.77 -0.250.35 0.99 0.351.35 0.70 1.98-2.81 0.00 -2.81-1.59 -5.63 0.00
1 2 13.61 3 0.00 0.00 40.4394 0.4134 0.7049
0 0.3766
0.18400.00-0.66-0.250.560.20-0.10-0.26
0.4134 0.17310.00
-2.36-0.910.290.20-0.32-3.10
0.73 -0.100.000.830.000.000.00
0.2951-10.00 -10.00 13.610.00 -1.36 -5.63-0.68 0.00 -0.790.00 1.16 0.700.58 0.00 0.670.00 -0.21 -0.77-10.10 -10.41 7.80
-10.51 9.77 -0.03-0.28 -0.30 -0.500.00 0.47 0.470.81 0.94 0.000.00
-0.298
-0.60
-2.584
0.00
0.205
-1.04 0.14010.00
-0.506-0.330.400.28
-0.14
-4.35 0.13370.00
-1.820-1.180.390.15
-0.13
0.00 0.19650.000.000.000.000.42
-0.21
5 6 -10.00 7 13.61 0.000.2869 0.3194 0.4693
0
-0.51 -0.230.230.67
-0.32-0.860.00
0.2383
0.3347
-3.47 -0.220.330.67
-1.17-3.100.00
0.2274
0.3194
-0.17 -0.360.180.000.000.000.00
0.3341
8
-10.00 13.61 0.000.00 -1.21 -4.35-0.52 -2.17 0.000.00 0.95 0.940.41 0.47 0.000.00 -0.33 -0.30-10.11 11.32 -3.71
-10.51 10.78 -0.98-0.29 -0.37 -0.330.00 0.32 0.470.55 0.94 0.520.00
-0.249
-0.45
-2.174
-1.64
0.132
-0.77 0.1773 0-0.640
-0.160.460.34
-0.24
-3.27 0.17120.00
-2.330-0.580.670.34
-0.26
0.00 0.22540.000.000.000.370.00
-0.24
9 10 -10.00 11 13.61 0.000.2135 0.2405 0.3166
0
-1.08 -0.500.570.93
-0.79-1.300.00
0.3602
0.2490
-6.16 -0.530.611.35
-2.86-4.730.00
0.3478
0.2405
0.85 -0.480.580.750.000.000.00
0.4580
12
-10.00 13.61 0.000.00 -0.90 -3.27-0.39 -1.64 0.000.00 0.64 0.940.28 0.47 0.260.00 -0.34 -0.37-10.11 11.84 -2.45
-10.49 9.93 -1.07-0.23 -0.43 -0.33
0.00 0.40 0.420.68 0.85 0.810.00
-1.005
-0.55
-6.80
-1.97
1.07
-0.94 0.43780.00
-1.58-0.651.150.47
-0.39
-3.95 0.41970.00
-5.71-2.371.220.68
-0.62
0.00 0.59120.000.000.001.170.37
-0.47
13 -10.00 13.61 0.000.2595 0.2902 0.4088
0 14 0.3027 15 0.2902 16
-10.00 13.61 0.000.00 -1.09 -3.95-0.47 -1.97 0.000.00 0.79 0.850.34 0.42 0.400.00 -0.27 -0.43-10.13 11.49 -3.13
DESARRO
LLO D
EL METO
DO
CROS PARA U
N D
ESPLAZAMIEN
TO EN
EL PISO 1 D
EBIDO
A UN
MO
MEN
TO CO
NO
CIDO
DE -10Tn.m
SISTEMA DE ECUACIONES LINEALES DE 3x3
A V R
A = Matriz de Coeficientes -2.300 15.600 -19.369 1.000
V = Matriz de Variables 15.868 -1.312 -7.800 = 2.000
R = Matriz de Resultados -4.457 13.951 -11.128 3.000
-0.106 0.083 0.127-0.182 0.052 0.280-0.186 0.032 0.211
0.440
0.763
0.511
X1
X2
X3
A-1
X1=
A-1 x R = X2=
X3=
TRABAJO DE INGENIERIA ANTISISMICACALCULO DE RIGIDEZ LATERAL
V1 V2 V3
3C3A C3B C3C C3DV1 V2 V3
3C2A C2B C2C C2DV1 V2 V3
3.5C1A C1B C1C C1D
4 5 7
DATOSColumna: Ec= 15000√f'c = 217370.65 Kg/cm2b= 0.3 mh= 0.4 m
Calculo de Inercias:
I colum= bxh3/12 = 160000.00 cm4 = 0.0016 m4I v1= bxh3/12 = 89322.92 cm4 = 0.000893229 m5I v2= bxh3/12 = 189843.75 cm4 = 0.001898438 m6I v3= bxh3/12 = 540000.00 cm4 = 0.0054 m7
Rigidez Lateral
En el Primer Nivel h= 350 cm 9734.15En el Segundo Nivel h= 300 cm 15457.47En el Tercer Nivel h= 300 cm 15457.47
KLE1=
KLE2=
KLE3=
3
12
bhI
3
12
h
EIK LE
Rigidez Relativa
ElementoInercia(cm4) Longitud K(Cm3)Caso de Elemento Empotrado
en un lado y continuo en el
C-1 160000.00 350 457.14C-2 160000.00 300 533.33C-3 160000.00 300 533.33V-1 89322.92 400 223.31V-2 189843.75 500 379.69V-3 540000.00 700 771.43
En el Primer Nivel
Columna K a
C1A 0.4884847 0.39722354 3866.63352
C1B 1.31905111 0.5480636 5334.93332
C1C 2.51806641 0.66799957 6502.40799
C1D 1.6875 0.59322034 5774.49576
SUMA 21478.471 Kg/cm2147.847 Tn/m
Caso de Elementos Continuos
en ambos Extremos
En el Segundo Nivel
Columna K a
C2A 0.41870117 0.17310992 2675.84143
C2B 1.13061523 0.36114794 5582.43341
C2C 2.15834263 0.51903915 8023.03212
C2D 1.44642857 0.41968912 6487.33197
SUMA 22768.639 Kg/cm2276.864 Tn/m
KLA
KLA
KV1 V2K
KC
LEL
C
VV
aKK
K
Ka
K
KKK
2
50.0
21
LEL
C
VVVV
aKK
K
Ka
K
KKKKK
2
24321
CK
KV4V3K
V2KKV1
En el Tercer Nivel
Columna K a
C2A 0.41870117 0.17310992 2675.84143
C2B 1.13061523 0.36114794 5582.43341
C2C 2.15834263 0.51903915 8023.03212
C2D 1.44642857 0.41968912 6487.33197
SUMA 22768.639 Kg/cm2276.864 Tn/m
Resumen de Rigidez Lateral en cada piso
Eje X-X (Pórticos Principales)
Pórtico
PISOS1 2 3
A 2147.847 2276.864 2276.864
B 2147.847 2276.864 2276.864
C 2147.847 2276.864 2276.864
Total 6443.5412 6830.5917 6830.5917
Calculo de la rigidez lateral total
K= 2232.169913 Tn/m
KLA
3
1
2
1
1
11
KKK
K
PISO V(Tn) ∆ (m) K1 -6 0.0025 -24002 -5 0.00222 -2252.25233 3 0.00138 2173.91304
TOTAL 2478.33921