Ejercicios Metodo de Osawa

15

2.60

20

2.60DATOS

VIGA: 0.30 0.50 25

COLUMNA: 0.50 0.30

2.60ESPESOR DE PLACA: 0.25 cm

f'c 280.00

E: 2509980.1

0.001 20

E/G 2.40

2.60R 7.00G 1045825.03

15CALCULOS PREVIOS

2.80IV 0.0031IC 0.0011

IP1 0.5625IP2 0.4333AP1 0.7500AP2 0.6875

Determinamos rigideces laterales estandar de las placas en cada piso:4455.594455.594455.594455.593841.81

cm2

cm2

kg/cm2

tn/m2

K0

D05D04D03D02D01

1

COEFICIENTES DE RIGIDEZ A FLEXIÓN DE LAS VIGAS DE BORDE (Kv)1.38

3.13 PLACA 1 29123.80

29123.80 61970.40

1.38 Kvn 6.05

2.1361970.40

1.25 PLACA 2 50096.31

2.25 34038.42

50096.31 Kvn 5.59

1.25

2.7534038.42

1.- CONTANTES DE ENTREPISO

Dcnivel eje 1 eje 2 (placa 1) eje 3 eje 4 (placa 2)

5 0.38 0.00 0.40 0.004 0.38 0.00 0.40 0.003 0.38 0.00 0.40 0.002 0.38 0.00 0.40 0.001 0.34 0.00 0.37 0.00

Kwhi nivel placa 1 placa 2

2.60 5 216.35 166.64 382.99

2.60 4 216.35 166.64 382.99

2.60 3 216.35 166.64 382.99

2.60 2 216.35 166.64 382.99

2.80 1 200.89 154.74 355.63

Nivel hi Xn5 2.60 382.99 1.16 1.44 1.014

4 2.60 382.99 1.16 1.44 1.0143 2.60 382.99 1.16 1.44 1.014

a21

b21 k21

k21 k23

a23

b23

k23

a43 k43

b43 k45

k43

a45

b45

k45

SKwn

S kwn SDc Awn

2 2.60 382.99 1.16 1.44 1.0141 2.80 355.63 1.04 1.44 1.012

Armamos la ecuacion de Osawa.

nivel 6*Kvn an5 69.81 455.434 69.81 841.053 69.81 841.052 69.81 841.051 69.81 813.99

455.43 -380.36 0.00 0.00 0.00-380.36 841.05 -380.36 0.00 0.00

0.00 -380.36 841.05 -380.36 0.000.00 0.00 -380.36 841.05 -380.360.00 0.00 0.00 -380.36 813.99

f5 1.55f4 1.76f3 2.00f2 2.02f1 1.52

CORTANTES Y MOMENTOS (PARA LAS DOS PLACAS)

hn NIVEL fn (f(n-1)+fn)*3 Zn Cn2.60 5 1.55 9.92 0.88 38.472.60 4 1.76 11.26 0.88 89.772.60 3 2.00 12.03 0.88 153.892.60 2 2.02 10.60 0.88 205.192.80 1 1.52 4.55 0.97 262.89

Determinacion de la Deformacion por Entrepisos

Nivel hi Don Qwn*hn/Kwn Qwn*hn/(G*Awn)5 2.60 4455.59 0.08 0.000024 2.60 4455.59 0.21 0.000053 2.60 4455.59 0.37 0.000102 2.60 4455.59 0.51 0.000131 2.80 3841.81 0.73 0.00017

Desplazamiento relativo en el rango elastico

Desplazamientos absolutos en el rango elastico.

Desplazamientos absolutos en el rango nolineal-desplazamientos absolutos para el sismo de diseño

Desplazamientos absolutos reales

Desplazamiento relativo real - rango no lineal para el sismo de diseño - con esto nosotros diseñamos la

junta de separacion entre los elementos estructurales y no estructurales

D : Distorsion. Dual debe ser menor al 0.007

Cortantes por Porticos y Placas.

Nivel Eje 1 Eje 2 (placa 1)hi Dc Qc KLc Qw Dw

2.60 5 0.38 1.16 1686.60 6.47 9383.072.60 4 0.38 1.40 1686.60 17.36 20938.382.60 3 0.38 1.59 1686.60 31.14 32936.672.60 2 0.38 1.52 1686.60 42.56 47082.432.80 1 0.34 0.79 1300.56 52.14 77173.96

tn/m tn/m

CALCULO DE LA RIGIDEZ LATERAL

Nivel Q A.E

5 15 0.000694 35 0.000833 60 0.000952 80 0.00090

dre :

dte :

dtr :

drr :

dre

1 95 0.00068

Momentos en vigas que ocurren a la placa.

