JHON AYALA CARDOZO

36
TRABAJO DE INGENIERIA ANTISISMICA CALCULO DE RIGIDEZ LATERAL V1 V2 V3 C2 C2 C2 C2 V1 V2 V3 C2 C2 C2 C2 V1 V2 V3 C1 C1 C1 C1 4 5 7 Predimensionamiento Luces: Nombre: Jhon = 4 Apellido Paterno: Ayala = 5 Apellido Materno: Cardozo = 7 Vigas: V1: Medidas Constructivas h = L/12 = 0.333 m = 0.35 m b= h/2 = 0.175 m = 0.25 m (ancho minimo E.060) V2: Medidas Constructivas h = L/12 = 0.417 m = 0.45 m b= h/2 = 0.225 m = 0.25 m (ancho minimo E.060) V3: Medidas Constructivas h = L/12 = 0.583 m = 0.6 m b= h/2 = 0.3 m = 0.3 m Columna: b= 0.3 m h= 0.4 m Datos: f'c = 210 Ec= 15000√f'c = 217370.65 Kg/cm2 2173706.5119 Tn/m2

Transcript of JHON AYALA CARDOZO

Page 1: 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

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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

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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 =

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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 =

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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=

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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)

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-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

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-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=

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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

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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

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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

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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

Page 13: JHON AYALA CARDOZO

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

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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

Page 15: JHON AYALA CARDOZO

-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

Page 16: JHON AYALA CARDOZO

K= 2244.583454 Tn/m

14

3

1

2

1

1

11

KKK

K

Page 17: JHON AYALA CARDOZO

6

M15-16

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7

-5.77

-6.42

2.08

0.69

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8

M14-15

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9

6.46

8.50

-8.68

-7.32

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10

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11

-1.07

-3.13

9.93

11.49

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15

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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

Page 25: JHON AYALA CARDOZO

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

Page 26: JHON AYALA CARDOZO

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

Page 27: JHON AYALA CARDOZO

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

Page 28: JHON AYALA CARDOZO

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

Page 29: JHON AYALA CARDOZO

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

Page 30: JHON AYALA CARDOZO

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=

Page 31: JHON AYALA CARDOZO

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

Page 32: JHON AYALA CARDOZO

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

Page 33: JHON AYALA CARDOZO

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

Page 34: JHON AYALA CARDOZO

PISO V(Tn) ∆ (m) K1 -6 0.0025 -24002 -5 0.00222 -2252.25233 3 0.00138 2173.91304

TOTAL 2478.33921