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
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