Nivel Kvn MvnPLACA #1

5 11.64 54.16 6.05 28.15 6.054 11.64 61.32 6.05 31.88 6.053 11.64 69.66 6.05 36.21 6.052 11.64 70.35 6.05 36.57 6.051 11.64 52.94 6.05 27.52 6.05

Kv 2-1 Mv 2-1 Kv 2-3

0.001

6.05

0.001

5.59

0.0010.433 0.433 0.43313.979 26.891 12.9110.875 0.931 0.8660.379 0.403 0.3750.001

6.05

0.001

5.59

0.0010.433 0.433 0.43313.979 26.891 12.9110.875 0.931 0.866

0.379 0.403 0.375

0.001

6.05

0.001

5.59

0.0010.433 0.433 0.43313.979 26.891 12.9110.875 0.931 0.866

0.379 0.403 0.3750.001

6.05

0.001

5.59

0.0010.433 0.433 0.43313.979 26.891 12.9110.875 0.931 0.8660.379 0.403 0.3750.001

6.05

0.001

5.59

0.0010.402 0.402 0.4027.527 14.480 6.9520.843 0.909 0.8320.339 0.365 0.334

4.50 3.00 3.50 3.50 2.75 4.006.00 5.00 4.88 5.38

Determinamos rigideces laterales estandar de las placas en cada piso:tn/mtn/mtn/mtn/mtn/m

1 2 3 4 5

2

12* *oon

n

K ED

h

COEFICIENTES DE RIGIDEZ A FLEXIÓN DE LAS VIGAS DE BORDE (Kv)

1.- CONTANTES DE ENTREPISO

Dceje 5

0.37 1.160.37 1.160.37 1.160.37 1.160.33 1.04

382.99382.99382.99382.99355.63

Zn Bn An Qn Cn0.88 380.36 385.62 15.00 38.470.88 380.36 385.62 35.00 89.770.88 380.36 385.62 60.00 153.89

SDc

SKwn

b = Le-Lp/2-a

Kw = Ip/(hi*K0)

Xn = 1 + SDc/SKwn + 12E*K0*f*SDc/(G*Awn*hi)

2 4vhLpa

ejeb L a

0.88 380.36 385.62 80.00 205.190.97 352.71 358.56 95.00 262.89


Bn Dn380.36 38.47380.36 128.24380.36 243.66380.36 359.08352.71 468.08

f5 38.47f4 128.24f3 243.66f2 359.08f1 468.08


Qwn Qcn 3*Kvn Mvn11.45 3.55 34.91 54.1630.73 4.27 34.91 61.3255.13 4.87 34.91 69.6675.34 4.66 34.91 70.3592.31 2.69 34.91 52.94


Qwn = (Cn - 3*(fn-1+fn)*zn)/hn

Qcn = Qn - Qwn

Mvn = 3*kvn*fn

ELASTICO Inelas.no linealQwn*hn/(G*Awn) D

0.00002 0.00069 0.0040 0.004 0.021 0.0014 OK0.00005 0.00083 0.0034 0.004 0.018 0.0017 OK0.00010 0.00095 0.0025 0.005 0.013 0.0019 OK0.00013 0.00090 0.0016 0.005 0.008 0.0018 OK0.00017 0.00068 0.0007 0.004 0.004 0.0013 OK





Eje 3 Eje 4 (placa 2) Eje 5Dc Qc KLc Qw Dw Dc Qc

0.40 1.24 1794.44 4.98 7227.35 0.37 1.150.40 1.49 1794.44 13.37 16127.88 0.37 1.380.40 1.70 1794.44 23.99 25369.62 0.37 1.580.40 1.62 1794.44 32.78 36265.46 0.37 1.510.37 0.95 1403.08 40.16 59443.60 0.33 0.87

tn/m


A.E klCOMPROVACIÓN

0.00069 21760.78 21760.780.00083 42216.62 42216.620.00095 63456.65 63456.650.00090 88498.24 88498.24

dre dte drr dtr

dre

0.00068 140606.16 140606.16


PLACA #1 PLACA #2

28.15 5.59 26.00 5.59 26.0031.88 5.59 29.44 5.59 29.4436.21 5.59 33.45 5.59 33.4536.57 5.59 33.78 5.59 33.7827.52 5.59 25.42 5.59 25.42

Mv 2-3 Kv 4-3 Mv4-3 Kv4-5 Mv4-5


Eje 5KLc

1669.321669.321669.321669.321284.95

dre = Qcn/(Don*SDcn)

dtr = dte*0,75*R

drr = dre*0,75*R

D=drr/hi

Qc = Qcn*Dc/SDcn

Qw = Qwn*Ip1/(Ip1+Ip2)

Dw=Qw/dre

KLc = 12*E*Dc*K0/hi2

15DATOS

3VIGA: 0.30 0.50

COLUMNA: 0.50 0.30ESPESOR DE PLACA: 0.25 cm

f'c 280.00 20E: 2509980.1

30.001

E/G 2.40R 7.00G 1045825.03 17.5

3CALCULOS PREVIOS

IV 0.0031 12IC 0.0011

3.5IP1 0.0407IP2 0.1117AP1 0.3125AP2 0.4375

Determinamos rigideces laterales estandar de las placas en cada piso:

3346.64 tn/m3346.64 tn/m3346.64 tn/m2458.76 tn/m

Determinamos rigideces al corte de las placas.

