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