0.50 PLACA 14.50 Kvn

9554.45

0.75 PLACA 2

6.257044.01 Kvn

0.75

cm2

cm2

kg/cm2

tn/m2

K0

D04D03D02D01

a12 k12

b12

k12

a32 k32

b32 k34

k32

a43

1

4.2511980.26

Constantes de entrepiso:

Dcnivel eje 1 placa 1 eje 2 eje 3 placa 2 eje 4

4 0.00 0.269 0.00 0.2353 0.00 0.269 0.00 0.2352 0.00 0.269 0.00 0.2351 0.00 0.224 0.00 0.200


3.00 4 13.56 37.22 50.78

3.00 3 13.56 37.22 50.78

3.00 2 13.56 37.22 50.78

3.50 1 11.63 31.90 43.53

Nivel hi Xn4 3.00 50.78 0.50 0.75 1.0183 3.00 50.78 0.50 0.75 1.0182 3.00 50.78 0.50 0.75 1.0181 3.50 43.53 0.42 0.75 1.015


nivel 6*Kvn an4 11.39 68.223 11.39 125.062 11.39 125.061 11.39 118.94

68.22 -44.72 0 0-44.72 125.06 -44.72 0

0 -44.72 125.06 -44.720 0 -44.72 118.94

f4f3f2

b43

k43

SKwn

S kwn SDc Awn

f1


hn NIVEL fn (f(n-1)+fn)*3 Zn Cn3.00 4 3.55 23.90 2.02 44.223.00 3 4.42 29.82 2.02 103.183.00 2 5.52 32.30 2.02 154.773.50 1 5.25 15.74 2.40 222.34


Nivel hi Don Qwn*hn/Kwn Qwn*hn/(G*Awn)5 3.00 3346.64 -0.08 -0.000014 3.00 3346.64 0.85 0.000053 3.00 3346.64 1.76 0.000111 3.50 2458.76 4.24 0.00024

Desplazamiento relativo en el rango elastico



Desplazamientos absolutos reales



D : Distorsion. Dual debe ser menor al 0.007


Nivel Eje 1 placa 1 Eje 2 hi Qw Dw Dc

3.00 4 -0.36 -37.06 0.273.00 3 -1.34 -109.70 0.273.00 2 14.32 1067.01 0.273.50 1 52.76 4681.96 0.22

tn/m


Nivel QA.E

4 15.00 0.00969

dre :

dte :

dtr :

drr :

dre

3 35.00 0.012262 52.50 0.013421 64.50 0.01127


Nivel Kvn MvnPLACA #1

4 1.90 20.19 0.63 6.753 1.90 25.17 0.63 8.412 1.90 31.42 0.63 10.511 1.90 29.87 0.63 9.99

Kv 1-2 Mv1-2

0.63

Ic 0.001

1.26

Ic 0.001Kc 0.375 Kc 0.375K 5.060 K 3.369a 0.717 a 0.627D 0.269 D 0.235

0.63

Ic 0.001

1.26

Ic 0.001Kc 0.375 Kc 0.375K 5.060 K 3.369a 0.717 a 0.627D 0.269 D 0.235

0.63

Ic 0.001

1.26

Ic 0.001Kc 0.375 Kc 0.375K 5.060 K 3.369a 0.717 a 0.627D 0.269 D 0.235

0.63

Ic 0.001

1.26

Ic 0.001Kc 0.321 Kc 0.321K 2.952 K 1.965a 0.697 a 0.622D 0.224 D 0.200

1.25 1.755.625 7.875 5.875

Determinamos rigideces laterales estandar de las placas en cada piso:

Determinamos rigideces al corte de las placas.

9554.450.63

7044.0111980.26

1.26

1 2 3 4

b = Le-Lp/2-a

2

12* *oon

n

K ED

h

2 4vhLpa

Constantes de entrepiso:

0.500.500.500.42

50.7850.7850.7843.53

Zn Bn An Qn Cn2.02 44.72 56.84 15.00 44.222.02 44.72 56.84 35.00 103.182.02 44.72 56.84 52.50 154.772.40 36.34 50.71 64.50 222.34


Bn Dn44.72 44.2244.72 147.4044.72 257.9436.34 377.11

f4 44.22* f3 = 147.40

f2 257.94f1 377.11

3.554.425.52

SDc

SKwn Kw = Ip/(hi*K0)


5.25


Qwn Qcn 3*Kvn Mvn-1.34 16.34 5.69 20.1914.32 20.68 5.69 25.1729.85 22.65 5.69 31.4252.76 11.74 5.69 29.87


ELASTICO Inelas.no linealQwn*hn/(G*Awn) D

-0.00001 0.00969 0.0466 0.051 0.017 0.0170.00005 0.01226 0.0369 0.005 0.014 0.0020.00011 0.01342 0.0247 0.005 0.009 0.0020.00024 0.01127 0.0113 0.004 0.004 0.001






Eje 2 Eje 3 placa 2 Eje 4 Qc KLc Qw Dw Dc Qc

8.71 899.49 -0.99 -101.71 0.24 7.6311.02 899.49 15.67 1278.40 0.24 9.6512.08 899.49 15.53 1156.79 0.24 10.576.21 550.92 0.00 0.00 0.20 5.54

tn/m tn/m


A.Ekl

COMPROVACIÓN0.00969 1548.19 1548.19

dre dte drr dtr

dre


Qcn = Qn - Qwn

Mvn = 3*kvn*fn

0.01226 2855.66 2855.660.01342 3910.76 3910.760.01127 5724.22 5724.22


PLACA #2

1.26 13.44 1.26 6.751.26 16.75 1.26 8.411.26 20.92 1.26 10.511.26 19.88 1.26 9.99

Kv 3-2 Mv3-2 Kv3-4 Mv3-4

MALOKOKOK


Eje 4 KLc

787.46787.46787.46491.33

tn/m



Mvn = 3*kvn*fn

dre = Qcn/(Don*SDcn)

dtr = dte*0,75*R

drr = dre*0,75*R

D=drr/hi

Qc = Qcn*Dc/SDcn

Qw = Qwn*Ip1/(Ip1+Ip2)

Dw=Qw/dre

KLc = 12*E*Dc*K0/hi2

15

2.80

0.0010.4023.1680.613

17 0.246DATOS

2.80VIGA: 0.30 0.50

COLUMNA: 0.50 0.30ESPESOR DE PLACA: 0.25 cm

f'c 280.00 20

E: 2509980.1

2.800.001

E/G 2.40R 7.00G 1045825.0 15

2.80CALCULOS PREVIOSIV 0.0031IC 0.0011 20

IP1 0.1667

3.00

0.001IP2 0.1215 0.375AP1 0.5000 1.697AP2 0.4500 0.594

0.2235.5

6.50

DETERMINACION DE RIGIDESES LATERALES ESTANDAR DE LAS PLACAS EN CADA PISO

3841.813841.813841.813841.813346.64

DETERMINACION DE RIGIDECES AL CORTE DE LAS PLACAS

0.875 PLACA 1

4.625

cm2

cm2

kg/cm2

tn/m2

K0

D05D04D03D02D01

a21 = k21

b21 = k23

1

11362.376 Kvn

0.875

6.025

7805.71702 PLACA 2

0.775

6.225 Kvn

7156.93717

0.775

4.525

11106.4062

CONSTANTES DE ENTREPISO

Dcnivel eje 1 eje 2 (placa 1) eje 3 placa 2 eje 4

4 0.246 0.00 0.00 1.003 1.2503 0.246 0.00 0.00 1.003 1.2502 0.246 0.00 0.00 1.003 1.2501 0.223 0.00 0.00 0.219 0.442


2.80 4 59.52 43.39 102.92

2.80 3 59.52 43.39 102.92

2.80 2 59.52 43.39 102.92

3.00 1 55.56 40.50 96.06

k21 =a23 =b23 =k23 = k32

a32 = k34

b32 =k32 =a34 =b34 =k34 =

SDc

SKwn

1.273 1.213

0.0010.4023.0180.6011.003

1.273 1.213

1.273 1.213

1.273 1.213

1.273 1.213

0.0010.3751.6170.5850.219

5.5 2.00 6.00 1.80 5.306.50 7.90 6.20

DETERMINACION DE RIGIDESES LATERALES ESTANDAR DE LAS PLACAS EN CADA PISO

tn/mtn/mtn/mtn/mtn/m

DETERMINACION DE RIGIDECES AL CORTE DE LAS PLACAS

11362.38

7805.72

2 3 4

1.27

7156.94

11106.41

1.21

CONSTANTES DE ENTREPISO

1.2501.2501.2500.442

SDc

Ejercicios Metodo de Osawa

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